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Showing papers in "Progress of Theoretical Physics in 2004"


Journal ArticleDOI
TL;DR: In this paper, the authors extended the formulation for perturbations of maximally symmetric black holes in higher dimensions developed by the present authors in a previous paper to a charged black hole background whose horizon is described by an Einstein manifold.
Abstract: We extend the formulation for perturbations of maximally symmetric black holes in higher dimensions developed by the present authors in a previous paper to a charged black hole background whose horizon is described by an Einstein manifold. For charged black holes, perturbations of electromagnetic fields are coupled to the vector and scalar modes of metric perturbations non-trivially. We show that by taking appropriate combinations of gauge-invariant variables for these perturbations, the perturbation equations for the Einstein-Maxwell system are reduced to two decoupled second-order wave equations describing the behaviour of the electromagnetic mode and the gravitational mode, for any value of the cosmological constant. These wave equations are transformed into Schrodinger-type ODEs through a Fourier transformation with respect to time. Using these equations, we investigate the stability of generalised black holes with charge. We also give explicit expressions for the source terms of these master equations with application to the emission problem of gravitational waves in mind.

345 citations


Journal ArticleDOI
TL;DR: In this paper, the authors investigated the instability of charged massive scalar fields in Kerr-Newman spacetime and obtained the growth rate of the amplitude of the scalar field.
Abstract: We investigate the instability of charged massive scalar fields in Kerr-Newman spacetime. Due to the super-radiant effect of the background geometry, the bound state of the scalar field is unstable, and its amplitude grows in time. By solving the Klein-Gordon equation of the scalar field as an eigenvalue problem, we numerically obtain the growth rate of the amplitude of the scalar field. Although the dependence of the scalar field mass and the scalar field charge on this growth rate agrees with the result of the analytic approximation, the maximum value of the growth rate is three times larger than that of the analytic approximation. We also discuss the effect of the electric charge on the instability of the scalar field.

160 citations


Journal ArticleDOI
TL;DR: In this paper, the time evolution of the lepton family asymmetries is derived by solving Boltzmann equations, and the authors show how each family asymmetry varies with one particular CP violating phase.
Abstract: In the leptogenesis scenario, decays of heavy Majorana neutrinos generate lepton family asymmetries, Ye ,Y µ and Yτ. These asymmetries are sensitive to CP violating phases in seesaw models. The time evolution of the lepton family asymmetries is derived by solving Boltzmann equations. Considering a minimal seesaw model, we show how each family asymmetry varies with one particular CP violating phase. For instance, we find the case in which the lepton asymmetry is dominated by Yµ or Yτ, depending on the choice of the CP violating phase. We also find the case in which the signs of the lepton family asymmetries Yµ and Yτ are opposite. Their absolute values can be larger than the total lepton asymmetry, and baryon asymmetry may result from the cancellation of the lepton family asymmetries.

153 citations


Journal ArticleDOI
TL;DR: In this article, the authors study a network of all-to-all interconnected phase oscillators as modeled by the Kuramoto model and show the existence of a collective behavior called phase locking: the phase differences between all oscillators are constant in time.
Abstract: We study a network of all-to-all interconnected phase oscillators as modeled by the Kuramoto model. For coupling strengths larger than a critical value, we show the existence of a collective behavior called phase locking: the phase differences between all oscillators are constant in time. As the coupling strength increases, the distance between each pair of phases decreases. Stability of each phase locking solution is proven for general frequency distributions. There exist one unique asymptotically stable phase locking solution. Furthermore a description is given of partial entrainment, which can be regarded as the finite number analogon of partial synchronization in the infinite number case. When the network is partially entraining some phase differences possess an upper and lower bound. Partial entrainment of the three-cell network is analyzed: an estimate of the onset of partial entrainment is given and the existence of partial entrainment is proven. Furthermore, local stability of partial entrainment is proven for the three-cell network with two identical oscillators.

