Showing papers in "Progress of Theoretical Physics in 2006"

The Complex Scaling Method for Many-Body Resonances and Its Applications to Three-Body Resonances

Abstract: Resonance phenomena in quantum physics are very familiar in many fields of physics, but we have not yet obtained a complete physical understanding, mathematical description or computational treatment, especially in the case of many-body resonances. Recently, in experimental developments concerning unstable nuclear physics and heavy-ion nuclear reactions, much interest has been concentrated on many-body resonance problems. In the last quarter century, theoretical and mathematical treatments of many-body resonances have experienced great development through application of the complex scaling method (CSM). We can now treat resonant states of three-body systems in the same way as those of twobody systems. In this article, starting from the definition of a resonant state and discussion of its norm, we present a summary of recent studies of CSM to treat many-body resonances and applications to three-body resonant states in two-neutron halo nuclei and three-cluster systems.

Kaluza-Klein Black Holes with Squashed Horizons

Abstract: We study geometrical structures of charged static black holes in the five-dimensional Einstein-Maxwell theory. The black holes we study have horizons in the form of squashed S 3 , and their asymptotic structure consists of a twisted S 1 bundle over the four-dimensional flat spacetime at the spatial infinity. The spacetime we consider is fully five-dimensional in the vicinity of the black hole and four-dimensional with a compact extra dimension at infinity.

Anomalous Transport Processes in Anisotropically Expanding Quark-Gluon Plasmas

Abstract: We derive an expression for the anomalous viscosity in an anisotropically expanding quark-gluon-plasma, which arises from interactions of thermal partons with dynamically generated color fields. The anomalous viscosity dominates over the collisional viscosity for large velocity gradients or weak coupling. This effect may provide an explanation for the apparent “nearly perfect” liquidity of the matter produced in nuclear collisions at RHIC without the assumption that it is a strongly coupled state.

Adiabatic Evolution of Orbital Parameters in Kerr Spacetime

Abstract: We investigate the adiabatic orbital evolution of a point particle in Kerr spacetime due to the emission of gravitational waves. In the case that the timescale of the orbital evolution is sufficiently smaller than the characteristic timescale of orbits, the evolution of orbits is characterized by the rates of change of three constants of motion, the energy E, the azimuthal angular momentum L, and the Carter constant Q. We can evaluate the rates of change of E and L from the fluxes of the energy and the angular momentum at infinity and on the event horizon, employing the balance argument. However, for the Carter constant, we cannot use the balance argument because we do not know the conserved current associated with it. Recently, Mino proposed a new method of evaluating the average rate of change rate of the Carter constant by using the radiative field. In a previous paper, we developed a simplified scheme for determining the evolution of the Carter constant based on Mino’s proposal. In this paper we describe our scheme in more detail and derive explicit analytic formulae for the rates of change of the energy, the angular momentum and the Carter constant.

Charge Screening Effect in the Hadron-Quark Mixed Phase

Abstract: The Coulomb interaction effect is consistently taken into account in the hadron-quark mixed phase. It is found that the finite-size effects, such as the surface effect and the charge screening effect, greatly alter the properties of the mixed phase and restrict its density region. In particular, the charge screening effect and the rearrangement of the charged particles are elucidated. As the Gibbs conditions are satisfied throughout the numerical procedure, we show that the Maxwell construction becomes physically meaningful and the equation of state becomes similar to that given by the Maxwell construction.

Double-Λ Hypernuclei in the Relativistic Mean-Field Theory

Abstract: We study the properties of double-Λ hypernuclei in the relativistic mean-field theory, which has been successfully used for the description of stable and unstable nuclei. With the meson-hyperon couplings determined by the experimental binding energies of single-Λ hypernuclei, we present a self-consistent calculation of double-Λ hypernuclei in the relativistic mean-field theory, and discuss the influence of hyperons on the nuclear core. The contribution of two mesons with dominant strange quark components (scalar σ ∗ and vector φ )t o theΛΛ binding energy of double-Λ hypernuclei is examined.

