Daniel N. Blaschke

Non-commutative U(1) gauge theory on with oscillator term and BRST symmetry

Inspired by the renormalizability of the non-commutative Φ4 model with added oscillator term, we formulate a non-commutative gauge theory, where the oscillator enters as a gauge fixing term in a BRST invariant manner. All propagators turn out to be essentially given by the Mehler kernel and the bilinear part of the action is invariant under the Langmann-Szabo duality. The model is a promising candidate for a renormalizable non-commutative U(1) gauge theory.

Translation-invariant models for non-commutative gauge fields

Motivated by the recent construction of a translation-invariant renormalizable non-commutative model for a scalar field [1], we introduce models for non-commutative U(1) gauge fields along the same lines. More precisely, we include some extra terms into the action with the aim of getting rid of the UV/IR mixing.

On the Problem of Renormalizability in Non-Commutative Gauge Field Models: A Critical Review

AbstractWhen considering quantum field theories on non-commutative spaces one inevitablyencounters the infamous UV/IR mixing problem. So far, only very few renormalizablemodels exist and all of them describe non-commutative scalar field theories on four-dimensional Euclidean Groenewold-Moyal deformed space, also known as ‘θ-deformedspace’ R 4θ . In this work we discuss some major obstacles of constructing a renormalizablenon-commutative gauge field model and sketch some possible ways out. 1 Introduction Ever since the first non-commutative quantum field theory models were constructed, thegreatest obstacle has been the infamous so-called UV/IR mixing problem [1], where certaintypes of Feynman graphs, the non-planar graphs, exhibit new unrenormalizable IR singular-ities in exceptional momenta (see [2, 3, 4] for a review). The situation improved dramaticallywhen the first renormalizable scalar non-commutative model, the Grosse-Wulkenhaar model,was put forward [5, 6, 7]. Later, a second renormalizable scalar non-commutative quantumfield theory was presented by Gurau

One-loop calculations for a translation invariant non-commutative gauge model

In this paper we discuss one-loop results for the translation invariant non-commutative gauge field model we introduced recently. This model relies on the addition of some carefully chosen extra terms in the action which mix long and short scales in order to circumvent the infamous UV/IR mixing, and which were motivated by the renormalizable non-commutative scalar model of Gurau et al. [arXiv:0802.0791].

Quantum Corrections for Translation-Invariant Renormalizable Non-Commutative Phi**4 Theory

In this paper we elaborate on the translation-invariant renormalizable 4 theory in 4-dimensional non-commu\-ta\-tive space which was recently introduced by the Orsay group. By explicitly performing Feynman graph calculations at one loop and higher orders we illustrate the mechanism which overcomes the UV/IR mixing problem and ultimately leads to a renormalizable model. The obtained results show that the IR divergences are also suppressed in the massless case, which is of importance for the gauge field theoretic generalization of the scalar field model.

Gauge independence of IR singularities in non-commutative QFT — and interpolating gauges

IR divergences of a non-commutative U(1) Maxwell theory are discussed at the one-loop level using an interpolating gauge to show that quadratic IR divergences are independent not only from a covariant gauge fixing but also independent from an axial gauge fixing.

Divergences in non-commutative gauge theories with the Slavnov term

The divergence structure of non-commutative gauge field theories (NCGFT) with a Slavnov extension [1],[2] is examined at one-loop level with main focus on the gauge boson self-energy. Using an interpolating gauge we show that even with this extension the quadratic IR divergence of the gauge boson self-energy is independent from a covariant gauge fixing as well as from an axial gauge. The proposal of Slavnov is based on the fact that the photon propagator shows a new transversality condition with respect to the IR dangerous terms. This novel transversality is implemented with the help of a new dynamical multiplier field. However, one expects that in physical observables such contributions disappear. A further new feature is the existence of new UV divergences compatible with the gauge invariance (BRST symmetry). We then examine two explicit models with couplings to fermions and scalar fields.

Improved localization of a renormalizable non-commutative translation invariant U(1) gauge model

Motivated by the recent work of Vilar et al. (arXiv:0902.2956) we enhance our non-commutative translation invariant gauge model (Blaschke D. N. et al., arXiv:0901.1681) by introducing auxiliary fields and ghosts forming a BRST doublet structure. In this way localization of the problematic term can be achieved without the necessity for any additional degrees of freedom. The resulting theory is suspected to be renormalizable. A rigorous proof, however, has not been accomplished up to now.

One-loop calculations and detailed analysis of the localized non-commutative p-2 U(1) Gauge model

This paper carries forward a series of articles describing our enterprise to con- struct a gauge equivalent for the -deformed non-commutative 1 p2 model originally introdu- ced by Gurau et al. (Comm. Math. Phys. 287 (2009), 275-290). It is shown that breaking terms of the form used by Vilar et al. (J. Phys. A: Math. Theor. 43 (2010), 135401, 13 pages) and ourselves (Eur. Phys. J. C: Part. Fields 62 (2009), 433-443) to localize the BRST co- variant operator D 2 2 D 2 1 lead to difficulties concerning renormalization. The reason is that this dimensionless operator is invariant with respect to any symmetry of the model, and can be inserted to arbitrary power. In the present article we discuss explicit one-loop calculations, and analyze the mechanism the mentioned problems originate from.

Wong's Equations and Charged Relativistic Particles in Non-Commutative Space

In analogy to Wongs equations describing the motion of a charged relativistic point particle in the presence of an external Yang{Mills field, we discuss the motion of such a particle in non-commutative space subject to an external U?(1) gauge field. We conclude that the latter equations are only consistent in the case of a constant field strength. This formulation, which is based on an action written in Moyal space, provides a coarser level of description than full QED on non-commutative space. The results are compared with those obtained from the different Hamiltonian approaches. Furthermore, a continuum version for Wongs equations and for the motion of a particle in non-commutative space is derived.