Related papers: A plactic algebra action on bosonic particle confi…
Motivated by the sharp contrast between classical and quantum physics as probability theories, in these lecture notes I introduce the basic notions of operator algebras that are relevant for the algebraic approach to quantum physics.…
Quadratic Poisson brackets on a vector space equipped with a bilinear multiplication are studied. A notion of a bracket compatible with the multiplication is introduced and an effective criterion of such compatibility is given. Among…
An explicit Lorentz covariant formulation of the canonical theory for classical fields is established on a space-like hypersurface. Hamilton's equations and a Poisson bracket are defined on the space-like hypersurface. The Poisson bracket…
Using a new presentation for partition algebras (J. Algebraic Combin. 37(3):401-454, 2013), we derive explicit combinatorial formulae for the seminormal representations of the partition algebras. These results generalise to the partition…
A finite-dimensional unital and associative algebra over $\mathbb{R}$, or what we shall call simply "an algebra" in this paper for short, generalities the construction by which we derive the complex numbers by "adjoining an element $i$" to…
The harmonic oscillator is one of the most studied systems in Physics with a myriad of applications. One of the first problems solved in a Quantum Mechanics course is calculating the energy spectrum of the simple harmonic oscillator with…
A proposal of an algebraic model for the relation between a quantum environment and certain classical particle system is given. The quantum environment is described by a category of possible quantum states, the initial particle system is…
An attempt to explain with the classical stands a number of statements of the quantum mechanics has been done. At this the Plank constant appears as consequence of demand of nucleon stability. Proton can be imagined as a rotating disk which…
A new tropical plactic algebra is introduced in which the Knuth relations are inferred from the underlying semiring arithmetics, encapsulating the ubiquitous plactic monoid $\mathcal{P}_n$. This algebra manifests a natural framework for…
We study a quantum spherically symmetric object which is based on radial plasma oscillations. Such a plasmoid is supposed to exist in a dense plasma containing electrons, ions, and neutral particles. The method of creation and annihilation…
We find a close correspondence between certain partition functions of ideal quantum gases and certain symmetric polynomials. Due to this correspondence it can be shown that a number of thermodynamic identities which have recently been…
Relativistic, scalar particles are considered, contained in a box with periodic boundary conditions. Although interactions are not expected to be a fundamental problem, we concentrate on free particles. By considering them to be harmonic…
The most general 2+1 dimensional spinning particle model is considered. The action functional may involve all the possible first order Poincare invariants of world lines, and the particular class of actions is specified thus the…
Various applications of quantum algebraic techniques in nuclear structure physics, such as the su$_q$(2) rotator model and its extensions, the use of deformed bosons in the description of pairing correlations, and the construction of…
For a cellular algebra $\A$ with a cellular basis $\ZC$, we consider a decomposition of the unit element $1_\A$ into orthogonal idempotents (not necessary primitive) satisfying some conditions. By using this decomposition, the cellular…
A formalism is developed for describing approximate classical behaviour in finite (but possibly large) quantum systems. This is done in terms of a structure common to classical and quantum mechanics, viz. a Poisson space with a transition…
The formalism of geometric algebra can be described as deformed super analysis. The deformation is done with a fermionic star product, that arises from deformation quantization of pseudoclassical mechanics. If one then extends the…
We study a representation of the (local) plactic monoid given by Schur operators $u_i$, which act on partitions by adding a box in column $i$ (if possible). In particular, we give a complete list of the relations that hold in the algebra of…
This paper discusses the no-cloning theorem in a logico-algebraic approach. In this approach, an orthoalgebra is considered as a general structure for propositions in a physical theory. We proved that an orthoalgebra admits cloning…
In this study, a new alternative model algorithm has been proposed for assembling amorphous structures, unifying the bosonic paradigm applicable at low temperatures with crystalline models relevant at room and higher temperatures. Physical…