Deformed Exterior Algebra, Quons and their Coherent States

Abstract

We review the notion of the deformation of the exterior wedge product. This allows us to construct the deformation of the algebra of exterior forms over a vector space and also over an arbitrary manifold. We relate this approach to the generalized statistics. we study quons, as a particular case of these generalized statistics. We also give their statistical properties.A large part of the work is devoted to the problem of constructing coherent states for the deformed oscillators. we give a review of all the approaches existing in the literature concerning this point and enforce it with many examples.

Deformed quons and bi-coherent states

“…During recent years several possible definitions of coherent states have been proposed for quons [12,[18][19][20]. More recently, coherent states related to D-PBs have also been proposed and studied [21][22][23][24].…”

Approaches to Embryonic Neurodevelopment: From Neural Cell to Neural Tube Formation through Mathematical Models

“…In addition, since the tissue grows continuously and changes in shape from the original tissue structure and morphology, it can be considered as a quotient space 39 such that G: (X, 𝜏 𝑚 ) → (𝑌, 𝜏 𝑛 ). Further, the quotient space could be regarded as a Banach subspace where referred to as vector space which is by definition a Hilbert space 40 . As we defined the neuronal cells as analogous to a differentiable manifold that is indicated by every point 𝑝 {𝑥,𝑦,𝑧} such that 𝑅 𝑛 = {(𝑥 41,42 .…”

Classical Model of Quons

“…However, statistical deviations from bosons or fermions can be observed in quasi-particle excitations that occur in various condensed matter systems. Therefore, the study of physical systems that obey non-conventional statistics is one of the pillars of contemporary statistical physics [6][7][8][9][10][11][12]. Their interest spans from the theoretical foundation of generalized statistical mechanics [13,14], Fermi gas superfluid [15], high-temperature gas [16] and high-T c superconductivity [17], Laughlin particle with fractional charge related to fractional quantum Hall effect [18,19], Josephson junctions [20] and applications to quantum computation [21,22].…”