Discussion of the classical mechanics of the spinning particle or of classical field theory with fermion fields (possibly but not necessarily super-symmetric) as taking place in supergeometry:
via (possibly infinite-dimensional) supermanifolds:
Felix A. Berezin, M. S. Marinov: Particle Spin Dynamics as the Grassmann Variant of Classical Mechanics, Annals of Physics 104 2 (1977) 336-362 [doi:10.1016/0003-4916(77)90335-9, pdf, pdf]
reprinted in Appendix I of: Alexandre A. Kirillov (ed.): Introduction to Superanalysis, Mathematical Physics and Applied Mathematics 9, Springer (1987) [doi:10.1007/978-94-017-1963-6]
Thomas Schmitt: The Cauchy Problem for Classical Field Equations with Ghost and Fermion Fields [arXiv:hep-th/9607133]
Thomas Schmitt: Supergeometry and Quantum Field Theory, or: What is a Classical Configuration?, Rev. Math. Phys. 9 (1997) 993-1052 [doi:10.1142/S0129055X97000348, arXiv:hep-th/9607132].
Thomas Schmitt: Supermanifolds of classical solutions for Lagrangian field models with ghost and fermion fields, Sfb 288 Preprint No. 270 [hep-th/9707104, inspire:445574]
Daniel Freed, What are fermions?, Lecture 1 in: Five lectures on supersymmetry, AMS (1999) [ISBN:978-0-8218-1953-1, spire:517862]
Giovanni Giachetta, Luigi Mangiarotti, Gennadi Sardanashvily, chapter 3 of: Advanced classical field theory, World Scientific (2009) [doi:10.1142/7189]
Gennadi Sardanashvily, Grassmann-graded Lagrangian theory of even and odd variables, [arXiv:1206.2508]
Gennadi Sardanashvily W. Wachowski: SUSY gauge theory on graded manifolds [arXiv:1406.6318, spire:1302860]
Viola Gattus, Apostolos Pilaftsis, Supergeometric Approach to Quantum Field Theory, CORFU2023, PoS 463 (2024) 156 [doi:10.22323/1.463.0156, arXiv:2404.13107]
and more generally via smooth super sets:
Discussion with focus on supersymmetry:
Leonardo Castellani, Riccardo D'Auria, Pietro Fré, section II.2.4 of: Supergravity and Superstrings - A Geometric Perspective, World Scientific (1991) [doi:10.1142/0224, toc: pdf, chII.2: pdf]
Pierre Deligne, Daniel Freed: Supersolutions, in: Quantum Fields and Strings, A course for mathematicians, 2 vols. Amer. Math. Soc. Providence (1999) 357-366 [arXiv:hep-th/9901094, ISBN:978-0-8218-2014-8, web version]
Daniel Freed, Classical field theory and Supersymmetry, IAS/Park City Mathematics Series 11 (2001) [pdf, pdf]
and specifically in the context of super- string theory (regarding worldsheets as super Riemann surfaces):
Last revised on August 31, 2024 at 08:37:42. See the history of this page for a list of all contributions to it.