Related papers: Dynamical inverse problem of representation theory…
A quantum version of the action principle in a simple covariant dynamical theory of two relativistic particles is formulated. The central object of this new formulation of quantum theory is a stationary eigenvalue of the quantum action.…
We consider quantum phase-space dynamics using Wigner's representation of quantum mechanics. We stress the usefulness of the integral form for the description of Wigner's phase-space current~$\bm J$ as an alternative to the popular Moyal…
Einstein's special theory of relativity starts with assumptions about how observations conducted in relatively moving inertial frames must compare. From these assumptions, conclusions can be drawn regarding the laws of physics in any one…
This is a brief overview of our work on the theory of group invariant solutions to differential equations. The motivations and applications of this work stem from problems in differential geometry and relativistic field theory. The key…
In this work we present the formal background used to develop the methods used in earlier works to extend the truncated Wigner representation of quantum and atom optics in order to address multi-time problems. The truncated Wigner…
Based on an identified quantum relativity symmetry the contraction of which gives the Newtonian approximation of Galilean relativity, a quantum model of the physical space can be formulated with the Newtonian space seen in a way as the…
We discuss new approaches to fundamental problems of mathematics and mathematical physics such as mathematical foundation of quantum field theory, the Riemann hypothesis, and construction of noncommutative algebraic geometry.
The use of the Wigner function for the study of quantum transport in open systems present severe criticisms. Some of the problems arise from the assumption of infinite coherence length of the electron dynamics outside the system of…
We apply Lie algebra deformation theory to the problem of identifying the stable form of the quantum relativistic kinematical algebra. As a warm up, given Galileo's conception of spacetime as input, some modest computer code we wrote zeroes…
The paper derived differential equations which solve the problem of restoration the motion parameters for a rigid reference frame from the known proper acceleration and angular velocity of its origin as functions of proper time. These…
In gauge theories, physical histories are represented by space-time connections modulo gauge transformations. The space of histories is thus intrinsically non-linear. The standard framework of constructive quantum field theory has to be…
We present a unified approach to representations of quantum mechanics on noncommutative spaces with general constant commutators of phase-space variables. We find two phases and duality relations among them in arbitrary dimensions.…
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…
A sketch is given of a circle of ideas relating quantum field theories with representation theory. The main mathematical ingredients are spinor geometry and the gauge group equivariant K-theory of the space of connections.
A central feature of quantum mechanics is the non-commutativity of operators used to describe physical observables. In this article, we present a critical analysis on the role of non-commutativity in quantum theory, focusing on its…
Following de Broglie and Vigier, a fully relativistic causal interpretation of quantum mechanics is given within the context of a geometric theory of gravitation and electromagnetism. While the geometric model shares the essential…
The Bertrand's theorem can be formulated as the solution of an inverse problem for a classical unidimensional motion. We show that the solutions of these problems, if restricted to a given class, can be obtained by solving a numerical…
With approaching quantum/noncommutative models for the deep microscopic spacetime in mind, and inspired by our recent picture of the (projective) Hilbert space as the model of physical space behind basic quantum mechanics, we reformulate…
Wigner's theorem asserts that an isometric (probability conserving) transformation on a quantum state space must be generated by a Hamiltonian that is Hermitian. It is shown that when the Hermiticity condition on the Hamiltonian is relaxed,…
In this talk I shall first make some brief remarks on quaternionic quantum mechanics, and then describe recent work with A.C. Millard in which we show that standard complex quantum field theory can arise as the statistical mechanics of an…