Abstract
In this chapter, we give a survey of various variational problems from theoretical/mathematical physics. We first describe the Kaluza-Klein Lagrangian, that combines general relativity with electromagnetism. We then give a presentation of the Poisson sigma-model, that plays an important role in the deformation quantization of Poisson manifolds. We then give a formulation of higher Chern-Simons theory, giving a nice physical application to the setting of non-abelian differential cohomology. We then describe the supersymmetric particle, superfields, the bosonic string, superstrings and supergravity. We systematically use here the setting of super-geometry to formalize super-fields consistently with our viewpoint of parametrized geometry, that gives a clear meaning to the space of fields, also in the super situation.
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Paugam, F. (2014). Variational Problems of Theoretical Physics. 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_16
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DOI: https://doi.org/10.1007/978-3-319-04564-1_16
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