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First a set of coherent states a la Klauder is formally constructed for the Coulomb problem in a curved space of constant curvature. Then the flat-space limit is taken to reduce the set for the radial Coulomb problem to a set of hydrogen…

Quantum Physics · Physics 2009-11-10 Myo Thaik , Akira Inomata

We extend the Euler-Bernoulli beam problem, formulated as a matrix string equation with a matrix-valued density, to a setting where the density takes values in a Clifford algebra, and we analyze its isospectral deformations. For discrete…

Exactly Solvable and Integrable Systems · Physics 2025-09-19 Richard Beals , Jacek Szmigielski

This paper discusses the canonical quantization of 1+1-dimensional Yang-Mills theory on a spacetime cylinder, from the point of view of coherent states, or equivalently, the Segal-Bargmann transform. Before gauge symmetry is imposed, the…

Quantum Physics · Physics 2009-11-06 Brian C. Hall

We study the evolution of time-like congruences in the vacuum solutions of Weyl conformal theory of gravity. Using the Raycaudhuri equation, we show that for positive values of the coeffcient of the linear term in the solution and in the…

General Relativity and Quantum Cosmology · Physics 2016-02-03 Morteza Mohseni , Mohsen Fathi

We study conformal properties of the quantum kinetic equations in curved spacetime. A transformation law for the covariant Wigner function under conformal transformations of a spacetime is derived by using the formalism of tangent bundles.…

General Relativity and Quantum Cosmology · Physics 2010-04-06 Oleg A. Fonarev

In this paper we show how to describe the general theory of a linear metric compatible connection with the theory of Clifford valued differential forms. This is done by realizing that for each spacetime point the algebra of Clifford…

Mathematical Physics · Physics 2007-05-23 E. Capelas de Oliveira , W. A. Rodrigues

A new 8-dim conformal gauging solves the auxiliary field problem and eliminates unphysical size change from Weyl's electromagnetic theory. We derive the Maurer-Cartan structure equations and find the zero curvature solutions for the…

High Energy Physics - Theory · Physics 2009-10-30 James T. Wheeler

In this paper we work in the `split' discrete Clifford analysis setting, i.e. the m-dimensional function theory concerning null-functions, defined on the grid Z^m, of the discrete Dirac operator D, involving both forward and backward…

Representation Theory · Mathematics 2017-01-27 Hilde De Ridder , Tim Raeymaekers

In this work we present a derivation of Dirac's equation in a curved space-time starting from a Weyl-invariant action principle in 4+K dimensions. The Weyl invariance of Dirac's equation (and of Quantum Mechanics in general) is made…

Quantum Physics · Physics 2021-03-10 Enrico Santamato , Francesco De Martini

We find the local form of all non-closed Lorentzian Weyl manifolds $(M,c,\nabla)$ with recurrent curvature tensor.If the dimension of the manifold is greater than 3, then the conformal structure is flat, and the recurrent Weyl structure is…

Differential Geometry · Mathematics 2024-08-15 Andrei Dikarev , Anton S. Galaev , Eivind Schneider

We investigate the space ${\cal M}$ of classical solutions to Witten's formulation of 2+1 gravity on the manifold ${\bf R} \times T^2$. ${\cal M}$ is connected, unlike the spaces of classical solutions in the cases where $T^2$ is replaced…

General Relativity and Quantum Cosmology · Physics 2010-04-06 Jorma Louko , Donald M. Marolf

We construct a family of coherent states transforms attached to generalized Bargmann spaces [C.R. Acad.Sci.Paris, t.325,1997] in the complex plane. This constitutes another way of obtaining the kernel of an isometric operator linking the…

Mathematical Physics · Physics 2010-03-30 Zouhair Mouayn

A classical theorem of Stone and von Neumann says that the Schr\"{o}dinger representation is, up to unitary equivalences, the only irreducible representation of the Heisenberg group on the Hilbert space of square-integrable functions on…

Mathematical Physics · Physics 2009-11-11 Maurice A. De Gosson

We extend constructions of classical Clifford analysis to the case of indefinite non-degenerate quadratic forms. Clifford analogues of complex holomorphic functions - called monogenic functions - are defined by means of the Dirac operators…

Complex Variables · Mathematics 2024-04-03 Chen Liang , Matvei Libine

The Heisenberg-Weyl group $HW(d)$ related to a $d$-dimensional Hilbert space $H(d)$, is enlarged into the Heisenberg-Weyl-parity group $HWP(d)$ that incorporates parity transformations. It consists of $2d^3$ elements, of which $d^3$…

Quantum Physics · Physics 2026-05-15 A. Vourdas

For the models of $N$-body identical harmonic oscillators interacting through potentials of homogeneous degree -2, the unitary operator that transforms a system of time-dependent parameters into that of unit spring constant and unit mass of…

Quantum Physics · Physics 2007-05-23 Dae-Yup Song

Exploring the concept of the extended Galilei group $\mathcal{G}$, a representation for the symplectic quantum mechanics in the manifold of $\mathcal{G}$, written in the light-cone of a five-dimensional De Sitter space-time, is derived…

High Energy Physics - Theory · Physics 2019-10-03 Gustavo Xavier Antunes Petronilo , Sergio Costa Ulhoa , Ademir Eugenio Santana

The Segal-Bargmann transform is a Lie algebra and Hilbert space isomorphism between real and complex representations of the oscillator algebra. The Segal-Bargmann transform is useful in time-frequency analysis as it is closely related to…

Functional Analysis · Mathematics 2022-07-15 Cameron L. Williams

The Weyl-gauge ($A_0^a=0)$ QCD Hamiltonian is unitarily transformed to a representation in which it is expressed entirely in terms of gauge-invariant quark and gluon fields. In a subspace of gauge-invariant states we have constructed that…

High Energy Physics - Phenomenology · Physics 2009-11-07 Kurt Haller , Hai-cang Ren

We construct a representation of the coherent state path integral using the Weyl symbol of the Hamiltonian operator. This representation is very different from the usual path integral forms suggested by Klauder and Skagerstan in…

Quantum Physics · Physics 2009-11-13 L. C. dos Santos , M. A. M. de Aguiar