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Showing papers on "Canonical transformation published in 1999"


Journal ArticleDOI
Konstadinos Sfetsos1
TL;DR: In this article, a new class of two-dimensional field theories with target spaces that are finite multiparameter deformations of the usual coset G/H-spaces was constructed, and the corresponding generating functionals are non-polynomial in the derivatives of the fields with respect to the space-like variable.

57 citations


Journal ArticleDOI
TL;DR: In this paper, a perturbation theory is developed for constructing stroboscopic and Poincare maps for Hamiltonian systems with small perturbations, which is based on a canonical transformation by which the evolution becomes unperturbed during the entire period while all perturbs are acting instantaneously during one kick per period.
Abstract: A perturbation theory is developed for constructing stroboscopic and Poincare maps for Hamiltonian systems with a small perturbation. It is based on a canonical transformation by which the evolution becomes unperturbed during the entire period while all perturbations are acting instantaneously during one kick per period. Matching of solutions before and after the kicks establishes a symplectic map which exactly describes the evolution. The generating function associated with this map satisfies the Hamilton-Jacobi equations. The solution of this equation is found in first order of perturbation theory. It is shown that the map reproduces correctly Poincare sections and statistical properties of typical orbits. It is shown that the well known perturbed twist mapping and, in particular, the standard map may be obtained from the symmetric map as an approximation. The method is also applied to construct Poincare maps at arbitrary sections of the phase space. In particularly, the maps describing a motion near the separatrix are derived.

43 citations


Journal ArticleDOI
Nanhua Xi1
TL;DR: The Canonical basis for type A,3 is discussed in this article, where it is shown that type A is the basis for the type A-type A. Communications in Algebra: Vol. 27, No. 11, pp. 5703-5710.
Abstract: (1999). Canonical basis for type A,3. Communications in Algebra: Vol. 27, No. 11, pp. 5703-5710.

33 citations


Book ChapterDOI
01 Jan 1999
TL;DR: In this article, it is shown how a dynamical time (an internal clock) can be constructed by means of a Hamilton-Jacobi formalism, and then used for a consistent canonical quantization, with the correct classical limit.
Abstract: The Wheeler-DeWitt equation is based on the use of canonical quantization rules that may be inconsistent for constrained dynamical systems, such as minisuperspaces subject to Einstein’s equations. The resulting quantum dynamics has no classical limit and it suffers from the infamous “problem of time.” In this article, it is shown how a dynamical time (an internal “clock”) can be constructed by means of a Hamilton-Jacobi formalism, and then used for a consistent canonical quantization, with the correct classical limit.

31 citations


Journal ArticleDOI
TL;DR: The canonical transformation and its unitary counterpart which relate the rational Calogero-Moser system to the free one were constructed in this article, and the canonical transformation was shown to be a unitary transformation.

30 citations


Journal ArticleDOI
TL;DR: In this article, Yang-Mills field theory is considered in the framework of the generalized Hamiltonian approach and the equivalent unconstrained system is obtained using the method of Hamiltonian reduction.
Abstract: $\mathrm{SU}(2)$ Yang-Mills field theory is considered in the framework of the generalized Hamiltonian approach and the equivalent unconstrained system is obtained using the method of Hamiltonian reduction. A canonical transformation to a set of adapted coordinates is performed in terms of which the Abelianization of the Gauss law constraints is trivialized and the pure gauge degrees of freedom drop out from the Hamiltonian after projection onto the constraint shell. For the remaining gauge invariant fields two representations are introduced where the three fields which transform as scalars under spatial rotations are separated from the three rotational fields. An effective low energy nonlinear sigma model type Lagrangian is derived which out of the six physical fields involves only one of the three scalar fields and two rotational fields summarized in a unit vector. Its possible relation to the effective Lagrangian proposed recently by Faddeev and Niemi is discussed. Finally the unconstrained analog of the well-known nonnormalizable ground state wave functional which solves the Schr\"odinger equation with zero energy is given and analyzed in the strong coupling limit.

