Related papers: Identical Particles and Permutation Group
We prove that, for the quon algebra, which interpolates between the Bose and Fermi statistics and depends on a free parameter q,it is possible to build an su(2) irreducible representation. One of the consequences of this fact is that the…
Using the corepresentation of the quantum supergroup OSp_q(1/2) a general method for constructing noncommutative spaces covariant under its coaction is developed. In particular, a one-parameter family of covariant algebras, which may be…
After a brief mention of Bose and Fermi oscillators and of particles which obey other types of statistics, including intermediate statistics, parastatistics, paronic statistics, anyon statistics and infinite statistics, I discuss the…
The "quantum duality principle" states that a quantisation of a Lie bialgebra provides also a quantisation of the dual formal Poisson group and, conversely, a quantisation of a formal Poisson group yields a quantisation of the dual Lie…
Inspired by a result in [Ga], we locate two $ k[q,q^{-1}] $-integer forms of $ F_q[SL(n+1)] $, along with a presentation by generators and relations, and prove that for $ q=1 $ they specialize to $ U({\mathfrak{h}}) $, where $…
New algebraic structure on electronic Fock space is studied in detail. This structure is defined in terms of a certain multiplication of many electron wave functions and has close interrelation with coupled cluster and similar approaches.…
A practical method is developed to deal with the second quantization of the many-body system containing the composite particles. In our treatment, the modes associated with composite particles are regarded approximately as independent ones…
Para-Bose and para-Fermi statistics are known to be associated with representations of the Lie (super)algebras of class B. We develop a framework for the generalization of quantum statistics based on the Lie superalgebras A(m|n), B(m|n),…
We study the higher spin anologs of the six vertex model on the basis of its symmetry under the quantum affine algebra $U_q(\slth)$. Using the method developed recently for the XXZ spin chain, we formulate the space of states, transfer…
Quantum and q-deformed algebras find their application not only in mathematical physics and field theoretical context, but also in phenomenology of particle properties. We describe (i) the use of quantum algebras U_q(su_n) corresponding to…
We construct all projective modules of the restricted quantum group $\bar{U}_q s\ell(2|1)$ at an even, $2p$th, root of unity. This $64p^4$-dimensional Hopf algebra is a common double bosonization, $B(X^*)\otimes B(X)\otimes H$, of two…
We consider the possibility that all particles in the world are fundamentally identical, i.e., belong to the same species. Different masses, charges, spins, flavors, or colors then merely correspond to different quantum states of the same…
It is shown that the measurement algebra of Schwinger, a characterization of the properties of Pauli measurements of the first and second kinds, forming the foundation of his formulation of quantum mechanics over the complex field, has a…
The symmetrization postulate and the associated Bose/Fermi (anti)-commutators for field mode operators are among the pillars on which local quantum field theory lays its foundations. They ultimately determine the structure of Fock space and…
The method of constructing the tomographic probability distributions describing quantum states in parallel with density operators is presented. Known examples of Husimi-Kano quasi-distribution and photon number tomography are reconsidered…
Quantum physics has revealed many interesting formal properties associated with the algebra of two operators, A and B, satisfying the partial commutation relation AB-BA=1. This study surveys the relationships between classical combinatorial…
Let $A$ be a unital operator algebra. Let us assume that every {\it bounded\/} unital homomorphism $u\colon \ A\to B(H)$ is similar to a {\it contractive\/} one. Let $\text{\rm Sim}(u) = \inf\{\|S\|\, \|S^{-1}\|\}$ where the infimum runs…
We discuss several topics of homological algebra for the Lie superalgebra osp(1|2n). First we focus on Bott-Kostant cohomology, which yields classical results although the cohomology is not given by the kernel of the Kostant quabla…
Let $k$ be a field and suppose $p, q\in k$. We prove that the two affine Hecke algebras $H_q$ and $H_p$ of type $A_n$ are isomorphic as $k$-algebras if and only if $p=q^{\pm 1}$.
This work continues the research of generalized Heisenberg algebras connected with several orthogonal polynomial systems. The realization of the annihilation operator of the algebra corresponding to a polynomial system by a differential…