相关论文: Quantum Canonical Transformations revisited

This paper is a generalization of previous work on the use of classical canonical transformations to evaluate Hamiltonian path integrals for quantum mechanical systems. Relevant aspects of the Hamiltonian path integral and its measure are…

This paper presents the general theory of canonical transformations of coordinates in quantum mechanics. First, the theory is developed in the formalism of phase space quantum mechanics. It is shown that by transforming a star-product, when…

We discuss the deformation quantization approach for the teaching of quantum mechanics. This approach has certain conceptual advantages which make its consideration worthwhile. In particular, it sheds new light on the relation between…

The functional integral has many triumphs in elucidating quantum theory. But incorporating charge fractionalization into that formalism remains a challenge.

Quantum canonical transformations are defined in analogy to classical canonical transformations as changes of the phase space variables which preserve the Dirac bracket structure. In themselves, they are neither unitary nor non-unitary. A…

We present a new approach for numerical solutions of ab initio quantum chemistry systems. The main idea of the approach, which we call canonical diagonalization, is to diagonalize directly the second quantized Hamiltonian by a sequence of…

Ambiguities arising in different approaches (canonical, quasiclassical, path integration) to quantization are discussed by an example of the mechanics of a point-like particle in the Riemannian space (the geodesic dynamics). A way to select…

We give here a covariant definition of the path integral formalism for the Lagrangian, which leaves a freedom to choose anyone of many possible quantum systems that correspond to the same classical limit without adding new potential terms…

The canonical quantization of the topological particle is described; it is shown that BRST quantization of the model gives the supersymmetric quantum mechanical model considered by Witten when investigating Morse theory, and the rigorous…

The path integral formulation of constrained systems leads to obtain the equations of motion as total differential equations in many variables. If these equations are integrable then one can constuct a valid and a canonical phase space…

Two quantum theories are physically equivalent if they are related, not by a unitary transformation, but by an isometric transformation. The conditions under which a quantum canonical transformation is an isometric transformation are given.

We propose a new way to perform path integrals in quantum mechanics by using a quantum version of Hamilton-Jacobi theory. In classical mechanics, Hamilton-Jacobi theory is a powerful formalism, however, its utility is not explored in…

Three elementary canonical transformations are shown both to have quantum implementations as finite transformations and to generate, classically and infinitesimally, the full canonical algebra. A general canonical transformation can, in…

Canonical transformations using the idea of quantum generating functions are applied to construct a quantum Hamilton-Jacobi theory, based on the analogy with the classical case. An operator and a c-number forms of the time-dependent quantum…

Any particular classical system and its quantum version are normally viewed as separate formulations that are strictly distinct. Our goal is to overcome the two separate languages and create a smooth and common procedure that provides a…

In this paper we review a proposed geometrical formulation of quantum mechanics. We argue that this geometrization makes available mathematical methods from classical mechanics to the quantum frame work. We apply this formulation to the…

The aim of the article is to show how a coordinate transformation can be applied to the path-integral formalism. For this purpose the unitary definition of the quantum measure, which guarantees the conservation of total probability, is…

It is often said that in relativistic quantum physics, a fundamental particle ontology is not viable. However, previous works have shown that certain relativistic quantum field theories can be reformulated as path integrals over particle…

Quantum canonical transformations are defined algebraically outside of a Hilbert space context. This generalizes the quantum canonical transformations of Weyl and Dirac to include non-unitary transformations. The importance of non-unitary…

Different approaches are compared to formulation of quantum mechanics of a particle on the curved spaces. At first, the canonical, quasi-classical and path integration formalisms are considered for quantization of geodesic motion on the…