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Gribov ambiguities in non-Abelian gauge theories

Granström, Fredrik LU (2021) FYTK02 20211
Theoretical Particle Physics
Abstract
This thesis investigates the quantization of field theories using the functional integral formalism. Gauge invariance necessitates a gauge-fixing procedure that chooses a unique field configuration from each gauge orbit. Faddeev and Popov suggested an adjustment to the action that implements gauge fixing in this framework, however it has been found that this procedure fails to uniquely fix the gauge of non-Abelian gauge theories. This problem is known as the Gribov ambiguity. This thesis reproduces and discusses the work of Gribov, and it is illustrated how the Gribov horizons divide the functional space into regions Cn. Then, the Coulomb gauge of SU(2) is considered as an explicit example of Gribov ambiguities. The equation of the Gribov... (More)
This thesis investigates the quantization of field theories using the functional integral formalism. Gauge invariance necessitates a gauge-fixing procedure that chooses a unique field configuration from each gauge orbit. Faddeev and Popov suggested an adjustment to the action that implements gauge fixing in this framework, however it has been found that this procedure fails to uniquely fix the gauge of non-Abelian gauge theories. This problem is known as the Gribov ambiguity. This thesis reproduces and discusses the work of Gribov, and it is illustrated how the Gribov horizons divide the functional space into regions Cn. Then, the Coulomb gauge of SU(2) is considered as an explicit example of Gribov ambiguities. The equation of the Gribov pendulum is derived, and the properties of its solutions are discussed. The thesis concludes with a short review of the consequences of the Gribov ambiguity, and of the possible restrictions to the integration range that have been proposed as a resolution to the problem. (Less)
Popular Abstract
The quantum world has often been described as a bizarre place full of obscure phenomena, and rightly so. Particles can exist in multiple places simultaneously, or tunnel through walls to spontaneously show up on the other side---not to mention Schrödinger’s famous cat, which is both alive and dead at the same time. The quantum world appears very different from our own, and one would be forgiven for asking what impact quantum physics, and its subdiscipline quantum field theory, has on our daily lives.

Quantum field theory studies the fundamental particles in nature and how they interact with each other. It is crucial for our understanding of nuclear physics, where it helps describe the forces that hold atomic nuclei together or cause... (More)
The quantum world has often been described as a bizarre place full of obscure phenomena, and rightly so. Particles can exist in multiple places simultaneously, or tunnel through walls to spontaneously show up on the other side---not to mention Schrödinger’s famous cat, which is both alive and dead at the same time. The quantum world appears very different from our own, and one would be forgiven for asking what impact quantum physics, and its subdiscipline quantum field theory, has on our daily lives.

Quantum field theory studies the fundamental particles in nature and how they interact with each other. It is crucial for our understanding of nuclear physics, where it helps describe the forces that hold atomic nuclei together or cause radioactive decay. Further, experiments in quantum field theory demanded the development of large-scale superconducting magnets, which later allowed for the invention of the MRI scanners found at hospitals all around the world. It is in this way that the pursuit of quantum field theory leaves behind ideas and technologies that can be used by other disciplines of science or medicine, like a kind family who plow the snow off their neighbour's driveway. These are just a few examples of how discoveries in quantum field theory can have a positive impact on our everyday life.

The modern description of quantum field theory dates back to the 1960’s, when it was discovered that protons and neutrons are not indivisible as was previously thought. Rather, they have constituent particles called quarks, which bind together in groups of three. The strong force is what binds these quarks together, just like glue that holds objects together. The particles which are responsible for this type of interaction are aptly named gluons, and their behaviour is described by quantum field theory. Without the presence of the strong force, quarks would not come together to form the protons and neutrons that make up everything we see around us. These miniature glue particles are necessary to our entire existence.

Making calculations in quantum field theory is very cumbersome, so particle collisions are often studied using computer simulations. Like a busy traffic intersection at rush hour, the insides of protons and neutrons are messy and chaotic. Quarks whiz around at velocities close to the speed of light, while virtual particles pop in and out of existence, all held together by an overflowing amount of gluons. Like cars, gluons have to be aware of their surroundings on the way to their destination. And as traffic congests, the strength of the interaction between gluons and quarks increases drastically. The aim of this thesis is to address this subatomic traffic jam that arises in quantum field theory by reviewing the Gribov Ambiguity. In particular, it investigates an over-counting problem that arises because quarks and gluons can rotate in strange ways that other particles cannot, which makes these kinds of particle collisions more complex than electromagnetic interactions. The calculations in this thesis can, for instance, be used to modify the description of how slow-moving gluons are transmitted through space and time. Hopefully, this could help facilitate future computer simulations of particle collisions. (Less)
Please use this url to cite or link to this publication:
author
Granström, Fredrik LU
supervisor
organization
course
FYTK02 20211
year
type
M2 - Bachelor Degree
subject
language
English
id
9055341
date added to LUP
2021-06-24 09:20:54
date last changed
2021-06-24 09:20:54
@misc{9055341,
  abstract     = {{This thesis investigates the quantization of field theories using the functional integral formalism. Gauge invariance necessitates a gauge-fixing procedure that chooses a unique field configuration from each gauge orbit. Faddeev and Popov suggested an adjustment to the action that implements gauge fixing in this framework, however it has been found that this procedure fails to uniquely fix the gauge of non-Abelian gauge theories. This problem is known as the Gribov ambiguity. This thesis reproduces and discusses the work of Gribov, and it is illustrated how the Gribov horizons divide the functional space into regions Cn. Then, the Coulomb gauge of SU(2) is considered as an explicit example of Gribov ambiguities. The equation of the Gribov pendulum is derived, and the properties of its solutions are discussed. The thesis concludes with a short review of the consequences of the Gribov ambiguity, and of the possible restrictions to the integration range that have been proposed as a resolution to the problem.}},
  author       = {{Granström, Fredrik}},
  language     = {{eng}},
  note         = {{Student Paper}},
  title        = {{Gribov ambiguities in non-Abelian gauge theories}},
  year         = {{2021}},
}