Showing papers on "Canonical transformation published in 1979"
01 Jan 1979
133 citations
TL;DR: In this paper, a canonical transformation is presented in order to diagonalize the radiation hamiltonian in the rotating wave approximation, and Dressing of atomic operators in the single and multi-atom cases is obtained explicitly and qualitatively discussed in connection with the problem of resonance fluorescence.
54 citations
TL;DR: In this paper, the authors show that the canonical transformations are nonlinear and non-bijective, and they recover the one-to-one correspondence between the arbitrariness in the phase of the representation and the choice of the variable conjugate to the action.
31 citations
TL;DR: In this paper, a canonical treatment of the damped harmonic oscillator is presented, where the Hamiltonian is made simpler by means of a suitable canonical transformation and the ensuing equations of motion for the transformed canonical variables are then solved by the Hamilton-Jacobi method.
Abstract: We present a canonical treatment of the damped harmonic oscillator. The Hamiltonian is made simpler by means of a suitable canonical transformation. The ensuing equations of motion for the transformed canonical variables are then solved by the Hamilton‐Jacobi method.
30 citations
TL;DR: In this article, it is shown that it is not sufficient for the Hamiltonian to merely generate the motion, but it must also be necessarily related via a canonical transformation to the total energy of the system.
Abstract: It is well known that to quantize any dynamical system it is necessary for a generator of the classical motion to exist in the form of a Hamiltonian function. It is shown, by using the example of a damped harmonic oscillator, that a particular class of inequivalent classical Hamiltonians exist which make quantization of the system ambiguous. Hence it is conclued that it is not sufficient for the Hamiltonian to merely generate the motion, but it must also be necessarily related via a canonical transformation to the total energy of the system.
29 citations
TL;DR: In this article, a representation on Hilbert space of canonical transformations to action and angle variables is given for a wide class of one-dimensional periodic motions, which extends the results discussed previously for the harmonic oscillator to problems not solvable in closed form.
Abstract: A representation on Hilbert space of canonical transformations to action and angle variables is given for a wide class of one-dimensional periodic motions. This extends the results discussed previously for the harmonic oscillator to problems not solvable in closed form. The concepts of ambiguity group and ambiguity spin continue to play a key role.
10 citations
TL;DR: In this paper, an algebraic method is presented for canonically transforming the Hamiltonians quadratic in coordinate and momentum operators into the Hamiltonian of non-interacting harmonic oscillators.
Abstract: An algebraic (matrix) method is presented for canonically transforming the Hamiltonians quadratic in coordinate and momentum operators into the Hamiltonian of non-interacting harmonic oscillators. The method is illustrated by transforming the Hamiltonian of a harmonic oscillator in a constant magnetic field into the Hamiltonian of the two-dimensional, in general anisotropic, harmonic oscillator. The results are found to be in agreement with those obtained previously for the same Hamiltonian using a different technique.
8 citations
TL;DR: In this article, the antiferromagnetic ground state and the electron-hole excitation energy gap of the conventional Hubbard model were transferred to describe the charge-ordered ground state.
Abstract: With a canonical transformation, the antiferromagnetic ground state and the electron-hole excitation energy gap of the conventional Hubbard model are transferred to describe the charge-ordered ground state and the similar excitation energy of a half-filled Hubbard model with negative $U$. The band-structure effect is also considered.
4 citations
TL;DR: In this article, the first variational equations of motion about the triangular points in the elliptic restricted problem are investigated by the perturbation theories of Hori and Deprit, which are based on Lie transforms.
Abstract: In this paper the first variational equations of motion about the triangular points in the elliptic restricted problem are investigated by the perturbation theories of Hori and Deprit, which are based on Lie transforms, and by taking the mean equations used by Grebenikov as our upperturbed Hamiltonian system instead of the first variational equations in the circular restricted problem. We are able to remove the explicit dependence of transformed Hamiltonian on the true anomaly by a canonical transformation. The general solution of the equations of motion which are derived from the transformed Hamiltonian including all the constant terms of any order in eccentricity and up to the periodic terms of second order in eccentricity of the primaries is given.
4 citations
TL;DR: In this article, the semi-classical correspondence relations derived from Moshinsky's equations for the exact unitary representation of an arbitrary canonical transformation are shown to be exact in the case of a linear canonical transformation.
Abstract: The semi-classical correspondence relations are derived from Moshinsky's equations for the exact unitary representation of an arbitrary canonical transformation. The correspondence relations are shown to be exact in the case of a linear canonical transformation.
