Abstract
In this chapter, we define general gauge theories and study their classical aspects. These may also be called local variational problems, because their action functional is a local functional. The corresponding equations of motion are given by an Euler-Lagrange partial differential equation, which we shall study in the setting of non-linear algebraic analysis, presented in Chap. 12. The main interest of our approach over the previous ones is that it is expressed in terms of functors of points. This allows us to always state the nature of the various spaces of functions in play. The chapter starts with a finite dimensional toy model. We then define general gauge theories and formalize their regularity properties, through the study of their higher Noether identities. We proceed to the study of the derived covariant phase space (Batalin-Vilkovisky formalism) and finish by a presentation of the gauge fixing procedure.
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Paugam, F. (2014). Gauge Theories and Their Homotopical Poisson Reduction. In: Towards the Mathematics of Quantum Field Theory. Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics, vol 59. Springer, Cham. https://doi.org/10.1007/978-3-319-04564-1_13
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DOI: https://doi.org/10.1007/978-3-319-04564-1_13
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