Occurrence of Hyperon Superfluidity in Neutron Star Cores

Abstract: proach. Numerical results for the equation of state (EOS) with the mixing ratios of the respective components and the hyperon energy gaps including the temperature dependence are presented. These are meant to serve as physical inputs for Y -cooling calculations of NSs. By paying attention to the uncertainties of the EOS and the YY interactions, it is shown that both Λ and Σ − are superfluid as soon as they appear although the magnitude of the critical temperature and the density region where superfluidity exists depend considerably on the YY pairing potential. Considering momentum triangle condition and the occurrence of superfluidity, it is found that a so-called “hyperon cooling”(neutrino-emission from direct Urca process including Y ) combined with Y -superfluidity may be able to account for observations of the colder class of NSs. It is remarked that Λ-hyperons play a decisive role in the hyperon cooling scenario. Some comments are given regarding the consequences of the less attractive ΛΛ interaction recently suggested by the “NAGARA event” 6He.

The Relativistic Gross-Pitaevskii Equation and Cosmological Bose-Einstein Condensation : Quantum Structure in the Universe

Abstract: We do not know the identity of 96% of the total matter in the universe at present. In this paper, a cosmological model is proposed in which dark energy (DE) is identified with the Bose-Einstein condensation (BEC) of some boson fi eld. The global cosmic acceleration caused by this BEC and multiple rapid collapses of BEC into black holes and other forms of localized matter [= dark matter (DM)] are examined on the basis of the relativistic version of the Gross-Pitaevskii equation. We propose (a) a novel mechanism of inflation, free from the slow-rolling condition, (b) a natural solution to the cosmic coincidence (‘Why now?’) problem through the transition from DE to DM, (c) very early formation of highly nonlinear objects, such as black holes, which might have triggered the first light as a form of quasars, and (d) log-z periodicity in the subsequent BEC collapsing time. All of these are based on a steady, slow BEC process. It is amazing that recent cosmological observations provide us with a wide range of knowledge and mysteries. It is also amazing that the standard ΛCDM cosmological model works perfectly without specifying most of the matter content of the universe. In this model, the basic concepts and the structure of matter and space are both very simple, and the basic assumptions are clear. Moreover, within this model, the temperature fluctuations, δT, in the sky and the large scale power spectrum, P (k) , of density fluctuations can be calculated precisely from the primordial density fluctuations; 1) they correctly describe most observations. However as a theory of physics, there are at least two unsatisfactory points in this standard model. One is that the theory lacks identification of matter. Although significant amount of unknown matter plays an important role in the theory, this is simply called dark matter and dark energy, and the specification of them has been postponed. Thus we still do not know 96% of the cosmic matter contents, dark energy (DE) and dark matter (DM). Moreover, we do not know the relation between them. The second point is that the successful description of and the harmony with the cosmological observations are limited to the linear regime. There are many peculiarities in the non-linear regime: the too early formation of objects and reionization at around z ≈ 20, the physical details of the biasing for galaxy formation, and a natural mechanism of how the first stars formed, etc. These facts force us to consider some other source of instability, in addition to ordinary gravity, in order to form clearly localized structures.

Yang-Mills Theory Constructed from Cho-Faddeev-Niemi Decomposition

Abstract: We give a new way of looking at the Cho-Faddeev-Niemi (CFN) decomposition of the Yang-Mills theory to answer how the enlarged local gauge symmetry respected by the CFN variables is restricted to obtain another Yang-Mills theory with the same local and global gauge symmetries as the original Yang-Mills theory. This may shed new light on the fundamental issue of the discrepancy between two theories for independent degrees of freedom and the role of the Maximal Abelian gauge in Yang-Mills theory. As a byproduct, this consideration gives new insight into the meaning of the gauge invariance and the observables, e.g., a gauge-invariant mass term and vacuum condensates of mass dimension two. We point out the implications for the Skyrme-Faddeev model.

