Renormalization of generalized scalar Duffin-Kemmer-Petiau electrodynamics

Abstract

The main goal of this work is to study systematically the quantum aspects of the interaction between scalar particles in the framework of Generalized Scalar Duffin-Kemmer-Petiau Electrodynamics (GSDKP). For this purpose the theory is quantized after a constraint analysis following Dirac's methodology by determining the Hamiltonian transition amplitude. In particular, the covariant transition amplitude is established in the generalized non-mixing Lorenz gauge. The complete Green's functions are obtained through functional methods and the theory's renormalizability is also detailed presented. Next, the radiative corrections for the Green's functions at α-order are computed; and, as it turns out, an unexpected m P -dependent divergence on the DKP sector of the theory is found. Furthermore, in order to show the effectiveness of the renormalization procedure on the present theory, a diagrammatic discussion on the photon self-energy and vertex part at α 2 -order are presented, where it is possible to observe contributions from the DKP self-energy function, and then analyse whether or not this novel divergence propagates to higherorder contributions. Lastly, an energy range where the theory is well defined: m 2 k 2 < m 2 p was also found by evaluating the effective coupling for the GSDKP. * rbufalo@ift.unesp.br † cardoso@ift.unesp.br ‡ nogueira@ift.unesp.br § pimentel@ift.unesp.br 1 arXiv:1510.04877v1 [hep-th] 16 Oct 20151 The historical development of this theory, among others, can be found in [1,2]. 2 Forsooth, Géhéniau decomposed Petiau's sixteen-dimensional algebra in terms of irreducible representations of ten dimensions (representing particles of spin 1), five dimensions (representing particles of spin 0), and a trivial representation without physical meaning of one dimension [7].3 This formalism can be extended to describe non-Abelian and gravitational fields [11].

BRST symmetry and fictitious parameters

“…In BFV formalism the method of Faddeev-Popov-DeWitte is elucidated and questions about attainability of gauges are discussed clearly. This work complements previous studies of the authors on covariant quantum dynamics [37,46] and opens the door to a more complete approach, involving the Matsubara-Fradkin formalism of quantum covariant dynamics in equilibrium [47].…”

“…attainable, but this condition increases the order of the derivatives in the Lagrangian. On the other hand, there is other gauge condition known as no-mixing gauge [36,37]…”

Radiative Corrections in GSDKP

“…This raises the question of what is role of this algebra in the study of the quantum interaction between the DKP fields (mesons) and Podolsky fields (generalized photons). The next step would be formulate the renormalization program and it is possible to study GSDKP at thermodynamical equilibrium with the Matsubara-Fradkin formalism [5,6].…”

Transition amplitude, partition function and the role of physical degrees of freedom in gauge theories

“…With the functional generator of GSDKP besides studying the Dyson-Schwinger covariant quantum equations and Ward-Takahashi identities from quantum gauge symmetry, we could establish the multiplicative renormalization procedure in the mass shell. An explicit calculation of the first radiative corrections (1-loop) associated with the photon propagator, meson propagator, vertex, photon-photon four point function utilizing the dimensional regularization method, where the gauge symmetry is manifest, will show two ways of evaluating the renormalization conditions for the pole and residue, due to DKP trilinear algebra, and we will also see that the DKP algebra ensures the functioning of the Ward-Takahashi (WT) identities in the first radiative corrections of the vertex and photon-photon four point function prohibiting UV divergences [47].…”