25 citations


Journal ArticleDOI
TL;DR: In this paper, the authors studied in the Hamiltonian framework the local transformations that leave invariant the Lagrangian action and obtained the manifest form of the symmetry and corresponding Noether identities.
Abstract: We study in the Hamiltonian framework the local transformations $\delta_\epsilon q^A(\tau)=\sum^{[k]}_{k=0}\partial^k_\tau\epsilon^a{} R_{(k)a}{}^A(q^B, \dot q^C)$ which leave invariant the Lagrangian action: $\delta_\epsilon S=div$. Manifest form of the symmetry and the corresponding Noether identities is obtained in the first order formalism as well as in the Hamiltonian one. The identities has very simple form and interpretation in the Hamiltonian framework. Part of them allows one to express the symmetry generators which correspond to the primarily expressible velocities through the remaining one. Other part of the identities allows one to select subsystem of constraints with a special structure from the complete constraint system. It means, in particular, that the above written symmetry implies an appearance of the Hamiltonian constraints up to at least $([k]+1)$ stage. It is proved also that the Hamiltonian symmetries can always be presented in the form of canonical transformation for the phase space variables. Manifest form of the resulting generating function is obtained.

23 citations


Journal ArticleDOI
Motomu Tsuda1
TL;DR: In this paper, the generalized Lagrangian of supergravity was generalized by using an arbitrary parameter, which corresponds to the inverse of Barbero's parameter, and the canonical formulation of the theory was derived from those of the usual $N=1$ SUGRA.
Abstract: We generalize the Lagrangian of $N=1$ supergravity (SUGRA) by using an arbitrary parameter $\ensuremath{\xi},$ which corresponds to the inverse of Barbero's parameter $\ensuremath{\beta}.$ This generalized Lagrangian involves the chiral one as a special case of the value $\ensuremath{\xi}=\ifmmode\pm\else\textpm\fi{}i.$ We show that the generalized Lagrangian gives the canonical formulation of $N=1$ SUGRA with the real Ashtekar variable after the $3+1$ decomposition of spacetime. This canonical formulation is also derived from those of the usual $N=1$ SUGRA by performing Barbero's type canonical transformation with an arbitrary parameter $\ensuremath{\beta}(={\ensuremath{\xi}}^{\ensuremath{-}1}).$ We give some comments on the canonical formulation of the theory.

17 citations


Journal ArticleDOI
TL;DR: In this paper, the authors elucidate the relationship between the linear oscillator with time-dependent frequency, damping, and driving, and the autonomous oscillator having unit frequency and no damping or driving.
Abstract: We elucidate the relationship between the linear oscillator with time-dependent frequency, damping, and driving, and the autonomous oscillator with unit frequency and no damping or driving. Such a relationship can be derived from a canonical transformation and a redefinition of the time. A study of the scalars of the transformation makes it possible to write down the evolving quantum states for the nonautonomous Hamiltonian given the evolving states for the autonomous harmonic oscillator.

16 citations


Journal ArticleDOI
TL;DR: In this article, the authors generalize the Serret-andoyer transformation to the case of Hamiltonian systems on T*SO(3) with left-invariant, hyperregular Hamiltonian functions.
Abstract: The Serret-Andoyer transformation is a classical method for reducing the free rigid body dynamics, expressed in Eulerian coordinates, to a 2-dimensional Hamiltonian flow. First, we show that this transformation is the computation, in 3-1-3 Eulerian coordinates, of the symplectic (Marsden-Weinstein) reduction associated with the lifted left-action of SO(3) on T*SO(3)—a generalization and extension of Noether's theorem for Hamiltonian systems with symmetry. In fact, we go on to generalize the Serret-Andoyer transformation to the case of Hamiltonian systems on T*SO(3) with left-invariant, hyperregular Hamiltonian functions. Interpretations of the Serret-Andoyer variables, both as Eulerian coordinates and as canonical coordinates of the co-adjoint orbit, are given. Next, we apply the result obtained to the controlled rigid body with momentum wheels. For the class of Hamiltonian controls that preserve the symmetry on T*SO(3), the closed-loop motion of the main body can again be reduced to canonical form. This simplifies the stability proof for relative equilibria , which then amounts to verifying the classical Lagrange-Dirichlet criterion. Additionally, issues regarding numerical integration of closed-loop dynamics are also discussed. Part of this work has been presented in LumBloch:97a.

