2014/05/24 by F. B. Estabrook, Estabrook, Frank B.
Physics and Astronomy · #35A15 #58A15 #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #High Energy Physics - Theory (hep-th) #Quantum Chromodynamics and Particle Interactions
paper · pdf · doi:10.48550/arxiv.1405.6247
openalex publication_date 2014/05/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Exterior Differential Systems (EDS) and Cartan forms, set in the state space of field variables taken together with four space-time variables, are formulated for classical gauge theories of Maxwell and SU(2) Yang-Mills fields minimally coupled to Dirac spinor multiplets. Cartan character tables are calculated, showing whether the EDS, and so the Euler-Lagrange partial differential equations, is well-posed. The first theory, with 22 dimensional state space (10 Maxwell field and potential components and 8 components of a Dirac field), anticipates QED. In the second, non-Abelian, case (30 Yang-Mills field components and 16 Dirac), only if three additional "ghost" fields are included (15 more scalar variables) is a well-posed EDS found. This classical formulation anticipates the need for introduction of Fadeev-Popov ghost fields in the quantum standard model.