129 citations


Journal ArticleDOI
TL;DR: In this paper, the geometry of static vacuum black holes in 6-dimensional gravity compactified on a circle was studied and the authors were able to find solutions with horizon radii approximately equal to the asymptotic compactification radius.
Abstract: We detail numerical methods to compute the geometry of static vacuum black holes in 6-dimensional gravity compactified on a circle. We calculate properties of these KaluzaKlein black holes for varying mass, keeping the asymptotic compactification radius fixed. For increasing mass, the horizon deforms into a prolate ellipsoid, and the geometry near the horizon and axis decompactifies. We are able to find solutions with horizon radii approximately equal to the asymptotic compactification radius. Having chosen 6 dimensions, we may compare these solutions to those of non-uniform strings compactified on a circle of the same radius found in a previous numerical work. We find the black holes achieve larger masses and horizon volumes than most non-uniform strings. This sheds doubt on whether these solution branches can merge via a topology changing solution. Further work is required to resolve whether there is a maximum mass for the black holes, or whether the mass can become arbitrarily large.

114 citations


Journal ArticleDOI
TL;DR: In this paper, the nonperturbative aspects of string theory are explored for non-critical string in two distinct formulations, loop equations and matrix models, and effects corresponding to the D-brane in these formulations are especially investigated in detail.
Abstract: The nonperturbative aspects of string theory are explored for non-critical string in two distinct formulations, loop equations and matrix models. The effects corresponding to the D-brane in these formulations are especially investigated in detail. It is shown that matrix models can universally yield a definite value of the chemical potential for an instanton while loop equations cannot. This implies that it may not be possible to formulate string theory nonperturbatively solely in terms of closed strings.

90 citations


Journal ArticleDOI
TL;DR: In this article, the authors describe a method to continue the fermionic renormalization group flow into phases with broken global symmetry, which does not require a Hubbard-Stratonovich decoupling of the interaction.
Abstract: We describe a method to continue the fermionic renormalization group flow into phases with broken global symmetry. This method does not require a Hubbard-Stratonovich decoupling of the interaction. Instead an infinitesimally small symmetry-breaking component is inserted into the initial action, as an initial condition for the flow of the self-energy. Its flow is driven by the interaction, and at low scales it saturates at a nonzero value if there is a tendency for spontaneous symmetry breaking in the corresponding channel. For the reduced BCS model, we show how a small initial gap amplitude flows to the value given by the exact solution of the model. We also discuss the emergence of the Goldstone boson in this approach.

83 citations


Journal ArticleDOI
TL;DR: In this article, the authors investigated the influence of an external magnetic field on chiral symmetry breaking in a four-fermion interaction model at finite temperature and chemical potential and found that a new phase appears for a large chemical potential.
Abstract: We investigate an influence of an external magnetic field on chiral symmetry breaking in a four-fermion interaction model at finite temperature and chemical potential. By using the Fock-Schwinger proper-time method, we calculate the effective potential for the four-fermion interaction model at the leading order of the $1/N_c$ expansion. A phase structure of the chiral symmetry breaking is shown on $T$-$\mu$, $H$-$T$ and $\mu$-$H$ planes. The external magnetic field modifies the phase structure. It is found that a new phase appears for a large chemical potential.

78 citations


Journal ArticleDOI
TL;DR: In this paper, a numerical method to compute the homogeneous solutions of the radial Teukolsky equation is discussed, which is the basic equation of the black hole perturbation method, using the formalism developed by Mano, Suzuki and Takasugi.
Abstract: We discuss a numerical method to compute the homogeneous solutions of the Teukolsky equation which is the basic equation of the black hole perturbation method. We use the formalism developed by Mano, Suzuki and Takasugi, in which the homogeneous solutions of the radial Teukolsky equation are expressed in terms of two kinds of series of special functions, and the formulas for the asymptotic amplitudes are derived explicitly. Although the application of this method was previously limited to the analytical evaluation of the homogeneous solutions, we find that it is also useful for numerical computation. We also find that so-called “renormalized angular momentum parameter”, ν, can be found only in the limited region of ω for each l, m if we assume ν is real (here, ω is the angular frequency, and l and m are degree and order of the spin-weighted spheroidal harmonics respectively). We also compute the flux of the gravitational waves induced by a compact star in a circular orbit on the equatorial plane around a rotating black hole. We find that the relative error of the energy flux is about 10 −14 which is much smaller than the one obtained by usual numerical integration methods.

