Introduction to Quantum Fields on a Lattice

This book provides a concise introduction to quantum fields on a lattice, explaining fundamental concepts such as triviality of Higgs fields and confinement of quarks and gluons into hadrons. It also covers chiral symmetry and chiral gauge theory, as well as quantized non-Abelian gauge fields, scaling, and universality.

Format: Paperback / softback
Publication date: 27 July 2023
Publisher: Cambridge University Press

This comprehensive book offers a concise yet thorough introduction to quantum fields on a lattice, providing a precise and non-perturbative definition of quantum field theory by replacing continuous space-time with a discrete set of points on a lattice. Through detailed explanations and concrete examples, the path integral on the lattice is elucidated using weak and strong coupling expansions. Fundamental concepts such as the triviality of Higgs fields, confinement of quarks and gluons into hadrons, and chiral symmetry and chiral gauge theory are introduced and illustrated with the results of numerical simulations. Additionally, the book delves into quantized non-Abelian gauge fields, scaling, and universality, making it an invaluable resource for advanced undergraduate and graduate courses. Originally published in 2002, this title has been reissued as an Open Access publication on Cambridge Core.

Introduction:
Quantum fields on a lattice offer a novel framework for understanding the behavior of particles in the quantum realm. By replacing continuous space-time with a discrete set of points on a lattice, we can obtain a precise and non-perturbative definition of quantum field theory. This book aims to provide a comprehensive introduction to this topic, covering key concepts and applications.

Definition of Quantum Field Theory on a Lattice:
The path integral on the lattice is a fundamental concept in quantum field theory on a lattice. It is a mathematical expression that describes the behavior of particles in a quantum field, taking into account the interactions between them. Weak and strong coupling expansions are used to describe the behavior of particles on the lattice, allowing for a detailed understanding of their interactions and properties.

Examples and Simulations:
The book provides numerous examples and simulations to illustrate the concepts discussed. These examples range from simple to complex, and they help to clarify the theoretical framework and make it more accessible to readers. The use of numerical simulations allows for a more realistic representation of particle behavior, and it enables researchers to study the effects of various parameters and interactions on the system.

Fundamental Concepts:
Several fundamental concepts are introduced in the book, including the triviality of Higgs fields, confinement of quarks and gluons into hadrons, and chiral symmetry and chiral gauge theory. These concepts are essential for understanding the behavior of particles in the quantum realm and have significant implications for modern physics.

Chiral Symmetry and Chiral Gauge Theory:
Chiral symmetry and chiral gauge theory are important topics in quantum field theory. They describe the behavior of particles in a magnetic field and have applications in various fields, such as particle physics, cosmology, and condensed matter physics. The book provides an introduction to these topics, including their mathematical foundations and their applications.

Quantized Non-Abelian Gauge Fields:
Quantized non-Abelian gauge fields are a fundamental concept in quantum field theory. They describe the behavior of particles in a magnetic field and have applications in various fields, such as particle physics, cosmology, and condensed matter physics. The book provides an introduction to these topics, including their mathematical foundations and their applications.

Scaling and Universality:
Scaling and universality are important concepts in quantum field theory. They describe the behavior of systems at large scales and have implications for understanding the behavior of the universe as a whole. The book provides an introduction to these topics, including their mathematical foundations and their applications.

Conclusion:
Quantum fields on a lattice offer a powerful tool for understanding the behavior of particles in the quantum realm. This book provides a comprehensive introduction to this topic, covering key concepts and applications. By providing detailed explanations and examples, the book aims to make quantum field theory more accessible to readers and researchers alike.

ISBN-13: 9781009402750