The Dirac Propagator in the Kerr-Newman Metric

Abstract: We give an alternative proof of the completeness of the Chandrasekhar ansatz for the Dirac equation in the Kerr-Newman metric. Based on this, we derive an integral representation for smooth compactly supported functions which in turn we use to derive an integral representation for the propagator of solutions of the Cauchy problem with initial data in the above class of functions. As a by-product, we also obtain the propagator for the Dirac equation in the Minkowski space-time in oblate spheroidal coordinates. One of the most spectacular predictions of general relativity are black holes which should form when a large mass is concentrated in a sufficiently small volume. The idea of a mass-concentration which is so dense that even light would be trapped goes back to Laplace in the 18th century. Shortly after Einstein developed general relativity, Karl Schwarzschild discovered in 1916 a mathematical solution to the equations of the theory that describes such an object. It was only much later, with the work of physicists like Oppenheimer, Volkoff and Snyder in the 1930’s, that the scientific community began to think seriously about the possibility that such objects might actually exist in the Universe. It was shown that when a sufficiently massive star runs out of fuel, it is unable to support itself against its own gravitational attraction and it should collapse into a black hole. Starting with the 1960’s and the 1970’s, in the so-called Golden Era of black hole research, new interesting phenomena like the Hawking radiation and superradiance were discovered but for their rigorous mathematical description we have to wait until the 1990’s and the beginning of the new century when the rigorous analysis of the propagation and of the scattering properties of classical and quantum fields on black hole space-times started to be developed. Whenever we attempt to analyze the scattering properties of fields in the more general framework of the Kerr-Newman black hole geometry, we are faced with several difficulties which are not present in the picture of the Schwarzschild metric. First of all, the Kerr-Newman solution is only axially symmetric (cylindrical symmetry) since it possesses only two commuting Killing vector fields, namely the time coordinate vector field ∂t and the longitude coordinate vector field ∂ϕ. This implies that there is no decomposition in spin-weighted spherical harmonics. Moreover, another difficulty is due to fact that the Kerr-Newman space-time is not stationary. In

Toward a no-go theorem for an accelerating universe through a nonlinear backreaction

Abstract: The backreaction of nonlinear inhomogeneities to the cosmic expansion is re-analyzed in the framework of general relativity. Apparent discrepancies regarding the effect of the nonlinear backreaction, which exist among the results of previous works in different gauges, are resolved. By defining the spatially averaged matter energy density as a conserved quantity in the large comoving volume, it is shown that the nonlinear backreaction neither accelerates nor decelerates the cosmic expansion in a matter-dominated universe. The present result in the Newtonian gauge is consistent with the previous results obtained in the comoving synchronous gauge. Although our work does not give a complete proof, it strongly suggests the following no-go theorem: No cosmic acceleration occurs as a result of the nonlinear backreaction via averaging.

Higher Order Terms in the Improved Mean Field Approximation for the IIB Matrix Model and the Emergence of Four-Dimensional Space-Time

Abstract: The spontaneous breakdown of SO(10) symmetry in the IIB matrix model has been studied using the improved mean field approximation (IMFA) In this report, the eighth-order contribution to the improved perturbative series is obtained, which involves the evaluation of 20410 planar two-particle irreducible vacuum diagrams We consider SO(d)-preserving configurations as an ansatz (d = 4,7) The development of a plateau, representing the condition of self-consistency, is seen in both ansatz A large ratio of the space-time extent of the d-dimensional part to that of the remaining (10 - d)-dimensional part is obtained for the SO(4) ansatz evaluated at representative points of the plateau This is interpreted as the emergence of four-dimensional space-time in the IIB matrix model

The π+ − π0 Mass Difference and the S Parameter in Large Nf QCD*)

Abstract: In the framework of the Schwinger-Dyson equation and the Bethe-Salpeter equation in the improved ladder approximation, we calculate the S parameter and an analogue of the π + − π 0 mass difference, ∆m 2 ≡ m 2+ − m 20 , as well as the NG boson decay constant, fπ, on the same footing in large Nf QCD, using the difference between the vector current correlator, Π VV , and the axial-vector current correlator, ΠAA. Approaching the chiral phase transition point α∗ → αcr(= π/4) from the broken phase, where α∗ is the the gauge coupling at the infrared fixed point, the quantities ∆m 2 and f 2 π go to zero with an essential-singularity scaling (Miransky scaling), while the ratio exhibits a blowing up enhancement, reflecting the characteristic behavior of large Nf QCD as a walking theory, which is expected to scale as ∆m 2/f 2 π ∼ (α∗/αcr − 1) −1/2 . By contrast, the S parameter takes values somewhat smaller than that in the case of actual QCD and displays slightly decreasing tendency as we approach the phase transition point.

Theory of Non-Equilibirum States Driven by Constant Electromagnetic Fields : Non-Commutative Quantum Mechanics in the Keldysh Formalism

Abstract: We develop a general theory of non-equilibrium states based on the Keldysh formalism, in particular, for charged-particle systems under static uniform electromagnetic fields. The Dyson equation for the uniform stationary state is rewritten in a compact gauge-invariant form by using the Moyal product in the phase space of energy-momentum variables, whcich originally do not commute in the case of the conventional operator algebra. Expanding the Dyson equation in electromagnetic fields, a systematic method for the order-by-order calculation of linear and non-linear responses from the zeroth-order Green’s functions is obtained. In particular, we find that for impurity problems, up to linear order in the electric field, the present approach provides a diagrammatic method for the St˘ reda formula. This approach also generalizes the semi-classical Boltzmann transport theory to fully quantummechanical and/or multi-component systems. In multi-component systems and/or for Hall transport phenomena, however, this quantum Boltzmann transport theory, constructed from the anti-symmetric combination of two different representations for the Dyson equation, does not uniquely specify the non-equilibrium state, but the symmetric combination is required. We demonstate the formalism to calculate longitudinal and Hall electric conductivities in an isotropic single-band electron system in the clean limit. It is found that the results are fully consistent with those obtained by Mott and Ziman in terms of the semi-classical Boltzmann transport theory.