70 citations


Journal ArticleDOI
TL;DR: In this paper, the authors investigated soliton collisions in the Manakov model, which is a system of coupled nonlinear Schrodinger equations that is integrable via the inverse scattering method.
Abstract: We investigate soliton collisions in the Manakov model, which is a system of coupled nonlinear Schrodinger equations that is integrable via the inverse scattering method. Com- puting the asymptotic forms of the general N -soliton solution in the limits t →∓ ∞ ,w e elucidate a mechanism that factorizes an N -soliton collision into a nonlinear superposition of N 2 pair collisions with arbitrary order. This removes the misunderstanding that multi- particle effects exist in the Manakov model and provides a new "set-theoretical" solution to the quantum Yang-Baxter equation. As a by-product, we also obtain a new nontrivial relation among determinants and extended determinants.

70 citations


Journal ArticleDOI
TL;DR: In this article, the dynamical determination of boundary conditions in SU(N) gauge theory on the orbifold S 1 /Z 2 is investigated, and the equivalence classes of the boundary conditions are classified and the vacuum energy density of the theory in each equivalence class is evaluated.
Abstract: The dynamical determination of the boundary conditions in SU(N) gauge theory on the orbifold S 1 /Z 2 is investigated. We classify the equivalence classes of the boundary conditions, and then the vacuum energy density of the theory in each equivalence class is evaluated at one loop order. Unambiguous comparison of the vacuum energy densities in the two theories in different equivalence classes becomes possible in supersymmetric theories. It is found that in the supersymmetric SU(5) models with the Scherk-Schwarz supersymmetry breaking, the theory with the boundary conditions yielding the standard model symmetry is in the equivalence class with the lowest energy density, though the low energy theory is not identically the minimal supersymmetric standard model. We also study how particular boundary conditions are chosen in the cosmological evolution of the universe.

Journal ArticleDOI
TL;DR: In this paper, it was shown that the measurement of the spin singlet and triplet cross sections for the reaction pp → Σ + Θ + will unambiguously determine the parity of the Θ+.
Abstract: With the recent discovery of the Θ(1540) pentaquark, the question of its parity is paramount since this will constrain the correct description of its internal structure. We show that the measurement of the spin singlet and triplet cross sections for the reaction pp → Σ + Θ + will unambiguously determine the parity of the Θ + .

Journal ArticleDOI
TL;DR: A review of the theoretical ideas concerning the mysterious pentaquark baryons proposed during the first year after its discovery is given in this article, focusing on the difficulties involved with the constituent quark models and the discrepancy between the QCD predictions and most of the phenomenological models.
Abstract: A review is given of the theoretical ideas concerning the mysterious pentaquark baryons proposed during the first year after its discovery. We focus on the difficulties involved with the constituent quark models and the discrepancy between the QCD predictions and most of the phenomenological models.

