Algebraic curves for commuting elements in the q-deformed Heisenberg algebra

R-deformed Heisenberg algebra

It is shown that the deformed Heisenberg algebra involving the reflection operator R (Rdeformed Heisenberg algebra) has finite-dimensional representations which are equivalent to representations of paragrassmann algebra with a special differentiation operator. Guon-like form of the algebra, related to the generalized statistics, is found. Some applications of revealed representations of the R-d...

Deformed Heisenberg algebra with reflection

A universality of deformed Heisenberg algebra involving the reflection operator is revealed. It is shown that in addition to the well-known infinite-dimensional representations related to parabosons, the algebra has also finite-dimensional representations of the parafermionic nature. We demonstrate that finite-dimensional representations are representations of deformed parafermionic algebra wit...

Dirac Oscillator via R-deformed Heisenberg Algebra

The complete energy spectrum for the Dirac oscillator via R-deformed Heisenberg algebra is investigated. PACS numbers: 11.30.Pb, 03.65.Fd, 11.10.Ef. To appear in the proceedings at the XXIII Brazilian National Meeting on Particles and Fields, October 15 to 19, 2002, Águas de Lindóia-SP, Brazil, site www.sbf1.if.usp.br/eventos/enfpc/xxiii.

Braided Chains of q-Deformed Heisenberg Algebrae

Given M copies of a q-deformed Weyl or Clifford algebra in the defining representation of a quantum group Gq, we determine a prescription to embed them into a unique, inclusive Gq-covariant algebra. The different copies are “coupled” to each other and are naturally ordered into a “chain”. In the case Gq = SLq(N) a modified prescription yields an inclusive algebra which is even explicitly SLq(M)...

Hq(4) Symmetry: The Linear q-Harmonic Oscillator Based on Generalized Irreps of the q-Deformed Heisenberg Algebra