New Treatment of Resonances with a Bound State Approximation Using a Pseudo-Potential

Abstract: We propose a new approach to extract the wave functions of resonances with the bound state approximation, which gives mixed states of the resonance components and continuum components. In our approach, on the basis of the method of analytic continuation in the )

Energy Density Associated with the Bianchi Type-II Space-Time

Abstract: To calculate the total energy distribution (due to both matter and fields including gravitation) associated with locally rotationally symmetric (LRS) Bianchi type-II space-times. We use the Bergmann-Thomson energy-momentum complex in both general relativity and teleparallel gravity. We find that the energy density in these different gravitation theories is vanishing at all times. This result is the same as that obtained by one of the present authors who solved the problem of finding the energy-momentum in LRS Bianchi type-II by using the energy-momentum complexes of Einstein and Landau and Lifshitz. The results of this paper also are consistent with those given in the previous works of Cooperstock and Israelit,

Unification of cosmology and the second law of thermodynamics : Proposal for solving the cosmological constant and inflation problems

Abstract: We seek to unify the second law of thermodynamics with other physical laws, or, at least to find a law underlying the second law of thermodynamics. Assuming no fine tuning, using a random Hamiltonian, we argue just from the equations of motion - without the second law - that entropy cannot first increase and then decrease except with the rather strict restriction S large < S small1 + S small2 . Here S large is the "large" entropy in the intermidiate era, while S small1 and S small2 are the entropies at certain times before and after the S large era. From this theorem asserting that there can exist no strong maximum for the entropy, we argue that an S 1 cyclic time model world could have entropy that varies by at most a factor of two and would not be phenomenologically realistic. With an open ended time axis (-∞, ∞) = R, some law underlying the second law of thermodynamics is needed if the entropy is not maximal (i.e. that heat death having y occurred at the start). We derive such a law behind the second law - or a unification of the second law with other laws - by assigning a probability weight P for finding the world/system in various places in phase space. In such a model, P is almost unified with the rest as P = exp(-2S Im ), with S Im being the imaginary part of the action. We quite naturally derive the second law for practical purposes, a Big Bang with two-sided time directions, and find that there is a need for a Hamiltonian density with a well-defined bottom. Assuming that the cosmological constant is a dynamical variable in the sense that it is counted as on "initial condition", we even solve in our model the cosmological constant problem without using the anthropic principle.

Color Confinement in Coulomb Gauge QCD

Abstract: We study the long-range behavior of the heavy quark potential in Coulomb gauge using a quenched SU(3) lattice gauge simulation with partial-length Polyakov line correlators. We show that the Coulomb heavy quark potential associated with the instantaneous part of gluon propagators in Coulomb gauge, presents a linearly rising behavior at large distances, and the resulting Coulomb string tension is greater than the Wilson loop string tension, which can be explained by Zwanziger’s inequality. The linearly rising behavior of the Coulomb heavy quark potential persists even in the deconfinement phase. The heavy quark potential in Lorentz gauge shows completely different behavior than that in Coulomb gauge. Our SU(3) result, i.e., the Coulomb heavy quark potential is confining, qualitatively agrees with that of the SU(2) analysis carried out by Greensite, Olejnik and Zwanziger.

Time-Dependent Supersymmetric Solutions in M-Theory and the Compactification-Decompactification Transition

Abstract: We show that the diagonal light-like solution with 16 supersymmetries in elevendimensional supergravity derived in our previous paper can be generalised to non-diagonal solutions preserving the same number of supersymmetries. Although the metric coefficients of this generalised light-like solution depend on only a single null coordinate, this class of solutions contains a subclass equivalent to the class of solutions found by Bin Chen that are dependent on the spatial coordinates. Utilising these solutions, we construct toroidally compactified solutions that smoothly connect a static compactified region with a dynamically decompactifying region along a null hypersurface.