Journal ArticleDOI
TL;DR: In this paper, neutrino emissivity of hyperon-mixed cores is studied using the properties of neutron star matter determined under the equation of state, which is obtained by introducing a repulsive three-body force universal for all the baryons so as to assure the maximum mass of neutron stars compatible with observations.
Abstract: For neutron stars with hyperon-mixed cores, neutrino emissivity is studied using the properties of neutron star matter determined under the equation of state, which is obtained by introducing a repulsive three-body force universal for all the baryons so as to assure the maximum mass of neutron stars compatible with observations. The case without a meson condensate is treated. We choose the inputs provided by nuclear physics, with a reliable allowance. Paying attention to the density dependence of the critical temperatures of the baryon superfluids, which reflect the nature of the baryon-baryon interaction and control neutron star cooling, we show what neutrino emission processes are efficient in regions both with and without hyperon mixing. By comparing the calculated emissivities with respect to densities, we can conclude that at densities lower than about 4 times the nuclear density, the Cooper-pair process arising from the neutron 3 P2 superfluid dominates, while at higher densities the hyperon direct Urca process dominates. For the hyperon direct Urca process to be a candidate responsible for rapid cooling compatible with observations, a moderately large energy gap of the Λ-particle 1 S0 superfliud is required to suppress its large emissivity. The implications of these results are discussed in the relation to thermal evolution of neutron stars.

Journal ArticleDOI
TL;DR: In this article, the authors considered 1/2 − baryon resonances as quasibounded states of low lying mesons (π, K, η) and baryons (N, N, Λ, Σ, Ξ).
Abstract: We study s-wave meson-baryon scattering using the chiral unitary model. We consider 1/2 − baryon resonances as quasibound states of the low lying mesons (π, K, η) and baryons (N, Λ, Σ, Ξ). In previous works, the subtraction constants which appear in loop integrals were found to largely depend on the channels, and it was necessary to fit these constants to reproduce the data. In order to extend this model to all channels with fewer parameters, we introduce flavor SU(3) breaking interactions in the framework of chiral perturbation theory. It is found, however, that the observed SU(3) breaking in meson-baryon scattering cannot be explained by the present SU(3) breaking interactions. The role and importance of the subtraction constants in the present framework are discussed.

Journal ArticleDOI
TL;DR: In this paper, a hamiltonian was proposed to mimic low-spin to high-spin transition in spin-crossover solids, which displays a vibrational-entropy-driven first-order phase transition.
Abstract: We propose a new hamiltonian intended to mimic low-spin to high-spin transition in spin-crossover solids, that displays a vibrational-entropy-driven first order phase transition. The present model is based on the existence of anharmonic intersite coupling (dependent on the electronic state of the sites) which alters the stiffness of the vibrations in the high temperature phase (high spin). The present exactly solvable model, studied at one dimension, clearly demonstrates the existence of a first-order transition accompanied with hetero-phase fluctuations around the transition temperature at higher dimensions.

Journal ArticleDOI
TL;DR: A closed form of the action of the supersymmetric CP N sigma model on noncommutative superspace in four dimensions is constructed and it is shown that this model has N = 1/2 supersymmetry and that the transformation law is not modified.
Abstract: We construct a closed form of the action of the supersymmetric $CP^N$ sigma model on noncommutative superspace in four dimensions We show that this model has $\mathcal{N}={1/2}$ supersymmetry and that the transformation law is not modified The supersymmetric $CP^N$ sigma model on noncommutative superspace in two dimensions is obtained by dimensional reducing the model in four dimensions

Journal ArticleDOI
TL;DR: In this article, the properties of infinite matter and finite nuclei are studied using the chiral sigma model in the framework of relativistic mean field theory, where the omega meson mass is generated dynamically by sigma condensation in the vacuum in the same manner as the nucleon mass.
Abstract: The properties of infinite matter and finite nuclei are studied using the chiral sigma model in the framework of relativistic mean field theory. We reconstruct an extended chiral sigma model in which the omega meson mass is generated dynamically by sigma condensation in the vacuum in the same manner as the nucleon mass. All the parameters of the chiral sigma model are essentially fixed by the hadron properties in free space. In nuclear matter, the saturation property is described correctly, but the incompressibility is too large, and the scalar and vector potentials are about half as large as their phenomenological values. This fact is reflected in the properties of finite nuclei. We carry out calculations for N = Z eveneven mass nuclei between N = 16 and N = 34. The extended chiral sigma model without the pion mean field leads to the result that the magic number appears at N = 18, instead of N = 20, and the magic number does not appear at N = 28, due to the above mentioned nuclear matter properties. The latter problem, however, could be removed through the

