On the Consistency of Twisted Gauge Theory
It is argued that the twisted gauge theory is consistent provided it exhibits also the standard noncommutative gauge symmetry.
hep-th↗
arXiv subjects
S. Giller
Publications and source records attributed to S. Giller.
Global Symmetries of Noncommutative Space-time
The global counterpart of infinitesimal symmetries of noncommutative space-time is discussed.
hep-th↗
Space-time symmetry of noncommutative field theory
We consider the deformed Poincare group describing the space-time symmetry of noncommutative field theory. It is shown how the deformed symmetry is related to the explicit symmetry breaking.
hep-th↗
Quadratic integrals of motion for the systems of identical particles
The dynamical systems of identical particles admitting quadratic integrals of motion are classified. The relevant integrals are explicitly constructed and their relation to separation of variables in H-J equation is clarified.
nlin.SI↗
Quadratic integrals of motions for the systems of identical particles-quantum case
The quantum dynamical systems of identical particles admitting an additional integral quadratic in momenta are considered. It is found that an appropriate ordering procedure exists which allows to convert the classical integrals into their quantum counterparts. The relation to the separation of variables in Schroedinger equation is discussed.
nlin.SI↗
Irreducible Representations of an Algebra underlying Hidden Symmetries of a class of Quasi Exactly Solvable Systems of Equations
The set of linear, differential operators preserving the vector space of couples of polynomials of degrees n and n-2 in one real variable leads to an abstract associative graded algebra A(2). The irreducible, finite dimensional representations of this algebra are classified into five infinite discrete sets and one exceptional case. Their matrix elements are given explicitely. The results are related to the theory of quasi exactly solvable equations.
solv-int↗
Remarks on central extensions of the Galilei group in 2+1 dimensions
Some properties of central extensions of 2+1 dimensional Galilei group are discussed. It is shown that certain families of extensions are isomorphic. An interpretation of new nontrivial cocycle is offered. A few bibliographical remarks are included.
q-alg↗
The Quantum Galilei Group
The quantum Galilei group $G_{\varkappa}$ is defined. The bicrossproduct structure of $G_{\varkappa}$ and the corresponding Lie algebra is revealed. The projective representations for the two-dimensional quantum Galilei group are constructed.
q-alg↗
Galilean invariance in 2+1 dimensions
The Galilean invariance in three dimensional space-time is considered. It appears that the Galilei group in 2+1 dimensions posses a three-parameter family of projective representations. Their physical interpretation is discussed in some detail.
hep-th↗
Differential calculus on deformed E(2) group
Fourdimensional bicovariant differential calculus on quantum E(2) group is constructed.
q-alg↗
Projectivised representations of $U_q osp(2,2)$
We construct representations of the enveloping algebra $U_q osp(2,2)$ in terms of finite difference operators and we discuss this result in the framework of quasi-exactly-solvable equations.
hep-th↗