Projective synchronization in fractional order chaotic systems and its control

Abstract: The chaotic dynamics of fractional (non-integer) order systems has begun to attract much attention in recent years. In this paper, we study the projective synchronization in two coupled fractional order chaotic oscillators. It is shown that projective synchronization can also exist in coupled fractional order chaotic systems. A simple feedback control method for controlling the scaling factor onto a desired value is also presented. Although fractional calculus has a mathematical history nearly as long as that of the integer-order calculus, the applications of it to physics and engineering are just a recent focus of interest. 1),2) Many systems are known to display fractional order dynamics, such as viscoelastic systems 3)–5) dielectric polarization, 6) electrodeelectrolyte polarization 7) and electromagnetic waves, 8) so it is important to study the properties of fractional order systems. The dynamics of fractional order systems has not yet been fully studied, and it is by no means trivial. The definitions of fractional order calculus are geometrically and physically less intuitive than the integer-order ones, and cannot be simulated directly in time-domain. It is still unclear whether the dynamics of fractional order systems is similar to the integer-order ones. More recently, many authors have begun to investigate the chaotic dynamics of fractional order dynamical systems. 9)–17) In 9), it was shown that the fractional order Chua’s system of order as low as 2.7 can produce a chaotic attractor. In 10), it was shown that nonautonomous Duffing systems of order less than 2 can still behave in a chaotic manner. In 11), chaotic behavior of the fractional order “jerk” model was studied, in which chaotic attractor was obtained with system orders as low as 2.1, and in 12) the control of this fractional order chaotic system was reported. In 13), chaotic behavior of the fractional order Lorenz system was studied, but unfortunately, the results presented in this paper are not correct. In 14) and 15), bifurcation and chaotic dynamics of the fractional order cellular neural networks were studied. In 16), chaos ˙ ˙ ˙ (a)

Stability of 4-Dimensional Space-Time from the IIB Matrix Model via the Improved Mean Field Approximation

Abstract: We investigate the origin of our four-dimensional space-time by considering dynamical aspects of the IIB matrix model using the improved mean field approximation. Previous works have focused on the specific choices of configurations as ansatz which preserve SO(d) rotational symmetry. In this report, an extended ansatz is proposed and examined up to a third-order approximation which includes both the SO(4) ansatz and the SO(7) ansatz in their respective limits. From the solutions of the self-consistency condition represented by the extrerna of the free energy of the system, it is found that some of the solutions found in the SO (4) or SO (7) ansatz disappear in the extended ansatz. This implies that the extension of ansatz can be used to distinguish stable solutions from unstable solutions. It is also found that there is a non-trivial accumulation of extrema including the SO(4)-preserving solution, which may lead to the formation of a plateau.

Quantum Field Theories in Nonextensive Tsallis Statistics

Abstract: Within the framework of Tsallis statistics with q ≃ 1, we construct a perturbation theory for treating relativistic quantum field systems. We find that there appear initial correlations, which do not exist in the Boltzmann-Gibbs statistics. Applying this framework to a quark-gluon plasma, we find that the so-called thermal masses of quarks and gluons are smaller than in the case of Boltzmann-Gibbs statistics.

Entropy Production and Pesin-Like Identity at the Onset of Chaos

Abstract: Asymptotically entropy of chaotic systems increases linearly and the sensitivity to initial conditions is exponential with time: these two types of behavior are related. Such relationship is analogous to and, under specific conditions, has been shown to coincide with the Pesin identity. Numerical evidence supports the proposal that the statistical formalism can be extended to the edge of chaos by using a specific generalization of the exponential and of the Boltzmann-Gibbs entropy. We extend this picture and a Pesin-like identity to a wide class of deformed entropies and exponentials using the logistic map as a test case. The physical criterion of finite-entropy growth strongly restricts the suitable entropies. The nature and characteristics of this generalization are clarified.

Boundary States in the Open String Channel and CFT near a Corner

Abstract: We generalize the idea of boundary states to the open string channel. They describe emission and absorption of open strings in the presence of intersecting D-branes. We construct the explicit oscillator representation for the free boson and fermionic ghost. The inner product of such states describes a disk amplitude of rectangular shape and possesses modular covariance with a nontrivial conformal weight. We compare the result obtained here with those obtained using two different methods, one employing the path integral formalism and one employing the conformal anomaly. We find that all these methods give consistent results. In our method, we must be careful in our treatment of the singularity of the CFT near the corners. Specifically, we derive the correction to the conformal weight of the primary field inserted at the corner, and it gives the modular weight of the rectangle amplitude. We also carry out explicit computations of the correlation functions.

