Showing papers on "Canonical transformation published in 1968"
TL;DR: In this article, a class of exact invariants for oscillator systems whose Hamiltonians are H=(1/2e)[p 2 + Ω 2 (t)q 2 ] is given in closed form in terms of a function ρ(t) which satisfies e 2 d 2 ρ/dt 2 + ǫ 2 (T)ρ−ρ −3 = 0.
Abstract: A class of exact invariants for oscillator systems whose Hamiltonians are H=(1/2e)[p 2 +Ω 2 (t)q 2 ] is given in closed form in terms of a function ρ(t) which satisfies e 2 d 2 ρ/dt 2 +Ω 2 (t)ρ−ρ −3 =0 .Each particular solution of the equation for ρ determines an invariant. The invariants are derived by applying an asymptotic theory due to Kruskal to the oscillator system in closed form. As a consequence, the results are more general than the asymptotic treatment, and are even applicable with complex Ω(t) and quantum systems. A generating function is given for a classical canonical transformation to a class of new canonical variables which are so chosen that the new momentum is any particular member of the class of invariants. The new coordinate is, of course, a cyclic variable. The meaning of the invariants is discussed, and the general solution for ρ(t) is given in terms of linearly independent solutions of the equations of motion for the classical oscillator. The general solution for ρ(t) is evaluated for some special cases. Finally, some aspects of the application of the invariants to quantum systems are discussed.
502 citations
TL;DR: In this article, a contraction on the Poincare group is performed, which leads to a group isomorphic to the poincare groups, and the authors show that this iso-Poincare Group describes the kinematics of a system of particles all with νz = 1.
42 citations
TL;DR: In this article, canonical Lagrangian representations of Sugawara's theory of currents are presented, which resemble phenomenological Lagrangians. But they do not have the same properties.
Abstract: We present canonical Lagrangian representations of Sugawara's theory of currents. Although there are some important differences, these Lagrangians resemble currently discussed phenomenological Lagrangians.
22 citations
TL;DR: In this paper, a canonical transformation which takes into account both pair correlations and the singleparticle condensate is made on the full Hamiltonian for a system of interacting bosons, and the quasi-particle interactions are neglected.
21 citations
17 citations
TL;DR: In this article, Souriau's space fiber quantifiant is shown under certain conditions to be realized in contact structure, and illustrative examples of contact structures are examined, and different geometric concepts in canonical quantization are discussed.
Abstract: Differential geometric concepts in canonical quantization are discussed. Souriau'sespace fibre quantifiant is shown under certain conditions to be realized in contact structure. Illustrative examples of contact structures are examined.
15 citations
01 Jan 1968
TL;DR: In this paper, the authors discuss the connection of the variational technique with other methods in the many-body problem, in particular with the thermal Hartree-Fock approximation, the method of canonical transformations, and the description of many-particle systems in terms of quasi-particles.
Abstract: During recent years, variational methods have become an increasingly popular tool in quantum-mechanical many-particle theory. It is the purpose of this chapter to present some of the general principles which form the mathematical background to this approach, and to discuss the connection of the variational technique with other methods in the many-body problem, in particular with the thermal Hartree-Fock approximation, the method of canonical transformations, and the description of many-particle systems in terms of quasi-particles.
11 citations
9 citations
TL;DR: The principle of compensation of dangerous diagrams (PCDD) was proposed by Bogoliubov to determine the coefficients in his canonical transformation in boson systems is obtained from four criteria: (1) the number of quasiparticles in the true ground state is a minimum; (2) the ''best'' approximation to the true density matrix and pair amplitude is made; (3) the expectation value of an arbitrary operator is diagonalized up to terms cubic in the qasiparticle operators; (4) the most convenient starting point for dressing the quaiparticles is
Abstract: The principle of compensation of dangerous diagrams (PCDD) postulated by Bogoliubov to determine the coefficients in his canonical transformation in boson systems is obtained from four criteria: (1) the number of quasiparticles in the true ground state is a minimum; (2) the ``best'' approximation to the true density matrix and pair amplitude is made; (3) the expectation value of an arbitrary operator is diagonalized up to terms cubic in the quasiparticle operators; (4) the most convenient starting point for dressing the quasiparticles is used. Quasiparticle Green's functions are introduced to obtain a diagrammatic expansion of the PCDD. The reducibility of the diagrams is also discussed.
4 citations
01 Mar 1968
TL;DR: In this article, the authors proposed a canonical transformation method to eliminate short period terms from Hamiltonian by means of canonical transformation, which they called canonical transformation of short period term elimination.
Abstract: Methods of eliminating short period terms from Hamiltonian by means of canonical transformation
3 citations
TL;DR: In this article, a simple and direct derivation of the properties of canonical transformations is given, starting from their fundamental property of leaving Hamilton's equations unaltered, and no appeal is made to the calculus of variations, and none but the most elementary calculus is used.
Abstract: A simple and direct derivation of the properties of canonical transformations is given, starting from their fundamental property of leaving Hamilton's equations unaltered. No appeal is made to the calculus of variations, and none but the most elementary calculus is used.
01 Nov 1968
TL;DR: Canonical transformation to investigate rotational motion of uniaxial orbiting rigid body influenced by gravity gradient torque was proposed in this paper, where the rotation of the rigid body was investigated.
Abstract: Canonical transformation to investigate rotational motion of uniaxial orbiting rigid body influenced by gravity gradient torque
TL;DR: In this paper, a simple recursion formula is introduced for the derivation of the canonical transformation in classical mechanics in the form of a power series in t, where the transformation relates a variable at the time t with its initial value given at t = 0.
Abstract: A simple recursion formula is introduced for the derivation of the generating function of the canonical transformation in classical mechanics in the form of a power series in t, where the transformation relates a variable at the time t with its initial value given at t = 0. A discussion is given of the relationship of this approach to the Hamilton-Jacobi differential equation, with emphasis on the comparison of the formal aspects of classical and quantum mechanics.
TL;DR: In this paper, it was shown that in the Froissart model describing dipole ghosts, the canonical formalism and definition of the vacuum state are not sufficient to determine the field operator uniquely.
Abstract: It is shown that in the Froissart model describing dipole ghosts, the canonical formalism (i.e., field equations+canonical commutation relations) and definition of the vacuum state are not sufficient to determine the field operator uniquely. The meaning of additional parameters describing different operator solutions of Froissart's set of field equations and canonical commutation relations is explained.
TL;DR: Canonical transformations which transform the nuclear two-body potential into the hermitian Brueckner matrix have been discussed in this article, where induced many-body forces and the influence of localized Bethe-Goldstone states are investigated.
Abstract: Canonical transformations are discussed which transform the nuclear two-body potential into the hermitian Brueckner matrix. Some of the properties of such transformations — induced many-body forces and the influence of localized Bethe-Goldstone states — are investigated.