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In this work we present the study of the renormalizability of the Generalized Quantum Electrodynamics ($GQED_{4}$). We begin the article by reviewing the on-shell renormalization scheme applied to $GQED_{4}$. Thereafter, we calculate the explicit expressions for all the counter-terms at one-loop approximation and discuss the infrared behavior of the theory as well. Next, we explore some properties of the effective coupling of the theory which would give an indictment of the validity regime of theory: $m^{2} leq k^{2} < m_{P}^{2}$. Afterwards, we make use of experimental data from the electron anomalous magnetic moment to set possible values for the theory free parameter through the one-loop contribution of Podolsky mass-dependent term to Paulis form factor $F_{2}(q^{2})$.
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We study the renormalizability of quantum gravity near two dimensions. Our formalism starts with the tree action which is invariant under the volume preserving diffeomorphism. We identify the BRS invariance which originates from the full diffeomorphism invariance. We study the Ward-Takahashi identities to determine the general structure of the counter terms. We prove to all orders that the counter terms can be supplied by the coupling and the wave function renormalization of the tree action. The bare action can be constructed to be the Einstein action form which ensures the full diffeomorphism invariance.
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 Diracs methodology by determining the Hamiltonian transition amplitude. In particular, the covariant transition amplitude is established in the generalized non-mixing Lorenz gauge. The complete Greens functions are obtained through functional methods and the theorys renormalizability is also detailed presented. Next, the radiative corrections for the Greens functions at $alpha $-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 $alpha ^{2}$-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 higher-order contributions. Lastly, an energy range where the theory is well defined: $m^{2}ll k^{2}<m_{p}^{2}$ was also found by evaluating the effective coupling for the GSDKP.
Quantum electrodynamics is considered to be a trivial theory. This is based on a number of evidences, both numerical and analytical. One of the strong indications for triviality of QED is the existence of the Landau pole for the running coupling. We show that by treating QED as the leading order approximation of an effective field theory and including the next-to-leading order corrections, the Landau pole is removed. Therefore, we conclude that the conjecture, that for reasons of self-consistency, QED needs to be trivial is a mere artefact of the leading order approximation to the corresponding effective field theory.
We confirm the stability of Podolskys generalized electrodynamics by constructing a series of two-parametric bounded conserved quantities which includes the canonical energy-momentum tensors. In addition, we evaluate the transition-amplitude of this higher derivative system in BV antifield formalism and obtain the desirable generalized radiation gauge condition by choosing appropriate gauge-fixing fermion. Within the framework of Lagrangian BRST cohomology, we present the constructions of consistent interactions in Podolskys model and when concentrating on the antighost number zero part of the master action after deformation process, we get the non-Abelian extensions of the Podolskys theory. Furthermore, we calculate the number of physical degrees of freedom in the resulting higher derivative system utilizing Dirac-Bergmann algorithm method and show that it is unchanged if the consistent interactions are included into the free theory.
The aim of this work is to discuss some aspects of the reduction of order formalism in the context of the Fadeev-Jackiw symplectic formalism, both at the classical and the quantum level. We start by reviewing the symplectic analysis in a regular theory (a higher derivative massless scalar theory), both using the Ostrogradsky prescription and also by reducing the order of the Lagrangian with an auxiliary field, showing the equivalence of these two approaches. The interpretation of the degrees of freedom is discussed in some detail. Finally, we perform the similar analysis in a singular higher derivative gauge theory (the Podolsky electrodynamics), in the reduced order formalism: we claim that this approach have the advantage of clearly separating the symplectic structure of the model into a Maxwell and a Proca (ghost) sector, thus complementing the understanding of the degrees of freedom of the theory and simplifying calculations involving matrices.
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