arXiv subjects

Christian Blohmann

Publications and source records attributed to Christian Blohmann.

24 records · Page 2Linked to original sources

arXiv2004

Perturbative Symmetries on Noncommutative Spaces

Perturbative deformations of symmetry structures on noncommutative spaces are studied in view of noncommutative quantum field theories. The rigidity of enveloping algebras of semi-simple Lie algebras with respect to formal deformations is reviewed in the context of star products. It is shown that rigidity of symmetry algebras extends to rigidity of the action of the symmetry on the space. This implies that the noncommutative spaces considered can be realized as star products by particular ordering prescriptions which are compatible with the symmetry. These symmetry preserving ordering prescriptions are calculated for the quantum plane and four-dimensional quantum Euclidean space. Using these ordering prescriptions greatly facilitates the construction of invariant Lagrangians for quantum field theory on noncommutative spaces with a deformed symmetry.

math.QA↗

arXiv2003

Free q-Deformed Relativistic Wave Equations by Representation Theory

In a representation theoretic approach a free q-relativistic wave equation must be such, that the space of solutions is an irreducible representation of the q-Poincare algebra. It is shown how this requirement uniquely determines the q-wave equations. As examples, the q-Dirac equation (including q-gamma matrices which satisfy a q-Clifford algebra), the q-Weyl equations, and the q-Maxwell equations are computed explicitly.

hep-th↗

arXiv2003

Der rechnende Dichter (The calculating poet)

A small and unsystematic selection of my favorite appearances of mathematicians and mathematics in German literature. It includes classic and romantic (Lessing, Goethe, Wezel, F. Schlegel, Kleist, Novalis, Grillparzer, Heine), modern (Wedekind, Doeblin, Morgenstern, Musil, Brecht, Eich), as well as post-modern authors (Hans-Magnus Enzensberger, Volker Braun, Botho Strauss).

math.HO↗

arXiv2002

Covariant Realization of Quantum Spaces as Star Products by Drinfeld Twists

Covariance of a quantum space with respect to a quantum enveloping algebra ties the deformation of the multiplication of the space algebra to the deformation of the coproduct of the enveloping algebra. Since the deformation of the coproduct is governed by a Drinfeld twist, the same twist naturally defines a covariant star product on the commutative space. However, this product is in general not associative and does not yield the quantum space. It is shown that there are certain Drinfeld twists which realize the associative product of the quantum plane, quantum Euclidean 4-space, and quantum Minkowski space. These twists are unique up to a central 2-coboundary. The appropriate formal deformation of real structures of the quantum spaces is also expressed by these twists.

math.QA↗

arXiv2001

Spin in the q-Deformed Poincare Algebra

We investigate spin as algebraic structure within the q-deformed Poincare algebra, proceeding in the same manner as in the undeformed case. The q-Pauli-Lubanski vector, the q-spin Casimir, and the q-little algebras for the massless and the massive case are constructed explicitly.

math.QA↗

arXiv2001

Spin Representations of the q-Poincare Algebra

The spin of particles on a non-commutative geometry is investigated within the framework of the representation theory of the q-deformed Poincare algebra. An overview of the q-Lorentz algebra is given, including its representation theory with explicit formulas for the q-Clebsch-Gordan coefficients. The vectorial form of the q-Lorentz algebra (Wess), the quantum double form (Woronowicz), and the dual of the q-Lorentz group (Majid) are shown to be essentially isomorphic. The construction of q-Minkowski space and the q-Poincare algebra is reviewed. The q-Euclidean sub-algebra, generated by rotations and translations, is studied in detail. The results allow for the construction of the q-Pauli-Lubanski vector, which, in turn, is used to determine the q-spin Casimir and the q-little algebras for both the massive and the massless case. Irreducible spin representations of the q-Poincare algebra are constructed in an angular momentum basis, accessible to physical interpretation. It is shown how representations can be constructed, alternatively, by the method of induction. Reducible representations by q-Lorentz spinor wave functions are considered. Wave equations on these spaces are found, demanding that the spaces of solutions reproduce the irreducible representations. As generic examples the q-Dirac equation and the q-Maxwell equations are computed explicitly and their uniqueness is shown.

math.QA↗