16 citations


Journal ArticleDOI
TL;DR: In this article, the relationship between the multipolar and minimal Hamiltonians through a canonical transformation is used to analyze the time dependence of quantum operators in the two formalisms, and it is shown that operators dependent on particle position, the vector potential and their time derivatives have the same time dependence.
Abstract: The relationship between the multipolar and minimal Hamiltonians through a canonical transformation is used to analyze the time dependence of quantum operators in the two formalisms. It is shown that operators dependent on particle position, the vector potential, and their time derivatives have the same time dependence. However, operators such as the photon number and the atomic population number evolve differently in the two cases. Expressions correct to second order in the electric-dipole moments for these are given. The expectation values of the photon number operator are calculated in the two formalisms and are used to predict natural line shapes. These theoretical shapes differ. The observed shape will depend on the particular setup of the experiment involving the radiative decay of an excited atom. A comparison with the theoretical predictions will determine which of the two frameworks is most appropriate to describe the decay. Finally, the energy density of the electromagnetic field in the neighborhood of an atom is calculated within the two formalisms.

Journal ArticleDOI
TL;DR: In this paper, a theory describing the effects of many-particle Coulomb correlations on the coherent ultrafast nonlinear optical response of semiconductors and metals was developed, which is based on a mapping of the nonlinear response of the "bare" system onto the linear response of a "dressed" system, characterized by effective time-dependent optical transition matrix elements, electron/hole dispersions, and interaction potentials.
Abstract: We develop a theory describing the effects of many-particle Coulomb correlations on the coherent ultrafast nonlinear optical response of semiconductors and metals. Our approach is based on a mapping of the nonlinear optical response of the "bare" system onto the linear response of a "dressed" system. The latter is characterized by effective time-dependent optical transition matrix elements, electron/hole dispersions, and interaction potentials, which in undoped semiconductors are determined by the single-exciton and two-exciton Green functions in the absence of optical fields. This mapping is achieved by eliminating the optically-induced charge fluctuations from the Hamiltonian using a Van Vleck canonical transformation. It takes into account all many-body contributions up to a given order in the optical fields as well as important Coulomb-induced quantum dynamics to all orders in the optical field. Our approach allows us to distinguish between optical nonlinearities of different origins and provides a physically-intuitive interpretation of their manifestations in ultrafast coherent nonlinear optical spectroscopy.

Journal ArticleDOI
TL;DR: In this paper, the translational Chern-Simons term is used as a generating function for a chiral reformulation of simple supergravity, and the resulting canonical transformation induces not only a decomposition of the gravitational fields into selfdual and anti-selfdual modes, but also a splitting of the Rarita-Schwinger fields into their chiral parts.
Abstract: Similarly as in the Ashtekar approach, the translational Chern-Simons term is, as a generating function, instrumental for a chiral reformulation of simple supergravity. After applying the algebraic Cartan relation between spin and torsion, the resulting canonical transformation induces not only a decomposition of the gravitational fields into selfdual and anti-selfdual modes, but also a splitting of the Rarita-Schwinger fields into their chiral parts in a natural way. In some detail, we also analyze the consequences for axial and chiral anomalies.

Journal ArticleDOI
TL;DR: In this article, a theory describing the effects of many-particle Coulomb correlations on the coherent ultrafast nonlinear optical response of semiconductors and metals was developed, which is based on a mapping of the nonlinear response of the ''bare'' system onto the linear response of a ''dressed'' system.
Abstract: We develop a theory describing the effects of many-particle Coulomb correlations on the coherent ultrafast nonlinear optical response of semiconductors and metals. Our approach is based on a mapping of the nonlinear optical response of the ``bare'' system onto the linear response of a ``dressed'' system. The latter is characterized by effective time-dependent optical transition matrix elements, electron/hole dispersions, and interaction potentials, which in undoped semiconductors are determined by the single-exciton and two-exciton Green functions in the absence of optical fields. This mapping is achieved by eliminating the optically-induced charge fluctuations from the Hamiltonian using a Van Vleck canonical transformation. It takes into account all many-body contributions up to a given order in the optical fields as well as important Coulomb-induced quantum dynamics to all orders in the optical field. Our approach allows us to distinguish between optical nonlinearities of different origins and provides a physically-intuitive interpretation of their manifestations in ultrafast coherent nonlinear optical spectroscopy.


Journal ArticleDOI
TL;DR: In this article, a more efficient tabular method for mapping on-set fixed polarity Reed-Muller coefficients for a given polarity vector from the canonical sum of products coefficients is developed.
Abstract: In this paper, a more efficient tabular method for mapping on-set fixed polarity Reed–Muller coefficients for a given polarity vector from on-set canonical sum of products coefficients is developed. Using this mapping technique, a heuristic algorithm for generating optimal pseudo Reed–Muller expressions from canonical sum of products expressions is also developed. Illustrative examples and experimental results are included to show the performance of the developed algorithms.

