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

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 [xμ,xν]=iθμν, where θμν 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

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 Poincaré 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 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.

A deformed Schwarzschild solution in noncommutative gauge theory of gravitation is obtained. The gauge potentials (tetrad fields) are determined up to the second order in the noncommutativity parameters Θμν. A deformed real metric is defined and its components are obtained. The noncommutativity correction to the red shift test of general relativity is calculated and it is concluded that the correction is too small to have observable effects. Implications of such a deformed Schwarzschild metric are also mentioned

Recently modified gravitational theories which mimic the behaviour of dark matter, the so-called “Mimetic Dark Matter”, have been proposed. We study the consistency of such theories with respect to the absence of ghost instability and propose a new tensor-vector-scalar theory of gravity, which is a generalization of the previous models of mimetic dark matter with additional desirable features. The original model proposed by Chamseddine and Mukhanov [JHEP 11 (2013) 135] is concluded to describe a regular pressureless dust, presuming that we consider only those configurations where the energy density of the mimetic dust remains positive under time evolution. For certain type of configurations the theory can become unstable. Both alternative modified theories of gravity, which are based on a vector field (tensor-vector theory) or a vector field and a scalar field (tensor-vector-scalar theory), are free of ghost instabilities.