The Lempel-Ziv Complexity of Non-Stationary Chaos in Infinite Ergodic Cases

Abstract: The large deviation properties of the Lempel-Ziv complexity are studied using a onedimensional non-hyperbolic chaos map called the “modified Bernoulli map”, where the transition between stationary and non-stationary chaos is clearly observed. The upper limit of the Lempel-Ziv complexity in the non-stationary regime is theoretically evaluated, and the relationship between the algorithmic complexity and the Lempel-Ziv complexity is discussed. Non-stationary processes are universal phenomena in non-hyperbolic systems, and they are usually characterized by an infinite ergodic measure and intrinsic long time tails, such as 1/f ν spectral fluctuations. It is shown that the Lempel-Ziv complexity obeys universal scaling laws and that the Lempel-Ziv complexity has the L 1 -function property, which guarantees the Darling-Kac-Aaronson theorem for an infinite ergodic system. The most striking result is that the maximum diversity appears at the transition point from stationary chaos to non-stationary chaos where the exact 1/f spectral process is generated.

The Equilibrium Facet Shape of the Staggered Body-Centered-Cubic Solid-on-Solid Model— Density Matrix Renormalization Group Study —

Abstract: We present a new method for the numerical calculation of the equilibrium crystal shape around a facet. Our method is based on the transfer matrix method with the product-wave-function renormalization group (PWFRG) algorithm for the asymmetric density matrix, which is an extension of the density matrix renormalization group (DMRG) algorithm. By applying this method to the staggered body-centered-cubic solid-on-solid model, which is known to exhibit the inverse roughening phenomena, we obtain the facet shape, shape exponents, and step tension.

Adiabatic Expansion for a Metric Perturbation and the Condition to Solve the Gauge Problem for the Gravitational Radiation Reaction Problem

Abstract: We examine the adiabatic approximation in the study of a relativistic two-body problem with the gravitational radiation reaction. We recently pointed out that the usual metric perturbation scheme using a perturbation of the stress-energy tensor may not be appropriate for study of the dissipative dynamics of the bodies due to the radiation reaction. Over a time scale during which the usual perturbation scheme is valid, the orbits may not deviate substantially relative to the orbits of the background orbits. As a result, one can eliminate the orbital deviation through a gauge transformation. This is called the gauge problem of the gravitational radiation reaction exerted on the bodies, and it has been reported that a careful gauge fixing may be necessary to produce a physically reasonable prediction for the evolution of the system. We recently proposed a possible approach to solve this problem with a linear black hole perturbation. This paper proposes a non-linear generalization of that method for a general application of this problem. We show that, under a specific gauge condition, the method actually allows us to avoid the gauge problem.

Semiclassical Approach for Bifurcations in a Smooth Finite-Depth Potential

Abstract: The analytical trace formula for a dense cascade of bifurcations was derived using the improved stationary phase method based on extensions of the semiclassical Gutzwiller path integral approach. For the integrable version of the famous Henon-Heiles Hamiltonian, our analytical trace formula solves all bifurcation problems, in particular, in the harmonic oscil- lator limit and the potential barrier limit. We obtain nice agreement with quantum results for gross to finer shell structures in level densities and for the shell structure energies, even near the potential barrier where there is a rather dense sequence of bifurcations.

Note on Massless Bosonic States in Two-Dimensional Field Theories

Abstract: In this paper, we show that in a wide class of GL ×GR invariant two-dimensional super-renormalizable field theories, the parity-odd part of the two-point function of global currents can be determined to all orders in perturbation theory. The twopoint function possesses a massless pole for any non-trivial fermion content, and this fact provides a simple criterion to determine the existence of massless bosonic physical states without solving the dynamics. Our argument is based on anomalous Ward-Takahashi (WT) identities and is somewhat similar to that for the ’t Hooft anomaly matching condition. 1)–3) In fact, applying the anomaly matching argument to the systems we consider (assuming that the anomalous behavior of the two-point function does not receive higher-order radiative corrections), one would arrive at a similar conclusion concerning massless states. (See, for example, Refs. 4)–6).) The point of this paper is, however, to show that in the two-dimensional systems we consider, an elementary argument suffices to obtain an explicit form of the twopoint function to all orders in perturbation theory. In particular, our argument is applicable even to systems in which the left and right moving modes are not