Space-Time Noncommutativity, Discreteness of Time and Unitarity

Violation of unitarity for noncommutative field theory on compact space-times is considered. Although such theories are free of ultraviolet divergences, they still violate unitarity while in a usual field theory such a violation occurs when the theory is nonrenormalizable. The compactness of space-like coordinates implies discreteness of the time variable which leads to appearance of unphysical modes and violation of unitarity even in the absence of a star-product in the interaction terms. Thus, this conclusion holds also for other quantum field theories with discrete time. Violation of causality, among others, occurs also as the nonvanishing of the commutation relations between observables at space-like distances with a typical scale of noncommutativity. While this feature allows for a possible violation of the spin-statistics theorem, such a violation does not rescue the situation but makes the scale of causality violation as the inverse of the mass appearing in the considered model, i.e., even more severe. We also stress the role of smearing over the noncommutative coordinates entering the field operator symbols.Comment: 10 pages, plain LaTe

Astrophysical Implications of the Superstring-Inspired E_6 Unification and Shadow Theta-Particles

We have developed a concept of parallel existence of the ordinary (O) and mirror (M), or shadow (Sh) worlds. E_6 unification, inspired by superstring theory, restores the broken mirror parity at the scale ~ 10^18 GeV. With the aim to explain the tiny cosmological constant, we consider the breakings: E_6 -> SO(10) X U(1)_Z - in the O-world, and E'_6 -> SU(6)' X SU(2)'_\theta - in the Sh-world. We assume the existence of shadow \theta-particles and the low energy symmetry group SU(3)'_C X SU(2)'_L X SU(2)'_\theta X U(1)'_Y in the shadow world, instead of the Standard Model. The additional non-Abelian SU(2)'_\theta group with massless gauge fields, "thetons", has a macroscopic confinement radius 1/\Lambda'_\theta. The assumption that \Lambda'_\theta\approx 2.3 X 10^-3 eV explains the tiny cosmological constant given by recent astrophysical measurements. Searching for the Dark Matter (DM), it is possible to observe and study various signals of theta-particles.Comment: 6 pages, 2 figures, presented at "Invisble Universe International Conference", Palais de l'UNESCO, Paris, France, June 29 - July 3, 200

Standard Model and Graviweak Unification with (Super)Renormalizable Gravity. Part I: Visible and Invisible Sectors of the Universe

We develop a self-consistent $Spin(4,4)$-invariant model of the unification of gravity with weak $SU(2)$ gauge and Higgs fields in the visible and invisible sectors of our Universe. We consider a general case of the graviweak unification, including the higher-derivative super-renormalizable theory of gravity, which is a unitary, asymptotically-free and perturbatively consistent theory of the quantum gravity.Comment: 27 page