Related papers: Classical Fermionic Dynamics
A summary of a recently proposed description of quantum-classical hybrids is presented, which concerns quantum and classical degrees of freedom of a composite object that interact directly with each other. This is based on notions of…
A canonical formulation of coupled classical-quantum dynamics is presented. The theory is named symmetric hybrid dynamics. It is proved that under some general conditions its predictions are consistent with the full quantum ones. Moreover…
Geometrical formulation of classical mechanics with forces that are not necessarily potential-generated is presented. It is shown that a natural geometrical "playground" for a mechanical system of point particles lacking Lagrangian and/or…
Classical limits of quantum systems are shown to lead to different conceptions of spaces different from the classical one underlying the process of quantization of such systems. The accent is put in situations where traces of…
Some of the important non-classical aspects of quantum mechanics can be described in more intuitive terms if they are reformulated in a geometrical picture based on an extension of the classical phase space. This contribution presents…
The paper develop the alternative formulation of quantum mechanics known as the phase space quantum mechanics or deformation quantization. It is shown that the quantization naturally arises as an appropriate deformation of the classical…
The investigation of quantum-classical correspondence may lead to gain a deeper understanding of the classical limit of quantum theory. We develop a quantum formalism on the basis of a linear-invariant theorem, which gives an exact…
Connecting ideas of geometric formulation of quantum mechanics with new results in symplectic geometry a new approach to geometrical quantization procedure is proposed. As a first result we verify that the correspondence between "classical"…
The representation of a Schrodinger equations as a classic Hamiltonian system allows to construct a unified perturbation theory both in classic, and in a quantum mechanics grounded on the theory of canonical transformations, and also to…
We present the full Hamiltonian analysis of electrodynamics, including fermions, photons, and their interaction, on a general curved spacetime in Ashtekar-Barbero variables. Only the time gauge is imposed and the theory is background…
Bosonic quantum conversion systems can be modeled by many-particle single-mode Hamiltonians describing a conversion of $n$ molecules of type A into $m$ molecules of type B and vice versa. These Hamiltonians are analyzed in terms of…
As a preparation for its quantization in the loop formalism, the 2-dimensional gravitation model of Jackiw and Teitelboim is analysed in the classical canonical formalism. The dynamics is of pure constraints as it is well-known. A partial…
We have previously shown how to construct a deformation quantization of any locally compact space on which a vector group acts. Within this framework we show here that, for a natural class of Hamiltonians, the quantum evolutions will have…
All classical Lie algebras can be realized \`a la Schwinger in terms of fermionic oscillators. We show that the same can be done for their $q$-deformed counterparts by simply replacing the fermionic oscillators with anyonic ones defined on…
By a quantum version of the Arnold transformation of classical mechanics, all quantum dynamical systems whose classical equations of motion are non-homogeneous linear second-order ordinary differential equations, including systems with…
We investigate the possibility that the semiclassical limit of quantum mechanics might be correctly described by a classical dynamical theory, other than standard classical mechanics. Using a set of classicality criteria proposed in a…
A carefully motivated symmetric variant of the Poisson bracket in ordinary (not Grassmann) phase space variables is shown to satisfy identities which are in algebraic correspondence with the anticommutation postulates for quantized Fermion…
The physical variables of classical thermodynamics occur in conjugate pairs such as pressure/volume, entropy/temperature, chemical potential/particle number. Nevertheless, and unlike in classical mechanics, there are an odd number of such…
We introduce a symmetric Poisson bracket that allows us to describe anticommuting fields on a classical level in the same way as commuting fields, without the use of Grassmann variables. By means of a simple example, we show how the Dirac…
A formalism for studying the dynamics of quantum systems embedded in classical spin baths is introduced. The theory is based on generalized antisymmetric brackets and predicts the presence of open-path off-diagonal geometric phases in the…