We find dispersion laws for the photon propagating in the presence of mutually orthogonal constant external electric and magnetic fields in the context of the $theta $-expanded noncommutative QED. We show that there is no birefringence to the first o
rder in the noncommutativity parameter $% theta .$ By analyzing the group velocities of the photon eigenmodes we show that there occurs superluminal propagation for any direction. This phenomenon depends on the mutual orientation of the external electromagnetic fields and the noncommutativity vector. We argue that the propagation of signals with superluminal group velocity violates causality in spite of the fact that the noncommutative theory is not Lorentz-invariant and speculate about possible workarounds.
We propose a generalizing gauge-invariant model of propagating torsion which couples to the Maxwell field and to charged particles. As a result we have an Abelian gauge invariant action which leads to a theory with nonzero torsion and which is consistent with available experimental data.
We return to the description of the damped harmonic oscillator by means of a closed quantum theory with a general assessment of previous works, in particular the Bateman-Caldirola-Kanai model and a new model recently proposed by one of the authors. W
e show the local equivalence between the two models and argue that latter has better high energy behavior and is naturally connected to existing open-quantum-systems approaches.
By using a coherent state quantization of paragrassmann variables, operators are constructed in finite Hilbert spaces. We thus obtain in a straightforward way a matrix representation of the paragrassmann algebra. This algebra of finite matrices reali
zes a deformed Weyl-Heisenberg algebra. The study of mean values in coherent states of some of these operators lead to interesting conclusions.
We analyze renormalizability properties of noncommutative (NC) theories with a bifermionic NC parameter. We introduce a new 4-dimensional scalar field model which is renormalizable at all orders of the loop expansion. We show that this model has an i
nfrared stable fixed point (at the one-loop level). We check that the NC QED (which is one-loop renormalizable with usual NC parameter) remains renormalizable when the NC parameter is bifermionic, at least to the extent of one-loop diagrams with external photon legs. Our general conclusion is that bifermionic noncommutativity improves renormalizablility properties of NC theories.
