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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 general, is closely related to) the starting point module M_0. We show that for a class of indecomposable Poincare modules the resulting theory is a Lagrangian gauge theory of the mixed-symmetry higher spin fields. The procedure is based on constructing the parent formulation of the theory. The Labastida formulation and the unfolded description of the mixed symmetry fields are reproduced through the appropriate reductions of the parent formulation. As an independent check we show that in the momentum representation the solutions form a unitary irreducible Poincare module determined by the respective module of the Wigner little group.
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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.
It is by now well known that the Poincare group acts on the Moyal plane with a twisted coproduct. Poincare invariant classical field theories can be formulated for this twisted coproduct. In this paper we systematically study such a twisted Poincare action in quantum theories on the Moyal plane. We develop quantum field theories invariant under the twisted action from the representations of the Poincare group, ensuring also the invariance of the S-matrix under the twisted action of the group . A significant new contribution here is the construction of the Poincare generators using quantum fields.
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 black hole thermodynamics. In the generalized framework of Riemann--Cartan spacetime with both curvature and torsion, the induced gravitational action is obtained for free nonminimally coupled scalar and Dirac fields. For a realistic matter content, the induced Newton constant is obtained to be of the magnitude of the ultraviolet cutoff, which implies that the cutoff is of the order of the Planck mass. Finally, we conjecture that the action for any gauge theory of gravity at low energies can be induced by Sakharovs mechanism. This is explicitly shown by obtaining the Poincare gauge theory of gravity.
In this paper we consider a model of Poincare gauge theory (PGT) in which a translational gauge field and a Lorentz gauge field are actually identified with the Einsteins gravitational field and a pair of ``Yang-Mills field and its partner, respectively.In this model we re-derive some special solutions and take up one of them. The solution represents a ``Yang-Mills field without its partner field and the Reissner-Nordstrom type spacetime, which are generated by a PGT-gauge charge and its mass.It is main purpose of this paper to investigate the interaction of massless Dirac fields with those fields. As a result, we find an interesting fact that the left-handed massless Dirac fields behave in the different manner from the right-handed ones. This can be explained as to be caused by the direct interaction of Dirac fields with the ``Yang-Mills field. Accordingly, the phenomenon can not happen in the behavior of the neutrino waves in ordinary Reissner-Nordstrom geometry. The difference between left- and right-handed effects is calculated quantitatively, considering the scattering problems of the massless Dirac fields by our Reissner-Nordstrom type black-hole.
We consider a general gauge theory with independent generators and study the problem of gauge-invariant deformation of initial gauge-invariant classical action. The problem is formulated in terms of BV-formalism and is reduced to describing the general solution to the classical master equation. We show that such general solution is determined by two arbitrary generating functions of the initial fields. As a result, we construct in explicit form the deformed action and the deformed gauge generators in terms of above functions. We argue that the deformed theory must in general be non-local. The developed deformation procedure is applied to Abelian vector field theory and we show that it allows to derive non-Abelain Yang-Mills theory. This procedure is also applied to free massless integer higher spin field theory and leads to local cubic interaction vertex for such fields.
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