In physics, lattice gauge theory is the study of gauge theories on a spacetime that has been discretized into a lattice. Gauge theories are important in particle physics, and include the prevailing theories of elementary particles: quantum electrodynamics, quantum chromodynamics (QCD) and particle physics' Standard Model. Non-perturbative gauge theory calculations in continuous spacetime formally involve evaluating an infinite-dimensional path integral, which is computationally intractable. By working on a discrete spacetime, the path integral becomes finite-dimensional, and can be evaluated by stochastic simulation techniques such as the Monte Carlo method. When the size of the lattice is taken infinitely large and its sites infinitesimally close to each other, the continuum gauge theory is recovered. In lattice gauge theory, the spacetime is Wick rotated into Euclidean space and discretized into a lattice with sites separated by distance and connected by links. In the most commonly considered cases, such as lattice QCD, fermion fields are defined at lattice sites (which leads to fermion doubling), while the gauge fields are defined on the links. That is, an element U of the compact Lie group G (not algebra) is assigned to each link. Hence, to simulate QCD with Lie group SU(3), a 3×3 unitary matrix is defined on each link. The link is assigned an orientation, with the inverse element corresponding to the same link with the opposite orientation. And each node is given a value in (a color 3-vector, the space on which the fundamental representation of SU(3) acts), a bispinor (Dirac 4-spinor), an nf vector, and a Grassmann variable. Thus, the composition of links' SU(3) elements along a path (i.e. the ordered multiplication of their matrices) approximates a path-ordered exponential (geometric integral), from which Wilson loop values can be calculated for closed paths. The Yang–Mills action is written on the lattice using Wilson loops (named after Kenneth G. Wilson), so that the limit formally reproduces the original continuum action.

About this result
This page is automatically generated and may contain information that is not correct, complete, up-to-date, or relevant to your search query. The same applies to every other page on this website. Please make sure to verify the information with EPFL's official sources.
Related courses (8)
PHYS-432: Quantum field theory II
The goal of the course is to introduce relativistic quantum field theory as the conceptual and mathematical framework describing fundamental interactions such as Quantum Electrodynamics.
PHYS-502: Interacting quantum matter
This course presents modern aspects of theoretical condensed matter physics with interfaces to statistical physics, quantum information theory, quantum field theory and quantum simulation.
PHYS-702: Advanced Quantum Field Theory
The course builds on the course QFT1 and QFT2 and develops in parallel to the course on Gauge Theories and the SM.
Show more
Related lectures (28)
Large N Expansion: Vector Models
Explores the Large N expansion in vector models, focusing on matrix models, gauge theories, and the Hooft coupling.
QED: Gauge Theories
Covers Quantum Electrodynamics (QED), instantons, Feynman rules, and gauge theories in modern particle physics.
Quantum Field Theory II: Gauge Theories
Explores Quantum Field Theory II, emphasizing Gauge Theories, including QED, fermion masses, vector bosons, and the Higgs mechanism.
Show more
Related publications (49)

The ABCD of topological recursion

Nicolas Gerson Orantin

Kontsevich and Soibelman reformulated and slightly generalised the topological recursion of [43], seeing it as a quantisation of certain quadratic Lagrangians in T*V for some vector space V. KS topological recursion is a procedure which takes as initial da ...
San Diego2024

QCD worldsheet axion from the bootstrap

Andrea Guerrieri, Victor Gorbenko

The worldsheet axion plays a crucial role in the dynamics of the Yang-Mills confining flux tubes. According to the lattice measurements, its mass is of order the string tension and its coupling is close to a certain critical value. Using the S-matrix Boots ...
New York2024

CosmoLattice: A modern code for lattice simulations of scalar and gauge field dynamics in an expanding universe

Daniel Garcia Figueroa, Adrien Florio, Wessel Valkenburg, Francisco Torrenti

This paper describes CosmoGattice, a modern package for lattice simulations of the dynamics of interacting scalar and gauge fields in an expanding universe. CosmoGattice incorporates a series of features that makes it very versatile and powerful: i) it is ...
ELSEVIER2023
Show more
Related concepts (14)
Higgs boson
The Higgs boson, sometimes called the Higgs particle, is an elementary particle in the Standard Model of particle physics produced by the quantum excitation of the Higgs field, one of the fields in particle physics theory. In the Standard Model, the Higgs particle is a massive scalar boson with zero spin, even (positive) parity, no electric charge, and no colour charge that couples to (interacts with) mass. It is also very unstable, decaying into other particles almost immediately upon generation.
Wilson loop
In quantum field theory, Wilson loops are gauge invariant operators arising from the parallel transport of gauge variables around closed loops. They encode all gauge information of the theory, allowing for the construction of loop representations which fully describe gauge theories in terms of these loops. In pure gauge theory they play the role of order operators for confinement, where they satisfy what is known as the area law. Originally formulated by Kenneth G.
Lattice field theory
In physics, lattice field theory is the study of lattice models of quantum field theory, that is, of field theory on a space or spacetime that has been discretised onto a lattice. Although most lattice field theories are not exactly solvable, they are of tremendous appeal because they can be studied by simulation on a computer, often using Markov chain Monte Carlo methods. One hopes that, by performing simulations on larger and larger lattices, while making the lattice spacing smaller and smaller, one will be able to recover the behavior of the continuum theory as the continuum limit is approached.
Show more

Graph Chatbot

Chat with Graph Search

Ask any question about EPFL courses, lectures, exercises, research, news, etc. or try the example questions below.

DISCLAIMER: The Graph Chatbot is not programmed to provide explicit or categorical answers to your questions. Rather, it transforms your questions into API requests that are distributed across the various IT services officially administered by EPFL. Its purpose is solely to collect and recommend relevant references to content that you can explore to help you answer your questions.