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Quantum Field Theory (QFT) on the Lattice

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Lattice Quantum Chromodynamics

Part of the book series: SpringerBriefs in Physics ((SpringerBriefs in Physics))

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Abstract

In 1964, Gell-Mann [1] and Zweig [2] proposed that hadrons, the particles which experience strong interactions, are made of quarks. Quarks are confined within hadrons and never seen in isolation. Electron-nucleon scattering experiments at large momentum transfer could be explained by assuming the nucleon is made of almost-free point-like constituents called partons [3–5].

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Notes

  1. 1.

    In the space of complex fields \(\varphi (\underline{x})\) the scalar product is defined as \((\varphi ,{\varphi }')=a^3\sum _{\underline{x}}\varphi (\underline{x})^*{\varphi }'(\underline{x})\). The adjoint \(\hat{A}^\dagger \) of an operator \(\hat{A}\) acting on the fields is defined as \((\varphi ,\hat{A}{\varphi }')=(\hat{A}^\dagger \varphi ,{\varphi }')\). A self-adjoint operator has \(\hat{A}^\dagger =\hat{A}\).

  2. 2.

    It is not necessary for the lattice action to reproduce the continuum action at the classical level. There may be a larger class of actions which share the same quantum continuum limit despite they do not reproduce the classical continuum form, see e.g. the so called topological actions for the non-linear sigma model [36].

  3. 3.

    http://luscher.web.cern.ch/luscher/openQCD/.

  4. 4.

    http://www.scholarpedia.org/article/Lattice_quantum_field_theory.

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Authors and Affiliations

  1. Department of Physics, School of Mathematics and Natural Sciences, University of Wuppertal, Wuppertal, 42119, Germany

    Francesco Knechtli

  2. Department of Mathematics, School of Mathematics and Natural Sciences, University of Wuppertal, Wuppertal, 42119, Germany

    Michael Günther

  3. School of Mathematics, Trinity College Dublin, Dublin 2, Ireland

    Michael Peardon

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  1. Francesco Knechtli
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  2. Michael Günther
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  3. Michael Peardon
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Correspondence to Francesco Knechtli .

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Knechtli, F., Günther, M., Peardon, M. (2017). Quantum Field Theory (QFT) on the Lattice. In: Lattice Quantum Chromodynamics. SpringerBriefs in Physics. Springer, Dordrecht. https://doi.org/10.1007/978-94-024-0999-4_1

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