Canonical transformation

About: Canonical transformation is a research topic. Over the lifetime, 1854 publications have been published within this topic receiving 38019 citations.

Massless Spinning Particles in All Dimensions and Novel Magnetic Monopoles

Abstract: There is a well-known description of a massless particle with spin in four dimensions in terms of position and momentum operators. The charge-monopole system can be obtained therefrom by a simple canonical transformation and a suitable choice of the Hamiltonian. In this paper, we generalize this description of a massless spinning particle to higher dimensions and then use the aforementioned transformation to define novel charge-monopole systems which are non-Abelian generalizations of the Abelian system of Dirac. The Lagrangian description of all these systems and their canonical quantization are also discussed. The analysis reveals the existence of symplectic structures which are likely to be original in the context of particle physics and which incidentally are capable of generalization to string theories. It further gives rise to new monopole fields which may be of use in the context of dimensional compactification.

Quantization of systems with time-dependent constraints. Example of a relativistic particle in a plane wave

Abstract: A modification of the canonical quantization procedure for systems with time-dependent second-class constraints is discussed and applied to the quantization of a relativistic particle in a plane wave. The time dependence of constraints appears in the problem in two ways. The Lagrangian depends on time explicitly by origin, and a special time-dependent gauge is used. Two possible approaches to the quantization are demonstrated in this case. One is to solve directly a system of operator equations, proposed by Tyutin and Gitman (1990) as a generalization of Dirac canonical quantization in the non-stationary case, and another is first to find a canonical transformation, which makes it possible to describe the dynamics in the physical sector by means of some effective Hamiltonian. Quantum mechanics in both cases proves to be equivalent to the Klein-Gordon theory of a relativistic particle in a plane wave. The general conditions for unitarity of the dynamics in the physical sector are discussed.

Fourth-order effective Hamiltonian for the Anderson lattice

Abstract: A canonical transformation of the Schrieffer-Wolff type is applied to the periodic Anderson model. The case of infinitely correlated $f$-like orbitals is dealt with, and these are described through standard basis operators, including spin degeneracy only. First- and third-order terms in the mixing parameter are eliminated. The resulting Hamiltonian contains terms up to fourth order. These describe several interaction processes including intersite spin and charge correlations, conduction-electron scattering, and excitonic interactions. A detailed analysis of the modified Ruderman-Kittel-Kasuya-Yosida interaction obtained is given. Possible extensions of some of the results to higher orders are discussed. The method provides a way to evaluate the spin and charge susceptibilities of the conduction-electron gas in this model. The possible relevance of these functions to a theory of the phonon spectrum and of magnetic ordering of intermediate-valence systems is mentioned.

Admissible gauges for constrained systems.

Abstract: Gauge-fixing and gaugeless methods for reducing the phase space in generalized Hamiltonian dynamics are compared with the aim to define the class of admissible gauges. In the gaugeless approach, the reduced phase space of a Hamiltonian system with first class constraints is constructed locally, without any gauge fixing, using the following procedure: Abelianization of constraints with a subsequent canonical transformation so that some of the new momenta are equal to the new Abelian constraints. As a result, the corresponding conjugate coordinates are ignorable (nonphysical) while the remaining canonical pairs correspond to the true dynamical variables. This representation of the phase space prompts the definition of the subclass of admissible gauges, canonical gauges, as functions depending only on the ignorable coordinates. A practical method to determine the canonical gauge is proposed. \textcopyright{} 1996 The American Physical Society.