Introduction to quantum fields on a lattice : 'a robust mate' / Jan Smit.

Format:

Book

Author/Creator:

Smit, Jan, 1943- author.

Series:

Cambridge lecture notes in physics ; 15.

Cambridge lecture notes in physics ; 15

Language:

English

Subjects (All):

Quantum field theory.

Lattice theory.

Physical Description:

1 online resource (xii, 271 pages) : digital, PDF file(s).

Edition:

1st ed.

Place of Publication:

Cambridge : Cambridge University Press, 2002.

Language Note:

English

Summary:

This book provides a concrete introduction to quantum fields on a lattice: a precise and non-perturbative definition of quantum field theory obtained by replacing continuous space-time by a discrete set of points on a lattice. The path integral on the lattice is explained in concrete examples using weak and strong coupling expansions. Fundamental concepts such as 'triviality' of Higgs fields and confinement of quarks and gluons into hadrons are described and illustrated with the results of numerical simulations. The book also provides an introduction to chiral symmetry and chiral gauge theory, as well as quantized non-abelian gauge fields, scaling and universality. Based on the lecture notes of a course given by the author, this book contains many explanatory examples and exercises, and is suitable as a textbook for advanced undergraduate and graduate courses.

Contents:

QED, QCD, and confinement

Scalar field

Path-integral and lattice regularization

Path integral in quantum mechanics

Regularization by discretization

Analytic continuation to imaginary time

Spectrum of the transfer operator

Latticization of the scalar field

Transfer operator for the scalar field

Fourier transformation on the lattice

Free scalar field

Particle interpretation

Back to real time

O(n) models

Goldstone bosons

O(n) models as spin models

Phase diagram and critical line

Weak-coupling expansion

Renormalization

Renormalization-group beta functions

Hopping expansion

Luscher-Weisz solution

Numerical simulation

Real-space renormalization group and universality

Universality at weak coupling

Triviality and the Standard Model

Gauge field on the lattice

QED action

QCD action

Lattice gauge field

Gauge-invariant lattice path integral

Compact and non-compact Abelian gauge theory

Hilbert space and transfer operator

The kinetic-energy operator

Hamiltonian for continuous time

Wilson loop and Polyakov line

U(1) and SU(n) gauge theory

Potential at weak coupling

Asymptotic freedom

Strong-coupling expansion

Potential at strong coupling

Confinement versus screening

Glueballs

Coulomb phase, confinement phase

Mechanisms of confinement

Scaling and asymptotic scaling, numerical results

Fermions on the lattice

Naive discretization of the Dirac action

Species doubling

Wilson's fermion method.

Notes:

Title from publisher's bibliographic system (viewed on 05 Oct 2015).

Includes bibliographical references (p. 261-266) and index.

ISBN:

9780511020780

0-511-14814-3

0-511-58397-4

0-511-02078-3

OCLC:

923616541