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J. Sobczyk

Publications and source records attributed to J. Sobczyk.

24 records · Page 2Linked to original sources
arXiv1994

The classical basis for $κ$-deformed Poincaré (super)algebra and the second $κ$-deformed supersymmetric Casimir

We present here the general solution describing generators of \kdef \poin algebra as the functions of classical \poin algebra generators as well as the inverse formulae. Further we present analogous relations for the generators of N=1 D=4 \kdef \poin superalgebra expressed by the classical \poin superalgebra generators. In such a way we obtain the \kdef \poin (super)algebras with all the quantum deformation present only in the coalgebra sector. Using the classical basis of \kdef \poin superalgebra we obtain as a new result the $\k$-deformation of supersymmetric covariant spin square Casimir.

hep-th↗
arXiv1994

$κ$-Deformation of Poincaré Superalgebra with Classical Lorentz Subalgebra and its Graded Bicrossproduct Structure

The $κ$-deformed $D=4$ Poincar{é} superalgebra written in Hopf superalgebra form is transformed to the basis with classical Lorentz subalgebra generators. We show that in such a basis the $κ$-deformed $D=4$ Poincare superalgebra can be written as graded bicrossproduct. We show that the $κ$-deformed $D=4$ superalgebra acts covariantly on $κ$-deformed chiral superspace.

hep-th↗
arXiv1994

Operator Formalism on General Algebraic Curves

The usual Laurent expansion of the analytic tensors on the complex plane is generalized to any closed and orientable Riemann surface represented as an affine algebraic curve. As an application, the operator formalism for the $b-c$ systems is developed. The physical states are expressed by means of creation and annihilation operators as in the complex plane and the correlation functions are evaluated starting from simple normal ordering rules. The Hilbert space of the theory exhibits an interesting internal structure, being splitted into $n$ ($n$ is the number of branches of the curve) independent Hilbert spaces. Exploiting the operator formalism a large collection of explicit formulas of string theory is derived.

hep-th↗
arXiv1994

Quantum Deformation of the Poincare Supergroup and $κ$-deformed Superspace

The classical $r$-matrix for $N=1$ superPoincar{é} algebra, given by Lukierski, Nowicki and Sobczyk is used to describe the graded Poisson structure on the $N=1$ Poincar{é} supergroup. The standard correspondence principle between the even (odd) Poisson brackets and (anti)commutators leads to the consistent quantum deformation of the superPoincar{é} group with the deformation parameter $q$ described by fundamental mass parameter $κ\quad (κ^{-1}=\ln{q})$. The $κ$-deformation of $N=1$ superspace as dual to the $κ$-deformed supersymmetry algebra is discussed.

hep-th↗
arXiv1993

Operator Formalism on the $Z_n$ Symmetric Algebraic Curves

In this work, the following conjectures are proven in the case of a Riemann surface with abelian group of symmetry: a) The $b-c$ systems on a Riemann surface $M$ are equivalent to a multivalued field theory on the complex plane if $M$ is represented as an algebraic curve; b) the amplitudes of the $b-c$ systems on a Riemann surface $M$ with discrete group of symmetry can be derived from the operator product expansions on the complex plane of an holonomic quantum field theory a la Sato, Jimbo and Miwa. To this purpose, the solutions of the Riemann-Hilbert problem on an algebraic curve with abelian monodromy group obtained by Zamolodchikov, Knizhnik and Bershadskii-Radul are used in order to expand the $b-c$ fields in a Fourier-like basis. The amplitudes of the $b-c$ systems on the Riemann surface are then recovered exploiting simple normal ordering rules on the complex plane.

hep-th↗