Journal ArticleDOI
TL;DR: In this article, the semiclassical distorted wave model is developed to describe (π -, K + ) inclusive spectra related to Σ-formation measured at KEK with p π = 1.2 GeV/c.
Abstract: The semiclassical distorted wave model is developed to describe (π - , K + ) inclusive spectra related to Σ - formation measured at KEK with p π = 1.2 GeV/c. The shape and magnitude of the spectrum obtained with a 28 Si target are satisfactorily reproduced using a repulsive Σ-nucleus potential whose strength is of the order of 30-50 MeV. This strength is not as large as the value of more than 100 MeV obtained using the estimation presented in the report of the experiment.

Journal ArticleDOI
TL;DR: In this article, a hierarchical structure of up-quark-type Yukawa couplings is given as a basic structure of flavor, and lepton mixings that are larger than the quark mixings and downquark type (and charged-lepton-type) mass hierarchies that are milder than the up quark type mass hierarchy can generically be obtained under a few natural assumptions.
Abstract: The results of this study indicate that in E 6 grand unified theories (GUTs), once a hierarchical structure of up-quark-type Yukawa couplings is given as a basic structure of flavor, lepton mixings that are larger than the quark mixings and down-quark-type (and charged-lepton-type) mass hierarchies that are milder than the up-quark-type mass hierarchy can generically be obtained under a few natural assumptions. The basic flavor structure is compatible with non-Abelian horizontal symmetry, which can solve the SUSY flavor problem. It is shown that in solving the SUSY flavor problem, the E 6 structure, which realizes bi-large neutrino mixings, also solves a problem that results from the large neutrino mixing angles.

Journal ArticleDOI
TL;DR: It is shown that the constraint in the AMD+GCM calculation is effective for the purpose of obtaining the K π =0 + band, which contains the 2α- 12 C structure as an important component.
Abstract: A new constraint of clustering for the AMD calculation is proposed. This constraint yields a significant improvement in the investigation of the cluster structure using AMD, which sometimes meets with difficulty in producing certain specific cluster configurations. The usefulness of this constraint is verified by applying it to the the study of the K π =0 + band of 20 Ne, which has been conjectured to have 2α- 12 C structure. This band is not easy to construct with AMD. We show that the constraint in the AMD+GCM calculation is effective for the purpose of obtaining the K π =0 + band, which contains the 2α- 12 C structure as an important component.

Journal ArticleDOI
TL;DR: In this paper, an expression for the moment of the partition function valid for any finite system size N and complex power n [Re(n) > 0] is obtained for a simple spin glass model termed the discrete random energy model (DREM).
Abstract: An expression for the moment of the partition function valid for any finite system size N and complex power n [Re(n) > 0] is obtained for a simple spin glass model termed the discrete random energy model (DREM). We investigate the behavior of this moment in the thermodynamic limit, N →∞ , using this expression, and we find that a phase transition occurs at a certain real value of the replica number when the temperature is sufficiently low. This represents a direct clarification of the scenario of replica symmetry breaking of the DREM in the replica number space without use of the replica trick. The validity of the expression is confirmed numerically.

Journal ArticleDOI
TL;DR: In this paper, the breakup of a one-neutron halo nucleus is studied in the eikonal approximation, taking full account of the recoil effect, the neutron-core relative energy distributio no f the breakup cross section is calculated for 11 Be and 19 C projectiles incident on 12 Ca nd 208 Pb targets and compared to experimental data.
Abstract: The breakup of a one-neutron halo nucleus is studied in the eikonal approximation. Both the nuclear and Coulomb breakup processes are taken into account. The continuum states, which are usually approximated by plane waves, are constrained to satisfy the condition of orthogonality to the bound states of the halo nucleus. Taking full account of the recoil effect, the neutron-core relative energy distributio no f the breakup cross section is calculated for 11 Be and 19 C projectiles incident on 12 Ca nd 208 Pb targets and compared to experimental data. All the data regarding the energy distribution for a 208 Pb target at beam energies of 68 and 520 MeV/nucleon are accurately reproduced, except for its peak at small relative energy. The experimental data regarding the relative energy distribution for the 11 Be+ 12 C system are also accurately reproduced. It is shown that use of orthogonalized plane waves leads to reduced cross sections and is necessary to account for the experimental data. The effect of the no-recoil limit is quantified.