Journal ArticleDOI
TL;DR: In this article, a real scalar field in thermal equilibrium is studied in the context of the new normal ordering and field split defined by Evans and Steer (Evans T S, Steer D A 1996 Nucl. Phys. B 474 481).
Abstract: We look at a real scalar field in thermal equilibrium in the context of the new normal ordering and field split defined by Evans and Steer (Evans T S and Steer D A 1996 Nucl. Phys. B 474 481). We show that the field split defines a natural canonical transformation, but that this transformation differs from others known in thermal field theory.

Journal ArticleDOI
TL;DR: In this paper, canonical perturbation theory is applied in the vicinity of the saddle point for a chemical reaction by applying successive canonical transformations in the scope of the Gustavson-Birkhoff approach.
Abstract: Classical canonical perturbation theory is applied in the vicinity of the saddle point for a chemical reaction. This is done by applying successive canonical transformations in the scope of the Gustavson–Birkhoff approach. It is shown that the calculated approximate classical integrals of motion can be used to describe classically forbidden tunnelling processes. They are also organically embedded into a hopping method to incorporate tunnelling effects into classical trajectory simulations of chemical reactions. The applicability of the proposed scheme is demonstrated for the collinear H+H2 exchange reaction using the double many-body expansion potential energy surface.

Book ChapterDOI
TL;DR: In this article, a canonical transformation given by zero-average trigonometrical series has no general solution at orders higher than the first in order to transform a Hamiltonian H = H 0(J) + ǫR(θ, J), (ǫ ≪ 1) into a new Hamiltonians H*(J*) (dependent only on the new actions J*).
Abstract: The word “average” and its variations became popular in the sixties and implicitly carried the idea that “averaging” methods lead to “average” Hamiltonians. However, given the Hamiltonian H = H 0(J) + ɛR(θ, J), (ɛ ≪ 1), the problem of transforming it into a new Hamiltonian H*(J*) (dependent only on the new actions J*), through a canonical transformation given by zero-average trigonometrical series has no general solution at orders higher than the first.


Journal ArticleDOI
TL;DR: In this paper, a relationship between the action-angle variables and the canonical transformation relating the rational Calogero-Moser system to the free one is discussed, and the authors also discuss the relationship between action angle variables and action angle transformations.
Abstract: A relationship between the action-angle variables and the canonical transformation relating the rational Calogero-Moser system to the free one is discussed.

Journal ArticleDOI
TL;DR: In this paper, the authors studied in the Hamiltonian framework the local transformations that leave invariant the Lagrangian action and obtained the manifest form of the symmetry and corresponding Noether identities.
Abstract: We study in the Hamiltonian framework the local transformations $\delta_\epsilon q^A(\tau)=\sum^{[k]}_{k=0}\partial^k_\tau\epsilon^a{} R_{(k)a}{}^A(q^B, \dot q^C)$ which leave invariant the Lagrangian action: $\delta_\epsilon S=div$. Manifest form of the symmetry and the corresponding Noether identities is obtained in the first order formalism as well as in the Hamiltonian one. The identities has very simple form and interpretation in the Hamiltonian framework. Part of them allows one to express the symmetry generators which correspond to the primarily expressible velocities through the remaining one. Other part of the identities allows one to select subsystem of constraints with a special structure from the complete constraint system. It means, in particular, that the above written symmetry implies an appearance of the Hamiltonian constraints up to at least $([k]+1)$ stage. It is proved also that the Hamiltonian symmetries can always be presented in the form of canonical transformation for the phase space variables. Manifest form of the resulting generating function is obtained.

Journal ArticleDOI
TL;DR: In this article, the authors investigated a version of the periodic Anderson model in which both the d- and f-electron subsystems are strongly correlated and derived the thermodynamic properties of the system in the approximation where the width of the conductance band vanishes.
Abstract: We investigate a version of the periodic Anderson model in which both the d- and f-electron subsystems are strongly correlated. The one-site hybridization of the electron quantum states in each subsystem and the possibility of the d-electron hopping between lattice sites are taken into account. To construct the canonical transformation S-matrix, we use the system of one-site orthonormalized functions belonging to the zero Hamiltonian matrix of rank 16. We solve the problem exactly and determine the thermodynamic properties of the system in the approximation where the width of the conductance band vanishes. We use the diagram technique to investigate the delocalization of electrons in each subsystem and the renormalization of the one-particle Green's functions. We find the quasiparticle energy spectrum of delocalized electrons in the chain diagram approximation. We show that there are eight energy subbands in the symmetrical case.

