Worldline Path-Integral Representations for Standard Model Propagators and Effective Actions

We develop the formalism to do worldline calculations relevant for the Standard Model. For that, we first figure out the worldline representations for the free propagators of massless chiral fermions of a single generation and gauge bosons of the Standard Model. Then we extend the formalism to the massive and dressed cases for the fermions and compute the QED vertex. We then go over fermionic one-loop effective actions and anomalies. To our knowledge, in the places where there has been an attempt at deriving the gauge boson propagator, the derivation is somewhat contrived, and we believe our derivation is more straightforward. Moreover, our incorporation of internal degrees of freedom is novel and sports some new features. The derivation of the QED vertex is also new. The treatment of the fermionic one-loop effective actions leads to a particularly economical derivation of chiral anomalies and the gauge anomaly freedom in the Standard Model, improving upon the state of the art in the literature. The appropriate worldline formalism developed thus sets the stage for Standard Model calculations beyond the tree and one-loop cases that incorporate Bern-Kosower type formulae for multiloop amplitudes, relevant for processes at the LHC.

The one-loop θ2 corrections of gauge boson propagator in the noncommutative scalar U(1) theory

In this paper, the quantum corrections of gauge field propagator are investigated in the noncommutative (NC) scalar U(1) gauge theory with Seiberg–Witten map (SWM) method. We focus on the simplest case where the gauge boson couples with a massless complex scalar field. The one-loop divergent corrections at θ2-order are calculated using the background field method. It is found that the divergences can be absorbed by making field redefinitions, leading to a good renormalizability at θ2-order.

Massive Gauge Boson and its generation: Some comments and discussion

Starting with proper application of Feynman gauge in quantum field theory the proposal has been made to remove the unphysical degree of freedom from the gauge boson propagator. It has also been shown that the unphysical degree of freedom corresponding to the goldstone boson and breaking of global U (1) symmetry alone is sufficient for generation of massive gauge boson.

THE NEUTRINO SELF-ENERGY IN A MAGNETIZED MEDIUM

In this work we calculate the neutrino self-energy in the presence of a magnetized medium. The magnetized medium consists of electrons, positrons, neutrinos and a uniform classical magnetic field. The calculation is done assuming that the background magnetic field is weak compared to the W-boson mass squared, as a consequence of which only linear order corrections in the field are included in the W-boson propagator. The electron propagator consists of all order corrections in the background field. Although the neutrino self-energy in a magnetized medium in various limiting cases has been calculated previously, in this paper we produce the most general expression of the self-energy in the absence of the Landau quantization of the charged gauge fields. We calculate the effect of the Landau quantization of the charged leptons on the neutrino self-energy in the general case. Our calculation is specifically suited for situations where the background plasma may be CP symmetric.

DIAGRAMMATICS AND FEYNMAN RULES IN THE LAGRANGIAN THEORY BASED ON THE spl(2,1) GRADED ALGEBRA

From the path-integral method, the diagrammatics and Feynman rules for the Lagrangian theory based on the spl(2,1) graded algebra are constructed. The first-order Lagrangian we have obtained is written in terms of the graded Hubbard operators. By using functional techniques, the correlation generating functional is given in terms of the proper effective Lagrangian of the model. Once the Feynman rules, propagators and vertices were found, a physical discussion about the free propagators is given. Finally, the expressions of the boson self-energy and the renormalized boson propagator are used to study the hole effects on the magnetic properties of the high-T c cuprates.