Journal ArticleDOI
TL;DR: In this paper, the authors studied the possibility of the formation of small-scale structure during baryogenesis and big bang nucleosynthesis and found that the value of η in the bubbles could be much larger than the usually accepted value and still be consistent with the existing data on light element abundances and the observed angular spectrum of cosmic microwave background radiation (CMBR).
Abstract: Recent observations have revealed that small-scale structure exists at high redshift. We study the possibility of the formation of such structure during baryogenesis and big bang nucleosynthesis. It is known that under certain conditions, high density baryonic bubbles are created in the Affleck-Dine model of baryogenesis, and these bubbles may occupy a relatively small fraction of space, while the dominant part of the cosmological volume is characterized by the normal observed baryon-to-photon ratio, η = 6.10 -10 . The value of η in the bubbles could be much larger than the usually accepted value (indeed, even close to unity) and still be consistent with the existing data on light element abundances and the observed angular spectrum of cosmic microwave background radiation (CMBR). We find upper bounds on η by comparing the abundances of heavy elements produced in big bang nucleosynthesis (BBN) and those of metal poor stars. We conclude that η should be smaller than 10 -5 in some metal poor star regions.

Journal ArticleDOI
TL;DR: In this article, the lowest order constrained variational (LOCV) method is reformulated to calculate the equation of state of nuclear and neutron matter with a new charge-dependent Reid potential (Reid93).
Abstract: The lowest order constrained variational (LOCV) method is reformulated to calculate the equation of state of nuclear and neutron matter with a new charge-dependent Reid potential (Reid93). The state-dependent correlation functions are calculated by performing a full functional minimization for each JLSTM T -channel and the resulting Euler Lagrange equations are solved up to J = 9. The correlation functions are compared with those coming from LOCV calculation with the old Reid68 potential. It is shown that unlike ∆-Reid68 and AV18 interactions, the new Reid93 over binds nuclear matter at much larger saturation density than Reid68. Finally, the results are being compared with similar calculations with other potentials and many-body techniques.

Journal ArticleDOI
TL;DR: In this paper, the Lorentz transformations of entangled Bell states with general momentum not necessarily orthogonal to the boost direction and spin are studied, and it is shown that quantum information along the direction perpendicular to a boost is eventually lost, and Bell's inequality is not always violated for entangled states in special relativity.
Abstract: In this paper, the Lorentz transformations of entangled Bell states with general momentum not necessarily orthogonal to the boost direction and spin are studied. We extend quantum correlations and Bell’s inequality to the relativistic regime by considering normalized relativistic observables. It is shown that quantum information along the direction perpendicular to the boost is eventually lost, and Bell’s inequality is not always violated for entangled states in special relativity. This could impose restrictions on certain quantum information processing, such as quantum cryptography using massive particles.

Journal ArticleDOI
TL;DR: In this paper, the dependence of the template space metric on the initial phase of the wave was not taken into account and an improved, efficient search method for the gravitational ringing of black holes was presented.
Abstract: A black hole has characteristic quasi-normal modes that are excited when it is formed or when the geometry is perturbed. The state of a black hole when the quasi-normal modes are excited is called ‘gravitational ringing’, and detections of it constitute a direct confirmation of the existence of black holes. To detect it, a method based on matched filtering needs to be developed. Generically, matched filtering requires a large number of templates, because one has to ensure the proper match of a real gravitational wave with one of template waveforms to keep the detection efficiency as high as possible. On the other hand, the number of templates must be kept as small as possible due to limits in computational capability. In a previous paper, assuming that the gravitational ringing is dominated by the least-damped (fundamental) mode with the smallest imaginary part of the frequency, we constructed an efficient method for tiling the template space. However, the dependence of the template space metric on the initial phase of the wave was not taken into account. This dependence arises because of an unavoidable mismatch between the parameters of the signal waveform and those given discretely in the template space. In this paper, we properly take this dependence into account and present an improved, efficient search method for the gravitational ringing of black holes.

