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We consider the regularization of a gauge quantum field theory following a modification of the Polchinski proof based on the introduction of a cutoff function. We work with a Poincare invariant deformation of the ordinary point-wise product of fields introduced by Ardalan, Arfaei, Ghasemkhani and Sadooghi, and show that it yields, through a limiting procedure of the cutoff functions, to a regularized theory, preserving all symmetries at every stage. The new gauge symmetry yields a new Hopf algebra with deformed co-structures, which is inequivalent to the standard one.
Starting with an indecomposable Poincare module M_0 induced from a given irreducible Lorentz module we construct a free Poincare invariant gauge theory defined on the Minkowski space. The space of its gauge inequivalent solutions coincides with (in g
It is well-known that de Sitter Lie algebra $mathfrak{o}(1,4)$ contrary to anti-de Sitter one $mathfrak{o}(2,3)$ does not have a standard $mathbb{Z}_2$-graded superextension. We show here that the Lie algebra $mathfrak{o}(1,4)$ has a superextension b
We show how the Newton-Hooke (NH) symmetries, representing a nonrelativistic version of de-Sitter symmetries, can be enlarged by a pair of translation vectors describing in Galilean limit the class of accelerations linear in time. We study the Cartan
We explore Sakharovs seminal idea that gravitational dynamics is induced by the quantum corrections from the matter sector. This was the starting point of the view that gravity has an emergent origin, which soon gained impetus due to the advent of bl
We analyze several integrable systems in zero-curvature form within the framework of $SL(2,R)$ invariant gauge theory. In the Drienfeld-Sokolov gauge we derive a two-parameter family of nonlinear evolution equations which as special cases include the