Editing Lattice field theory

{{Short description|Quantum field theory on a lattice}}
[[File:Square_grid_graph.svg|thumb|260x260px|In lattice field theory, space or spacetime is discretised onto a lattice.]]
{{Renormalization and regularization}}
In [[physics]], '''lattice field theory''' is the study of [[lattice model (physics)|lattice models]] of [[quantum field theory]]. This involves studying field theory on a space or spacetime that has been discretised onto a [[lattice (group)|lattice]].

==Details==
Although most lattice field theories are not [[exactly solvable]], they are immensely appealing due to their feasibility for computer simulation, 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. 

Just as in all lattice models, numerical simulation provides access to field configurations that are not accessible to [[perturbation theory]], such as [[soliton]]s. Similarly, non-trivial [[vacuum state]]s can be identified and examined. 

The method is particularly appealing for the quantization of a [[gauge theory]] using the [[Wilson action]]. Most quantization approaches maintain [[Poincaré invariance]] manifest but sacrifice manifest [[gauge symmetry]] by requiring  [[gauge fixing]]. It's only after [[renormalization]] that [[gauge invariance]] can be recovered. Lattice field theory differs from these in that it keeps '''manifest gauge invariance''', but sacrifices manifest Poincaré invariance—recovering it only after [[renormalization]]. The articles on [[lattice gauge theory]] and [[lattice QCD]] explore these issues in greater detail.

==See also==
* [[Fermion doubling]]

==Further reading==
* Creutz, M., ''Quarks, gluons and lattices'', Cambridge University Press, Cambridge, (1985). {{ISBN|978-0521315357}} (renewed version: (2023) {{ISBN|978-1009290395}})
* DeGrand, T., DeTar, C., ''[https://books.google.com/books?id=r8bICgAAQBAJ&q=%22Lattice+gauge+theory%22 Lattice Methods for Quantum Chromodynamics]'', World Scientific, Singapore, (2006). {{ISBN|978-9812567277}}
* Gattringer, C., Lang, C. B., ''Quantum Chromodynamics on the Lattice'', Springer, (2010). {{ISBN|978-3642018497}}
* Knechtli, F., Günther, M., Peardon, M., ''Lattice Quantum Chromodynamics: Practical Essentials'', Springer, (2016). {{ISBN|978-9402409970}}
* Lin, H., Meyer, H.B., ''Lattice QCD for Nuclear Physics'', Springer, (2014). {{ISBN|978-3319080215}}
* Makeenko, Y., ''Methods of contemporary gauge theory'', Cambridge University Press, Cambridge, (2002). {{ISBN|0-521-80911-8}}.
* Montvay, I., Münster, G., ''[https://books.google.com/books?id=NHZshmEBXhcC&q=%22Lattice+gauge+theory%22 Quantum Fields on a Lattice]'', Cambridge University Press, Cambridge, (1997). {{ISBN|978-0521599177}}
* Rothe, H., ''Lattice Gauge Theories, An Introduction'', World Scientific, Singapore, (2005). {{ISBN|978-9814365857}}
* [[Jan Smit (physicist)|Smit, J.]], ''Introduction to Quantum Fields on a Lattice'', Cambridge University Press, Cambridge, (2002). {{ISBN|978-0521890519}}

[[Category:Lattice field theory| ]]


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