By invoking the concept of twisted Poincaré 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 ] = iθ µν , where θ µν is a constant real antisymmetric matrix, can be interpreted in a Lorentz-invariant way. The implications of the twisted Poincaré 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 Poincaré symmetry. PACS: 11.10.Nx Consequently, the commutators of operators are replaced by Moyal brackets and the equiv-

We have calculated the energy levels of the hydrogen atom and as well the Lamb shift within the noncommutative quantum electrodynamics theory. The results show deviations from the usual QED both on the classical and on the quantum levels. On both levels, the deviations depend on the parameter of space/space noncommutativity.

We present a systematic framework for noncommutative (NC) QFT within the new concept of relativistic invariance based on the notion of twisted Poincaré symmetry (with all 10 generators), as proposed in ref. [7]. This allows 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 Poincaré 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 Haag's theorem.

No abstract

A noncommutative version of the usual electro-weak theory is constructed. We discuss how to overcome the two major problems: 1) although we can have noncommutative U (n) (which we denote by U ⋆ (n)) gauge theory we cannot have noncommutative SU (n) and 2) the charges in noncommutative QED are quantized to just 0, ±1. We show how the latter problem with charge quantization, as well as with the gauge group, can be resolved by taking U ⋆ (3) × U ⋆ (2) × U ⋆ (1) gauge group and reducing the extra U (1) factors in an appropriate way. Then we proceed with building the noncommutative 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 noncommutative Standard Model (NCSM). In addition, among several peculiar features of our model, we address the inherent CP violation and new neutrino interactions.

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.

We study the thermodynamics of degenerate electron and charged vector boson gases in very intense magnetic fields. In degenerate conditions of the electron gas, the pressure transverse to the magnetic field B may vanish, leading to a transverse collapse. For W bosons an instability arises because the magnetization diverges at the critical field B(c) = M(2)(W)/e. If the magnetic field is self-consistently maintained, the maximum value it can take is of the order of 2B(c)/3, but in any case the system becomes unstable and collapses.

No abstract