Related papers: Current algebra, statistical mechanics and quantum…
The aim of the paper is to derive essential elements of quantum mechanics from a parametric structure extending that of traditional mathematical statistics. The main extensions, which also can be motivated from an applied statistics point…
A rigorous mathematical theory of dimensional analysis, systematically accounting for the use of physical quantities in science and engineering, perhaps surprisingly, was not developed until relatively recently. We claim that this has…
Gravity theory based on current algebra is formulated. The gauge principle rather than the general covariance combined with the equivalence principle plays the pivotal role in the formalism, and the latter principles are derived as a…
In recent years, many new developments in theoretical physics, and in practical applications rely on different techniques of noncommutative algebras. In this review, we introduce the basic concepts and techniques of noncommutative physics…
The long-standing problem of time in canonical quantum gravity is the source of several conceptual and technical issues. Here, recent mathematical results are used to provide a consistent algebraic formulation of dynamical symplectic…
The quon algebra is an approach to particle statistics in order to provide a theory in which the Pauli exclusion principle and Bose statistics are violated by a small amount. The quons are particles whose annihilation and creation operators…
We study the possibility of applying statistical mechanics to generally covariant quantum theories with a vanishing Hamiltonian. We show that (under certain appropiate conditions) this makes sense, in spite of the absence of a notion of…
Physical systems, characterized by an ensemble of interacting elementary constituents, can be represented and studied by different algebras of observables or operators. For example, a fully polarized electronic system can be investigated by…
These notes are intended as an introduction to a study of applications of noncommutative calculus to quantum statistical Physics. Centered on noncommutative calculus we describe the physical concepts and mathematical structures appearing in…
We extend the recently developed kinematical framework for diffeomorphism invariant theories of connections for compact gauge groups to the case of a diffeomorphism invariant quantum field theory which includes besides connections also…
An algebraic model based on Lie-algebraic and discrete symmetry techniques is applied to the analysis of thermodynamic vibrational properties of molecules. The local anharmonic effects are described by a Morse-like potential and the…
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…
We introduce a unified Gaussian quantum operator representation for fermions and bosons. The representation extends existing phase-space methods to Fermi systems as well as the important case of Fermi-Bose mixtures. It enables simulations…
Gauge-invariant polynomial functions of matrix and tensor variables capture combinatorial structures of gauge-string duality, which can be usefully organised using finite-dimensional associative algebras. I review recent work on eigenvalue…
Gauge theories form the foundation of modern physics, with applications ranging from elementary particle physics and early-universe cosmology to condensed matter systems. We perform quantum simulations of the unitary dynamics of a U(1)…
In this paper, the power flow in electrical systems is modelled in the time domain by using Geometric Algebra and the Hilbert Transform. The use of this mathematical framework overcomes some of the limitations shown by the existing…
Nonequilibrium Green's functions provide a powerful tool for computing the dynamical response and particle exchange statistics of coupled quantum systems. We formulate the theory in terms of the density matrix in Liouville space and…
This paper is devoted to constructing and studying exactly solvable dynamical systems in discrete time obtained from some algebraic operations on matrices, to reductions of such systems leading to classical field theory models in…
We consider the fermion-boson mapping in three dimensional space-time, in the Abelian case, from the current algebra point of view. We show that in a path-integral framework one can derive a general bosonization recipe leading, in the…
A generalized algebra of quantum observables, depending on extra dimensional constants, is considered. Some limiting forms of the algebra are investigated and their possible applications to the descriptions of interactions of fundamental…