Abstract
The principle of gauge symmetries can be motivated by the Lagrangian density of the free Dirac field, which is covariant under.
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Notes
- 1.
Note that in classical formulations \(D_{\mu }\) is sometimes introduced as \(D_{\mu }= \partial _{\mu }-ieA_{\mu }\). Here it will be introduced with a “\(+\)” sign to keep consistency with the canonical formulation of the SM later on.
- 2.
Note that the book follows the convention to sum over re-appearing identical indices as in the case of the Einstein sum convention.
- 3.
The additional index \(Y\) is tribute to the hypercharge \(Y\) in the covariant derivative.
- 4.
The general usage of the variable name “\(e\)” for the elementary charge of the electron has been replaced by “\(q\)” in this and the following sections to prevent misunderstandings in cases, where “\(e\)” is used for other objects, e.g. like the electron spinor.
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Wolf, R. (2015). The Higgs Boson in the Standard Model of Particle Physics. In: The Higgs Boson Discovery at the Large Hadron Collider. Springer Tracts in Modern Physics, vol 264. Springer, Cham. https://doi.org/10.1007/978-3-319-18512-5_2
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