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Mathematical Gauge Theory pp 401–444Cite as

Chapter 7 The Classical Lagrangians of Gauge Theories

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Abstract

Lagrangians can be categorized depending on which types of fields and interactions they involve: there are Lagrangians for free fields, Lagrangians for a single interacting field and Lagrangians for several interacting fields.In this chapter we will discuss the Lagrangians that appear in the Standard Model: the Yang-Mills-Lagrangian, the Klein-Gordon and Higgs Lagrangian, and the Dirac Lagrangian, as well as Yukawa couplings.

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Notes

  1. 1.

    I thank Anthony Britto for pointing out this reference.

  2. 2.

    An exception, that we do not discuss in this book, is the topological theta term \(\left \langle F_{M}^{A},{\ast}F_{M}^{A}\right \rangle _{\mathrm{Ad}(P)}\), that appears in some modifications of QCD and in supersymmetric gauge theories.

  3. 3.

    There is another concept of unitarity (unitarity of the S-matrix, i.e. of time evolution) that we do not consider here.

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Hamilton, M.J.D. (2017). Chapter 7 The Classical Lagrangians of Gauge Theories. In: Mathematical Gauge Theory. Universitext. Springer, Cham. https://doi.org/10.1007/978-3-319-68439-0_7

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