Gauge theory of elementary particle physics: Problems and solutions (original) (raw)

Gauge-Field Theory of Particles. II. Fermions

Physical Review D, 1972

We construct classes of Lagrangians which describe families of fermions containing an infinite number of particles. The Lagrangians depend on Rarita-Schwinger fields with k Lorentz indices, k =1, 2, ... , which have bilinear interactions among themselves. These Lagrangians are invariant under gauge transformations of the second kind. The physical states appear as the normal modes of these field theories, and by suitable choices of the masses of the underlying gauge fields, the physical fermions can be made to lie on linearly rising Regge trajectories. The currents have nontrivial diagonal matrix elements, and also have matrix elements between states of different spin. By considering time-ordered products of currents between single-particle states, we are able to construct onand off-mass-shell N-point functions in the narrow-resonance approximation.

Gauge Theory in Elementary Particle Physics: A Comprehensive Overview

RG, 2024

Gauge theory has revolutionized our understanding of elementary particles and their interactions. This research paper explores the principles and applications of gauge theory in particle physics, focusing on its development, theoretical framework, and experimental confirmations. We delve into the fundamental forces, gauge invariance, and the significance of the Standard Model. Additionally, we examine recent advancements and ongoing research in the field.

Gauge Field Theory of Particles. I. Bosons

Physical Review D, 1971

We suggest that it is a reasonable approximation to consider the bosons and fermions found in nature as the normal modes of an underlying field theory which is invariant under gauge transformations of the second kind. The field theories for the boson and fermion "trajectories" contain an infinite number of fields with bilinear interactions between nearest neighbors in the index space of the finite-dimensional (2k, 2k) representations of the Lorentz group.

Gauge-independent off-shell fermion self-energies at two loops: The cases of QED and QCD

Physical Review D, 2002

We use the pinch technique formalism to construct the gauge-independent off-shell two-loop fermion self-energy, both for Abelian (QED) and non-Abelian (QCD) gauge theories. The new key observation is that all contributions originating from the longitudinal parts of gauge boson propagators, by virtue of the elementary tree-level Ward identities they trigger, give rise to effective vertices, which do not exist in the original Lagrangian; all such vertices cancel diagrammatically inside physical quantities, such as current correlation functions or S-matrix elements. We present two different, but complementary derivations: First, we explicitly track down the aforementioned cancellations inside two-loop diagrams, resorting to nothing more than basic algebraic manipulations. Second, we present an absorptive derivation, exploiting the unitarity of the S-matrix, and the Ward identities imposed on tree-level and one-loop physical amplitudes by gauge invariance, in the case of QED, or by the underlying Becchi-Rouet-Stora symmetry, in the case of QCD. The propagator-like sub-amplitude defined by means of this latter construction corresponds precisely to the imaginary parts of the effective self-energy obtained in the former case; the real part may be obtained from a (twice subtracted) dispersion relation. As in the one-loop case, the final two-loop fermion self-energy constructed using either method coincides with the conventional fermion self-energy computed in the Feynman gauge.

Inclusive hadron-hadron scattering in the Feynman gauge

Nuclear Physics B, 1985

We analyze the structure of high-energy inclusive hadron-hadron scattering in the Feynman gauge. We show that final-state interactions cancel on a graph-by-graph basis after a sum over final states. We go on to show that the leading high-energy behavior of disconnected parton scatterings in the Feynman gauge is the same as in physical gauges, after a sum over gaugeinvariant sets of graphs. We point out that this result is in general not true for individual diagrams in the Feynman gauge, where ghion longitudinal degrees of freedom may lead to power infrared divergences. Our results justify the use of the Feynman gauge in arguments for factorization of leading-twist cross sections, and also in the analysis of disconnected multiparton scattering.

An introduction to quantum field theory

1995

Even the uninitiated will know that Quantum Field Theory cannot be introduced systematically in just four lectures. I try to give a reasonably connected outline of part of it, from second quantization to the path-integral technique in Euclidean space, where there is an immediate connection with the rules for Feynman diagrams and the partition function of Statistical Mechanics.

New approach to the calculation ofF1(α)in massless quantum electrodynamics

Physical Review D, 1977

F,(a) is defined as the contribution of the one-fermion-loop diagrams to the divergent part of the photon propagator in massless quantum electrodynamics. To sixth order, the perturbation expansion of F,(a) has rational coefficients: F,(a) = (2/3)(a/2~) + (a/2n.)'-(1/4)(a/2n.)' +.".It is not known whether the next term in this series is a rational number; however, we propose a new method, which uses integration by parts, for evaluating Feynman integrals which give rational numbers. Using this method we easily rederive the first three terms in the series for F,(a) and three other two-loop integrals, including the fourth-order correction to the vertex function I "(p,p). We believe that our new integration techniques are powerful enough to evaluate the fourth term in the series for F,(a) if it is a rational number.