Supermanifolds of classical solutions for Lagrangian field models with ghost and fermion fields

1997/07/11 by Thomas Schmitt, Thomas P. Schmitt, Schmitt, Thomas
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Quantum Chromodynamics and Particle Interactions #dg-ga #hep-th #math.DG

paper · pdf · doi:10.48550/arxiv.hep-th/9707104

28 pages, AmsLaTeX 1.2

arxiv created 1997/07/11 · openalex publication_date 1997/07/11 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Using a supergeometric interpretation of field functionals, we show that for a class of classical field models used for realistic quantum field theoretic models, an infinite-dimensional supermanifold (smf) of classical solutions in Minkowski space can be constructed. That is, we show that the smf of smooth Cauchy data with compact support is isomorphic with an smf of corresponding classical solutions of the model.

Citations

• The Cauchy Problem for Abstract Evolution Equations with Ghost and Fermion Degrees of Freedom

Related

• The Cauchy Problem for Classical Field Equations with Ghost and Fermion Fields
• The Cauchy Problem for Abstract Evolution Equations with Ghost and Fermion Degrees of Freedom
• Supersymmetric field equations from momentum space
• Minimal Supergeometric Quantum Field Theories
• A classical approach to smooth supermanifolds