相关论文: Quantum canonical transformations in Weyl-Wigner-G…
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…
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…
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…
A theory of non-unitary-invertible as well as unitary canonical transformations is formulated in the context of Weyl's phase space representations. That all quantum canonical transformations without an explicit $\hbar$ dependence are also…
The algebra of generalized linear quantum canonical transformations is examined in the prespective of Schwinger's unitary-canonical basis. Formulation of the quantum phase problem within the theory of quantum canonical transformations and…
The knowledge of quantum phase flow induced under the Weyl's association rule by the evolution of Heisenberg operators of canonical coordinates and momenta allows to find the evolution of symbols of generic Heisenberg operators. The quantum…
A theory of nonunitary-invertible as well as unitary canonical transformations is formulated in the context of Weyl's phase space representations. Exact solutions of the transformation kernels and the phase space propagators are given for…
Canonical transformation in a three-dimensional phase space endowed with Nambu bracket is discussed in a general framework. Definition of the canonical transformations is constructed as based on canonoid transformations. It is shown that…
There are different operators of quark and gluon momenta, orbital angular momenta, and gluon spin in the nucleon structure study. The precise meaning of these operators are studied based on gauge invariance, Lorentz covariance and canonical…
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…
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…
In this paper, the generic part of the gauge theory of gravity is derived, based merely on the action principle and on the general principle of relativity. We apply the canonical transformation framework to formulate geometrodynamics as a…
In this tenth paper of the series we aim at showing that our formalism, using the Wigner-Moyal Infinitesimal Transformation together with classical mechanics, endows us with the ways to quantize a system in any coordinate representation we…
We characterize point transformations in quantum mechanics from the mathematical viewpoint. To conclude that the canonical variables given by each point transformation in quantum mechanics correctly describe the extended point…
We consider scalar-tensor theories of gravity defined in Weyl integrable space-time and show that in the ADM formalism Weyl transformations corresponding to change of frames induce canonical transformations between different representations…
Generalised Wigner and Weyl transformations of quantum operators are defined and their properties, as well as those of the algebraic structure induced on the phase-space are studied. Using such transformations, quantum linear evolution…
We review the main features of the Weyl-Wigner formulation of noncommutative quantum mechanics. In particular, we present a $\star$-product and a Moyal bracket suitable for this theory as well as the concept of noncommutative Wigner…
The quantum-to-classical transition is considered from the point of view of contractions of associative algebras. Various methods and ideas to deal with contractions of associative algebras are discussed that account for a large family of…
Four formulations of quantum mechanics on noncommutative Moyal phase spaces are reviewed. These are the canonical, path-integral, Weyl-Wigner and systematic formulations. Although all these formulations represent quantum mechanics on a…
A gauge transformation in quantum electrodynamics involves the product of field operators at the same space-time point and hence does not have a well-defined meaning. One way to avoid this difficulty is to generalize the gauge…