Related papers: Fractional Fourier Transform and Geometric Quantiz…
In this second in a series of four articles we create a mathematical formalism sufficient to represent nontrivial hamiltonian quantum dynamics, including resonances. Some parts of this construction are also mathematically necessary. The…
The canonical quantum theory of a free field using arbitrary foliations of a flat two-dimensional spacetime is investigated. It is shown that dynamical evolution along arbitrary spacelike foliations is unitarily implemented on the same Fock…
Quantum mechanics is among the most important and successful mathematical model for describing our physical reality. The traditional formulation of quantum mechanics is linear and algebraic. In contrast classical mechanics is a geometrical…
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 phase space of quantum mechanics can be viewed as the complex projective space endowed with a Kaehlerian structure given by the Fubini-Study metric and an associated symplectic form. We can then interpret the Schrodinger equation as…
The kinematical foundations of Schwinger's algebra of selective measurements were discussed in a previous paper (arXiv:1905.12274) and, as a consequence of this, a new picture of quantum mechanics based on groupoids was proposed. In this…
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…
We consider the space of probabilities {P(x)}, where the x are coordinates of a configuration space. Under the action of the translation group there is a natural metric over the space of parameters of the group given by the Fisher-Rao…
We study Fourier theory on quantum Euclidean space. A modified version of the general definition of the Fourier transform on a quantum space is used and its inverse is constructed. The Fourier transforms can be defined by their Bochner's…
In this paper and a companion paper, we show how the framework of information geometry, a geometry of discrete probability distributions, can form the basis of a derivation of the quantum formalism. The derivation rests upon a few…
In quantum mechanics, the momentum space and position space wave functions are related by the Fourier transform. We investigate how the Fourier transform arises in the context of geometric quantization. We consider a Hilbert space bundle H…
We have previously presented a version of the Weak Equivalence Principle for a quantum particle as an exact analog of the classical case, based on the Heisenberg picture analysis of free particle motion. Here, we take that to a full…
In physics, experiments ultimately inform us as to what constitutes a good theoretical model of any physical concept: physical space should be no exception. The best picture of physical space in Newtonian physics is given by the…
Within the Hamiltonian framework, the propositions about a classical physical system are described in the Borel {\sigma}-algebra of a symplectic manifold (the phase space) where logical connectives are the standard set operations.…
This paper studies the nature of fractional linear transformations in a general relativity context as well as in a quantum theoretical framework. Two features are found to deserve special attention: the first is the possibility of…
Geometric quantization is an attempt at using the differential-geometric ingredients of classical phase spaces regarded as symplectic manifolds in order to define a corresponding quantum theory. Generally, the process of geometric…
The aim of this paper is to introduce and analyze a new gauge symmetry that appears in complex holomorphic systems. This symmetry allow us to project the system, using different gauge conditions, to several real systems which are connect by…
Familiar textbook quantum mechanics assumes a fixed background spacetime to define states on spacelike surfaces and their unitary evolution between them. Quantum theory has changed as our conceptions of space and time have evolved. But…
Quantum mechanics in its presently known formulation requires an external classical time for its description. A classical spacetime manifold and a classical spacetime metric are produced by classical matter fields. In the absence of such…
In this paper, we investigate the connection between Classical and Quantum Mechanics by dividing Quantum Theory in two parts: - General Quantum Axiomatics (a system is described by a state in a Hilbert space, observables are self-adjoint…