1,064 research outputs found
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.Comment: 38 pages, late
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.Comment: 6 pages, no figure
-Deformed Statistics and Classical Fourmomentum Addition Law
We consider -deformed relativistic symmetries described algebraically
by modified Majid-Ruegg bicrossproduct basis and investigate the quantization
of field oscillators for the -deformed free scalar fields on
-Minkowski space. By modification of standard multiplication rule, we
postulate the -deformed algebra of bosonic creation and annihilation
operators. Our algebra permits to define the n-particle states with classical
addition law for the fourmomenta in a way which is not in contradiction with
the nonsymmetric quantum fourmomentum coproduct. We introduce -deformed
Fock space generated by our -deformed oscillators which satisfy the
standard algebraic relations with modified -multiplication rule. We
show that such a -deformed bosonic Fock space is endowed with the
conventional bosonic symmetry properties. Finally we discuss the role of
-deformed algebra of oscillators in field-theoretic noncommutative
framework.Comment: LaTeX, 12 pages. V2: second part of chapter 4 changed, new references
and comments added. V3: formula (14) corrected. Some additional explanations
added. V4: further comments about algebraic structure are adde
Differential calculus on the quantum Heisenberg group
The differential calculus on the quantum Heisenberg group is conlinebreak
structed. The duality between quantum Heisenberg group and algebra is proved.Comment: AMSTeX, Pages
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.Comment: 6 pages, no figure
Projective representation of k-Galilei group
The projective representations of k-Galilei group G_k are found by
contracting the relevant representations of k-Poincare group. The projective
multiplier is found. It is shown that it is not possible to replace the
projective representations of G_k by vector representations of some its
extension.Comment: 15 pages Latex fil
Canonical and Lie-algebraic twist deformations of -Poincare and contractions to -Galilei algebras
We propose canonical and Lie-algebraic twist deformations of
-deformed Poincare Hopf algebra which leads to the generalized
-Minkowski space-time relations. The corresponding deformed
-Poincare quantum groups are also calculated. Finally, we perform the
nonrelativistic contraction limit to the corresponding twisted Galilean
algebras and dual Galilean quantum groups.Comment: 16 pages, no figures, v3: few changes provided - version for journal,
v2: submitted incidentally, v4: the page numbers for all references in
preprint version are provide
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