Gauge theory of elementary particle Physics (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 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.

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.

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-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.

Path Integrals in Quantum Physics

Lecture Notes in Physics Monographs

These lectures are intended for graduate students who want to acquire a working knowledge of path integral methods in a wide variety of fields in physics. In general the presentation is elementary and path integrals are developed in the usual heuristic, non-mathematical way for application in many diverse problems in quantum physics. Three main parts deal with path integrals in non-relativistic quantum mechanics, manybody physics and field theory and contain standard examples (quadratic Lagrangians, tunneling, description of bosons and fermions etc.) as well as specialized topics (scattering, dissipative systems, spin & color in the path integral, lattice methods etc.). In each part simple Fortran programs which can be run on a PC, illustrate the numerical evaluation of (Euclidean) path integrals by Monte-Carlo or variational methods. Also included are the set of problems which accompanied the lectures and their solutions. Content 0. Contents First, an overview over the planned topics. The subsections marked by ⋆ are optional and may be left out if there is no time available whereas the chapters printed in blue deal with basic concepts. Problems from the optional chapters or referring to "Details" are marked by a ⋆ as well.

Path Integrals in Quantum Physics Lectures given at ETH Zurich

2016

These lectures are intended for graduate students who want to acquire a working knowledge of path integral methods in a wide variety of fields in physics. In general the presentation is elementary and path integrals are developed in the usual heuristic, non-mathematical way for application in many diverse problems in quantum physics. Three main parts deal with path integrals in non-relativistic quantum mechanics, manybody physics and field theory and contain standard examples (quadratic Lagrangians, tunneling, description of bosons and fermions etc.) as well as specialized topics (scattering, dissipative systems, spin & color in the path integral, lattice methods etc.). In each part simple Fortran programs which can be run on a PC, illustrate the numerical evaluation of (Euclidean) path integrals by Monte-Carlo or variational methods. Also included are the set of problems which accompanied the lectures and their solutions. Content 0. Contents First, an overview over the planned topics. The subsections marked by ⋆ are optional and may be left out if there is no time available whereas the chapters printed in blue deal with basic concepts. Problems from the optional chapters or referring to "Details" are marked by a ⋆ as well.

Nuclear and Particle Physics Section

2000

Polyakov’s spin factor enters as a weight in the path-integral description of particlelike modes propagating in Euclidean space-times, accounting for particle spin. The Fock-Feynman-Schwinger path integral applied to QCD accomodates Polyakov’s spin factor in a natural manner while, at the same time, it identifies Wilson line (loop) operators as sole agents of interaction dynamics among matter and gauge field quanta. A direct application of such a separation between spin content and dynamics is the emergence of master expressions for the perturbative series involving either open or closed fermionic lines which provide new, comprehensive approaches to perturbative QCD. 1. Introductory remarks. The Fock[1]-Feynman[2]-Schwinger[3] path integral, also known as worldline formalism [4-7], constitutes a tool by which one is able to study a quantum field theoretical system in terms of the propagation of its particle quanta. Polyakov’s path integral [8], on the other hand, amounts to a direct...