Related papers: Gauss Sums and Quantum Mechanics
In this work we explore the structure of the branching graph of the unitary group using Schur transitions. We find that these transitions suggest a new combinatorial expression for counting paths in the branching graph. This formula, which…
In the language of Feynman path integrals the quantization of gauge theories is most easily carried out with the help of the Schr\"odinger Functional (SF). Within this formalism the essentially unique gauge fixing condition is $A_{\circ} =…
We show how quantum mechanics can be understood as a space-time theory provided that its spatial continuum is modelled by a variable real number (qrumber) continuum. Such a continuum can be constructed using only standard Hilbert space…
The Liouville equation differs from the von Neumann equation 'only' by a characteristic superoperator. We demonstrate this for Hamiltonian dynamics, in general, and for the Jaynes-Cummings model, in particular. -- Employing superspace…
It is first pointed out that there is a common mathematical model for the universe and the quantum computer. The former is called the histories approach to quantum mechanics and the latter is called measurement based quantum computation.…
A reformulation of a physical theory in which measurements at the initial and final moments of time are treated independently is discussed, both on the classical and quantum levels. Methods of the standard quantum mechanics are used to…
We give a review of concepts related to connection of classical and quantum theories, from the phase space perspective. Quantum theory is described by non-commutative operators of coordinates and momenta, results in values having a certain…
I propose a new and direct connection between classical mechanics and quantum mechanics where I derive the quantum mechanical propagator from a variational principle. This variational principle is Hamilton's modified principle generalized…
By using path integrals, the stochastic process associated to the time evolution of the quantum probability density is formally rewritten in terms of a stochastic differential equation, given by Newton's equation of motion with an…
For a general quantum theory that is describable by a path integral formalism, we construct a mathematical model of the universe as a sample point of an accumulative stochastic process. The model give predictions that are nearly identical…
We consider the distribution of the polygonal paths joining partial sums of classical Kloosterman sums, as their parameter varies modulo a prime tending to infinity. Using independence of Kloosterman sheaves, we prove convergence in the…
The theory of quantum mechanics is examined using non-standard real numbers, called quantum real numbers (qr-numbers), that are constructed from standard Hilbert space entities. Our goal is to resolve some of the paradoxical features of the…
We describe the "Feynman diagram" approach to nonrelativistic quantum mechanics on R^n, with magnetic and potential terms. In particular, for each classical path \gamma connecting points q_0 and q_1 in time t, we define a formal power…
We first apply Connes' noncommutative geometry to a finite point space. The explicit form of the action functional of U(1) gauge field on this n-point space is obtained. We then consider the case when the n-point space is replaced by…
We study, from a combinatorial viewpoint, the quantized coordinate ring of mxn matrices over an infinite field K (also called quantum matrices) and its torus-invariant prime ideals. The first part of this paper shows that this algebra,…
The path integral is calculated for the statistical sum of the microcanonical ensemble in a generic time-parametrization invariant gravitational model with the Friedman-Robertson-Walker (FRW) metric. This represents the first example of a…
In this paper the Feynman path integral technique is applied to two-dimensional spaces of non-constant curvature: these spaces are called Darboux spaces $\DI$--$\DIV$. We start each consideration in terms of the metric and then analyze the…
The additivity of classical probabilities is only the first in a hierarchy of possible sum-rules, each of which implies its successor. The first and most restrictive sum-rule of the hierarchy yields measure-theory in the Kolmogorov sense,…
Feynman path integrals formalism for non-relativistic quantum mechanics is revisited. A comparison is made with the cases of light progagation (Huygens principle) and Brownian motion. The difficulties for a physical model behind Feynman…
We discuss path integrals for quantum mechanics with a potential which is a perturbation of the upside-down oscillator. We express the path integral (in the real time) by the Wiener measure. We obtain the Feynman integral for perturbations…