Journal ArticleDOI
TL;DR: In this paper, the analogues of u and v$ performing Bogoliubov transformation are derived in the case of anisotropic multiband superconductors, where n is a number of bands relevant to superconducting pairing.
Abstract: Equations for the analogues of u and $v$ performing Bogoliubov transformation are derived in the case of anisotropic multiband superconductors. They are now represented by $n\ifmmode\times\else\texttimes\fi{}n$ matrices, where n is a number of bands relevant to superconducting pairing. We demonstrate that minimization of the ground-state energy does not fix all the parameters of canonical transformation at low temperatures, and thus additional minimization of the free energy due to the excited states is required.

Posted Content
TL;DR: In this article, an integro-differential equation model for pulse propagation in optical transmission lines with dispersion management, is shown to be integrable at the leading nonlinear order.
Abstract: We show that an integro-differential equation model for pulse propagation in optical transmission lines with dispersion management, is integrable at the {\it leading nonlinear order}. This equation can be transformed into the nonlinear Schroedinger equation by a near-identity canonical transformation for the case of weak dispersion. We also derive the next order (nonintegrable) correction.

Journal ArticleDOI
TL;DR: In this paper, a canonical transformation is performed on the phase space to simplify the scalar constraint, and the quantization program for this model has been developed using the standard general procedure by Ashtekar and co-workers.
Abstract: In this paper, we consider Kantowski-Sachs (ks)minisuperspace model with a minimally coupled masslessscalar field. A canonical transformation is performed onthe phase space to simplify the scalar constraint.Then the quantization programme for this modelhas been developed using the standard general procedureby Ashtekar and co-workers. Finally, the wave functionfor this model has been evaluated in the pathintegral formalism.

Journal ArticleDOI
TL;DR: In this paper, a canonical transformation is introduced to dress a driven three-level system and the non-decaying state is investigated as spontaneous emission to a fourth level is included.

Journal ArticleDOI
TL;DR: In this article, a one-dimensional hydrogen molecular ion under the Born-Oppenheimer approximation was studied and the quantum Schrodinger equation was solved analytically and the electronic energy curves showed that the bound states of this 1D model differ from the 2D and 3D H-2(+).
Abstract: We present a study on a one-dimensional hydrogen molecular ion under the Born-Oppenheimer approximation. A canonical transformation produces the classical system directly to be a pendulum. The quantum Schrodinger equation is solved analytically and the electronic energy curves show that the bound states of this 1D model differ from the 2D and 3D H-2(+). The vibration spectroscopy is also obtained by employing the Morse's eigen wavefunctions as basis vectors to diagonalize the Hamiltonian for R. The semiclassical quantization yields electronic energies in agreement with the quantum ones reasonably.

Journal ArticleDOI
TL;DR: In this paper, the authors introduce a new localization principle, which is a generalized canonical transformation, which unifies BRST localization, the non-Abelian localization principle and a special case of the conformal Duistermaat-Heckman integration formula of Paniak, Semenoff, and Szabo.
Abstract: We introduce a new localization principle, which is a generalized canonical transformation. It unifies BRST localization, the non-Abelian localization principle and a special case of the conformal Duistermaat–Heckman integration formula of Paniak, Semenoff, and Szabo. The heat kernel on compact Lie groups is localized in two ways. First, using a non-Abelian generalization of the derivative expansion localization of Palo and Niemi and second, using the BRST localization principle and a configuration space path integral. In addition, we present some new formulas on homogeneous spaces, which might be useful in a possible localization of Selberg’s trace formula on locally homogeneous spaces.

Journal ArticleDOI
TL;DR: In this paper, the translational Chern-Simons term is used as a generating function for a chiral reformulation of simple (N=1) supergravity, and the resulting canonical transformation induces not only decomposition of the gravitational fields into selfdual and antiselfdual modes, but also a splitting of the Rarita-Schwinger fields into their chiral parts in a natural way.
Abstract: Similarily as in the Ashtekar approach, the translational Chern-Simons term is, as a generating function, instrumental for a chiral reformulation of simple (N=1) supergravity. After applying the algebraic Cartan relation between spin and torsion, the resulting canonical transformation induces not only decomposition of the gravitational fields into selfdual and antiselfdual modes, but also a splitting of the Rarita-Schwinger fields into their chiral parts in a natural way. In some detail, we also analyze the consequences for axial and chiral anomalies.