Journal ArticleDOI
TL;DR: In this paper, the mass of the pentaquark baryons Θ + and Ξ is derived in the Maldacena prototype model for supersymmetric QCD and a more realistic model for ordinary QCD.
Abstract: The recently observed pentaquark baryons Θ + and Ξ -- are studied in the dual gravity theory of QCD. By developing a general formulation useful for studying the branched string web in a curved space, simple mass formulae of the pentaquark baryons are derived in the Maldacena prototype model for supersymmetric QCD and a more realistic model for ordinary QCD. Even though the approximations adopted here in deriving these formulae are extremely naive, the predicted values of the masses do not differ significantly from their experimental values. We thus conclude that this approach is promising for the purpose of obtaining a description of the observed masses of pentaquarks and of their extremely narrow decay widths. With the aim of constructing more reliable mass formulae, a preliminary sketch is given of how spin, the hyperfine interaction and parity are considered in the string picture.

Journal ArticleDOI
TL;DR: In this article, the authors examined the localization of vector multiplets using the N = 1 supersymmetric U (1) gauge theory with the Fayet-Iliopoulos term coupled to charged chiral multiplets in four dimensions.
Abstract: The localization of vector multiplets is examined using the N = 1 supersymmetric U (1) gauge theory with the Fayet-Iliopoulos term coupled to charged chiral multiplets in four dimensions. The vector field becomes localized on a BPS wall connecting two different vacua that break the gauge symmetry. The vacuum expectation values of charged fields vanish (approximately) around the center of the wall, causing the Higgs mechanism to be ineffective. The mass of the localized vector multiplet is found to be the inverse width of the wall. The model gives an explicit example of this general phenomenon. A five-dimensional version of the model can also be constructed if we abandon supersymmetry.

Journal ArticleDOI
TL;DR: A review of the method for solving quantum field theory in the Heisenberg picture, developed by Abe and Nakanishi since 1991, can be found in this article, where exact solutions to various 2-dimensional gauge-theory and quantum-gravity models are found explicitly.
Abstract: This paper is a review of the method for solving quantum field theory in the Heisenberg picture, developed by Abe and Nakanishi since 1991. Starting from field equations and canonical (anti)commutation relations, one sets up a (q-number) Cauchy problem for the totality of d-dimensional (anti)commutators between the fundamental fields, where d is the number of spacetime dimensions. Solving this Cauchy problem, one obtains the operator solution of the theory. Then one calculates all multiple commutators. A representation of the operator solution is obtained by constructing the set of all Wightman functions for the fundamental fields; the truncated Wightman functions are constructed so as to be consistent with all vacuum expectation values of the multiple commutators mentioned above and with the energy-positivity condition. By applying the method described above, exact solutions to various 2-dimensional gauge-theory and quantum-gravity models are found explicitly. The validity of these solutions is confirmed by comparing them with the conventional perturbation-theoretical results. However, a new anomalous feature, called the field-equation anomaly, is often found to appear, and its perturbation-theoretical counterpart, unnoticed previously, is discussed. The conventional notion of an anomaly with respect to symmetry is reconsidered on the basis of the field-equation anomaly, and the derivation of the critical dimension in the BRS-formulated bosonic string theory is criticized. The method outlined above is applied to more realistic theories by expanding everything in powers of the relevant parameter, but this expansion is not equivalent to the conventional perturbative expansion. The new expansion is BRS-invariant at each order, in contrast to that in the conventional perturbation theory. Higher-order calculations are generally extremely laborious to perform explicitly.