Grassmann variables on quantum spaces

2007

J. High Energy Phys.

“…Their explicit form can be found in Refs. [32,35]. It should also be mentioned that these L-matrices realize the generators of the quantum group SU q (2) within the algebra U q (su (2)).…”

Section: The Three-dimensional Q-deformed Euclidean Superalgebramentioning

confidence: 99%

“…In our previous work [31][32][33][34][35][36][37] attention was concentrated on space-time structures that arise from q-deformation [38]. More concretely, we are interested in q-deformed quantum spaces that could prove useful in physical applications.…”

Section: Introductionmentioning

confidence: 99%

q-Deformed Superalgebras

Schmidt

2007

J. High Energy Phys.

“…The L-matrices for q-deformed Euclidean space in three or four dimensions and those for q-deformed Minkowski space can easily be read off from the results in Refs. [38] and [43].…”

Section: Definition Of Star Products and Q-deformed Tensor Productsmentioning

confidence: 99%

ANALYSIS ON q-DEFORMED QUANTUM SPACES

2007

Int. J. Mod. Phys. A

A q-deformed version of classical analysis is given to quantum spaces of physical importance, i.e. Manin plane, q-deformed Euclidean space in three or four dimensions, and q-deformed Minkowski space. The subject is presented in a rather complete and selfcontained way. All relevant notions are introduced and explained in detail. The different possibilities to realize the objects of q-deformed analysis are discussed and their elementary properties are studied. In this manner attention is focused on star products, q-deformed tensor products, qdeformed translations, q-deformed partial derivatives, dual pairings, q-deformed exponentials, and q-deformed integration. The main concern of this work is to show that these objects fit together in a consistent framework, which is suitable to formulate physical theories on quantum spaces. *

“…We calculate the action of the L ij on a product of antisymmetrised vector coordinates (for their definition see Ref. [26]), i.e.…”

Section: Quantum Lie Algebra Of U Q (So 4 ) and Its Casimir Operatorsmentioning

confidence: 99%

“…In our previous work [21][22][23][24][25][26][27] attention was focused on q-deformed quantum spaces of physical importance, i.e. two-dimensional Manin plane, qdeformed Euclidean space in three or four dimensions and q-deformed Minkowski space.…”

Section: Introductionmentioning

confidence: 99%

-Deformed quantum Lie algebras

Schmidt

Journal of Geometry and Physics

2006

Attention is focused on q-deformed quantum algebras with physical importance, i.e. U q (su 2 ), U q (so 4 ) and q-deformed Lorentz algebra. The main concern of this article is to assemble important ideas about these symmetry algebras in a consistent framework which shall serve as starting point for representation theoretic investigations in physics, especially quantum field theory. In each case considerations start from a realization of symmetry generators within the differential algebra. Formulae for coproducts and antipodes on symmetry generators are listed. The action of symmetry generators in terms of their Hopf structure is taken as q-analog of classical commutators and written out explicitly. Spinor and vector representations of symmetry generators are calculated. A review of the commutation relations between symmetry generators and components of a spinor or vector operator is given. Relations for the corresponding quantum Lie algebras are computed. Their Casimir operators are written down in a form similar to the undeformed case. *