The functional-integral quantization of non-Abelian gauge theories is affected by the Gribov Their occurrence (lack of global cross-sections from the point of view of differential geometry) is called Gribov ambiguity, and is here presented within the framework of a global approach to quantum field theory. We first give a simple (standard) example for the SU (2) group and spherically symmetric potentials, then we discuss this phenomenon in general relativity, and recent developments, including lattice calculations.
We show that if photon possesses a tiny but non-vanishing mass the universe
cannot be electrically neutral. Cosmological electric asymmetry could be
generated either at an early stage by different evaporation rates of primordial
black holes with respect to positively and negatively charged particles or by
predominant capture of protons in comparison to electrons by heavy galactic
black holes in contemporary universe. An impact of this phenomenon on the
generation of large scale magnetic fields and on the universe acceleration is
considered.Comment: 15 pages, no figures, text added, typos corrected, refs. improve
Starting from the equation of motion of the quantum operator of a real scalar field ϕ in de Sitter space-time, a simple differential equation is derived which describes the evolution of quantum fluctuations ϕ 2 of this field. Full de Sitter invariance is assumed and no ad hoc infrared cutoff is introduced. This equation is solved explicitly and in massive case our result agrees with the standard one. In massless case the large time behavior of our solution differs by sign from the expression found in earlier papers. A possible cause of discrepancy may be a spontaneous breaking of de Sitter invariance.
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