Related papers: IDENTICAL PARTICLES AND PERMUTATION GROUP
Using twisted realizations of the symmetric groups, we show that Bose and Fermi statistics are compatible with transformations generated by compact quantum groups of Drinfel'd type.
Quantum fields are considered as generators of infinite-dimensional Clifford algebra $Cl(\infty)$, which can be either orthogonal (in case of fermions) or symplectic (in case of bosons). A generic quantum state can be expressed as a…
The abelian sigma model in (1+1) dimensions is a field theoretical model which has a field $ \phi : S^1 \to S^1 $. An algebra of the quantum field is defined respecting the topological aspect of the model. It is shown that the zero-mode has…
We study quantization of a class of inhomogeneous Lie bialgebras which are crossproducts in dual sectors with Abelian invariant parts. This class forms a category stable under dualization and the double operations. The quantization turns…
The meaning of quantum group transformation properties is discussed in some detail by comparing the (co)actions of the quantum group with those of the corresponding Lie group, both of which have the same algebraic (matrix) form of the…
Coordinate atypical representation of the orthosymplectic superalgebra osp(2/2) in a Hilbert superspace of square integrable functions constructed in a special way is given. The quantum nonrelativistic free particle Hamiltonian is an…
The concept of quantum commutativity with respect to an action or coaction of a given Hopf algebra is used for the algebraic description of a system of particles and their interaction with certain quantum field. Graded commutativity and…
This paper seeks to construct a representation of the algebra of angular momentum (SU(2) algebra) in terms of the operator relations corresponding to Gentile statistics in which one quantum state can be occupied by $n$ particles. First, we…
Fock space representations of the Lie superalgebra $sl(n+1|m)$ and of its quantum analogue $U_q[sl(n+1|m)]$ are written down. The results are based on a description of these superalgebras via creation and annihilation operators. The…
The super version of imprimitivity theorem is available now to describe global supersymmetry of systems using the representations of super Lie groups (SLG). This result uses the equivalence between super Harish- Chandra pairs and super Lie…
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.…
The annihilation-creation operators $a^{(\pm)}$ are defined as the positive/negative frequency parts of the exact Heisenberg operator solution for the `sinusoidal coordinate'. Thus $a^{(\pm)}$ are hermitian conjugate to each other and the…
We establish operator structure identities for quantum channels and their error-correcting and private codes, emphasizing the complementarity relationship between the two perspectives. Relevant structures include correctable and private…
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…
We introduce a symmetric operad whose algebras are the Operator Product Expansion (OPE) Algebras of quantum fields. There is a natural classical limit for the algebras over this operad and they are commutative associative algebras with…
Superparticle models with $OSp(N|2)$ supersymmetry group are studied. We first consider the $N=4$ case and construct the models with $\kappa$-symmetry on the coset spaces of the $OSp(4|2)$ supergroup. In addition, within the canonical…
In the case of systems composed of identical particles, a typical instance in quantum statistical mechanics, the standard approach to separability and entanglement ought to be reformulated and rephrased in terms of correlations between…
There is a simple and natural quantization of differential forms on odd Poisson supermanifolds, given by the relation [f,dg]={f,g} for any two functions f and g. We notice that this non-commutative differential algebra has a geometrical…
The algebraic structures related with integrable structure of superconformal field theory (SCFT) are introduced. The SCFT counterparts of Baxter's Q-operator are constructed. The fusion-like relations for the transfer-matrices in different…
We consider isomorphisms and automorphisms of quantum groups. Let $k$ be a field and suppose $p, q\in k^*$ are not roots of unity. We prove that the two quantum groups $U_q(\mathfrak {sl}_2)$ and $U_p(\mathfrak{sl}_2)$ over a field $k$ are…