Anca Tureanu

On a Lorentz-invariant interpretation of noncommutative space-time and its implications on noncommutative QFT

Abstract By invoking the concept of twisted Poincare symmetry of the algebra of functions on a Minkowski space–time, we demonstrate that the noncommutative space–time with the commutation relations [ x μ , x ν ] = i θ μ ν , where θ μ ν is a constant real antisymmetric matrix, can be interpreted in a Lorentz-invariant way. The implications of the twisted Poincare symmetry on QFT on such a space–time is briefly discussed. The presence of the twisted symmetry gives justification to all the previous treatments within NC QFT using Lorentz invariant quantities and the representations of the usual Poincare symmetry.

New concept of relativistic invariance in noncommutative space-time: twisted poincare symmetry and its implications.

We present a systematic framework for noncommutative (NC) quantum field theory (QFT) within the new concept of relativistic invariance based on the notion of twisted Poincare symmetry, as proposed by Chaichian et al. [Phys. Lett. B 604, 98 (2004)]. This allows us to formulate and investigate all fundamental issues of relativistic QFT and offers a firm frame for the classification of particles according to the representation theory of the twisted Poincare symmetry and as a result for the NC versions of CPT and spin-statistics theorems, among others, discussed earlier in the literature. As a further application of this new concept of relativism we prove the NC analog of Haags theorem.

Non-commutative standard model: model building

Abstract.A non-commutative version of the usual electro-weak theory is constructed. We discuss how to overcome the two major problems: (1) although we can have non-commutative U(n) (which we denote by U*(n)) gauge theory we cannot have non-commutative SU(n) and (2) the charges in non-commutative QED are quantized to just

Noncommutative gauge field theories: A No go theorem

0, \pm 1

Aharonov-Bohm effect in noncommutative spaces

. We show how the latter problem with charge quantization, as well as with the gauge group, can be resolved by taking the

On the ΛCDM Universe in f(G) gravity

U_{*}(3)\times U_{*}(2)\times U_{*}(1)

Corrections to Schwarzschild solution in noncommutative gauge theory of gravity

gauge group and reducing the extra U(1) factors in an appropriate way. Then we proceed with building the non-commutative version of the standard model by specifying the proper representations for the entire particle content of the theory, the gauge bosons, the fermions and Higgs. We also present the full action for the non-commutative standard model (NCSM). In addition, among several peculiar features of our model, we address the inherentCP violation and new neutrino interactions.

Spin-statistics and CPT theorems in noncommutative field theory

Abstract Studying the general structure of the noncommutative (NC) local groups, we prove a no-go theorem for NC gauge theories. According to this theorem, the closure condition of the gauge algebra implies that: (1) the local NC u(n) algebra only admits the irreducible n×n matrix-representation. Hence the gauge fields are in n×n matrix form, while the matter fields can only be in fundamental, adjoint or singlet states; (2) for any gauge group consisting of several simple-group factors, the matter fields can transform nontrivially under at most two NC group factors. In other words, the matter fields cannot carry more than two NC gauge group charges. This no-go theorem imposes strong restrictions on the NC version of the Standard Model and in resolving the standing problem of charge quantization in noncommutative QED.

Quantum theories on noncommutative spaces with nontrivial topology: Aharonov-Bohm and Casimir effects

Abstract The Aharonov–Bohm effect on the noncommutative plane is considered. Developing the path integral formulation of quantum mechanics, we find the propagation amplitude for a particle in a noncommutative space. We show that the corresponding shift in the phase of the particle propagator due to the magnetic field of a thin solenoid receives certain gauge invariant corrections because of the noncommutativity. Evaluating the numerical value for this correction, an upper bound for the noncommutativity parameter is obtained.

Modified F(R) Hořava–Lifshitz gravity: a way to accelerating FRW cosmology

In the context of the so-called Gauss–Bonnet gravity, where the gravitational action includes function of the Gauss–Bonnet invariant, we study cosmological solutions, especially the well-known ΛCDM model. It is shown that the dark energy contribution and even the inflationary epoch can be explained in the frame of this kind of theories with no need of any other kind of component. Other cosmological solutions are constructed and the rich properties that this kind of theories provide are explored.