4 citations
TL;DR: In this article, the electrodynamics of a nonlinear, complex scalar field is developed from the basis of a Hamiltonian formalism, by means of a canonical transformation.
Abstract: The electrodynamics of a nonlinear, complex scalar field is developed from the basis of a Hamiltonian formalism. By means of a canonical transformation, the equations for a stationary state are red...
TL;DR: In this article, it was shown that only linear and point canonical transformations are quantized into quantum canonical transformations, and that this invariance holds only for special classes of phase-space functions.
Abstract: We find that only linear and point canonical transformations are quantized into quantum canonical transformations This result does not depend on the quantization procedure We examine quantization rule invariance under linear and point canonical transformations and show that it holds only for special classes of phase-space functions However, Weyl’s rule (and only this rule) is found to be invariant under linear canonical transformations forall phase-space functions
TL;DR: In this article, the effect of a finite correlation length of the Peierls distortion on optical properties, width and position of the Raman line from the amplitude mode, and Knight shift in linear conductors is described.
Abstract: A model is presented which describes the effect of a finite correlation length of the Peierls distortion on optical properties, width and position of the Raman line from the amplitude mode, and Knight shift in linear conductors. A canonical transformation to amplitude and phase variables is used which generalizes the linear transformation of Lee, Rice and Anderson. The non-linear effects are shown to be essential for the interpretation of experimental data in KCP.
TL;DR: In this article, a quasi-Fock representation of canonical commutation relations (CCR) is studied and sufficient conditions for the invertibility of the linear canonical transformation are proved.
TL;DR: In this article, the authors extended the canonical transformation method of Leach for the quadratic Hamiltonian to deal with nonlinear non-conservative classical systems and showed that the linear time dependent canonical transformations are not adequate to remove the time dependence of any arbitrary time-dependent nonlinear Hamiltonian.
Abstract: The recently proposed time‐dependent canonical transformation method of Leach for the quadratic Hamiltonian has been extended to deal with nonlinear nonconservative classical systems. It is observed that the linear time dependent canonical transformations are not adequate to remove the time dependence of any arbitrary time‐dependent nonlinear Hamiltonian. Alternatively, we propose that such a Hamiltonian may be transformed to a quadratic form by means of successive nonlinear canonical transformations. It is also shown that the canonical method is useful to obtain solutions for differential equations governing certain dissipative classical systems.
TL;DR: In this article, the large-order behavior of perturbative expansion is investigated for a quantum thermodynamic system of interacting bosons in one space dimension, which makes essential use of the classical solutions for the total Hamiltonian and of the oscillations about them.
Abstract: The recently proposed method for investigating the large-order behaviour of the perturbative expansion is applied to a quantum thermodynamical system of interacting bosons in one space dimension. The method makes essential use of the classical solutions for the total Hamiltonian and of the oscillations about them. The contribution of these oscillations is calculated by using a canonical transformation related to the inverse scattering method, the relevant equation being the nonlinear Schrodinger equation. The leading-order corrections to the Bose-Einstein distribution are obtained explicitly.
TL;DR: In this paper, the authors investigated the possibility of bypassing the no-interaction theorem of Currie, Jordan, and Sudarshan for direct action Lagrangians by solving for the field variables in terms of the particle variables, which paves the way to write an action-at-a-distance Hamiltonian.
Abstract: We investigate the possibility of bypassing the no-interaction theorem of Currie, Jordan, and Sudarshan for direct action Lagrangians. Starting with the field-theoretic description of a two-body electrodynamic problem, we solve for the field variables in terms of the particle variables, which paves the way to write an action-at-a-distance Hamiltonian for the problem. A suitable transformation is found which uncouples the field and the particle variables in the interaction up to order e/sup 2/. It is shown that this transformation leaves the statement of Newton's second law unchanged which also agrees with the standard results of electrodynamics. This allows for the identification of canonical variables for the proper action-at-a-distance problem.
TL;DR: In this article, the authors apply the Wang-Hioe procedure and the Power-Zinau-Babiker canonical transformation to determine the thermodynamical properties of systems.
TL;DR: The theory of canonical transformations can be developed without the use of generating functions, and is perhaps to be preferred as this approach is closer to the study of tensor analysis with which most students are familiar.
Abstract: The theory of canonical transformations can be developed without the use of generating functions, and is perhaps to be preferred as this approach is closer to the study of tensor analysis with which most students are familiar. The explicit general condition for a transformation to be canonical is exploited in proving that such transformations have Jacobian +1. As well, invariance properties of certain types of integrals in phase space are proved in a similar manner, all without reference to generating functions.