Related papers: A Quantum Mechanical Example for Hodge Theory
We study the phase space structure and the quantization of a pointlike particle in 2+1 dimensional gravity. By adding boundary terms to the first order Einstein Hilbert action, and removing all redundant gauge degrees of freedom, we arrive…
We analyze the partition function of three-dimensional quantum gravity on the twisted solid tours and the ensuing dual field theory. The setting is that of a non-perturbative model of three dimensional quantum gravity--the Ponzano-Regge…
Quantum mechanics is formulated on a Hilbert space that is assumed to be separable. However, there seems to be no clear reason justifying this assumption. Does it have physical implications? We answer in the positive by proposing a test…
This article reports on the confluence of two streams of research, one emanating from the fields of numerical analysis and scientific computation, the other from topology and geometry. In it we consider the numerical discretization of…
On the basis of the results of some experiments dealing with the violation of Local Lorentz Invariance (LLI) and on the formalism of the Deformed Special Relativity (DSR), we examine the connections between the local geometrical structure…
The existence of several nilpotent Noether charges in the decoupled formulation of two-dimensional gauge theories does not imply that all of these are required to annihilate the physical states. We elucidate this matter in the context of…
We consider a problem of the consistent deformation of physical system introducing a new features, but preserving its fundamental properties. In particular, we study how to implement the noncommutativity of space-time without violation of…
The rapid growth of multimodal intelligence on resource-constrained and heterogeneous domestic hardware exposes critical bottlenecks: multimodal feature heterogeneity, real-time requirements in dynamic scenarios, and hardware-specific…
We introduce a Homothetic Hodge de Rham (HHDR) theory that extends the de Rham complex and Hodge decomposition to homothetically dressed differential forms. The dressing, governed by a dilaton field and a Weyl weight $w$, defines the…
Here I present a new discrete model of quantum mechanics for relativistic 1-electron systems, in which particle movement is described by a directed space-time graph with attached 4-spinors, but without any continuous wave functions. These…
For the newly proposed coupled (but equivalent) Lagrangians for the supersymmetric (SUSY) system of a one (0 + 1)-dimensional spinning relativistic particle, we derive the Noether conserved charges corresponding to its (super)gauge,…
We demonstrate that the celebrated St$\ddot u$ckelberg formalism gets modified in the case of a massive four (3+1)-dimensional (4D) Abelian 2-form theory due to the presence of a self-duality discrete symmetry in the theory. The latter…
The space discreteness hypothesis asserts that the nature of space at short distances is radically different from that at large distances. Based on the Bronstein inequality, here, we use a totally disconnected topological space…
The nilpotent BRST, anti-BRST, dual-BRST and anti-dual-BRST symmetry transformations are constructed in the context of noncommutative (NC) 1-form as well as 2-form gauge theories. The corresponding Noether's charges for these symmetries on…
A new functional calculus, developed recently for a fully non-perturbative treatment of quantum gravity, is used to begin a systematic construction of a quantum theory of geometry. Regulated operators corresponding to areas of 2-surfaces…
Standard quantum mechanics unquestionably violates the separability principle that classical physics (be it point-like analytic, statistical, or field-theoretic) accustomed us to consider as valid. In this paper, quantum nonseparability is…
We revisit the algebraic description of shape invariance method in one-dimensional quantum mechanics. In this note we focus on four particular examples: the Kepler problem in flat space, the Kepler problem in spherical space, the Kepler…
Several conceptual aspects of quantum gravity are studied on the example of the homogeneous isotropic LQC model. In particular: $(i)$ The proper time of the co-moving observers is showed to be a quantum operator {and} a quantum spacetime…
In this work we present a novel structure-preserving scheme for the discretization of the Godunov-Peshkov-Romenski (GPR) model of continuum mechanics written in Lagrangian form. This model admits an extra conservation law for the total…
We show the existence of a co(dual)-BRST symmetry for the usual BRST invariant Lagrangian density of an Abelian gauge theory in two dimensions of space-time where a U(1) gauge field is coupled to the Noether conserved current (constructed…