Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Exterior Differential Systems for Field Theories   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.

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The categories of this paper are: plasm-ph
9
The categories of this paper are: nlin
28
The categories of this paper are: alg-geom
19
The categories of this paper are: eess
10
The categories of this paper are: q-bio
26
The categories of this paper are: bayes-an
12
The categories of this paper are: nucl-th
4
The categories of this paper are: cond-mat
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The categories of this paper are: adap-org
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The categories of this paper are: atom-ph
6
The categories of this paper are: astro-ph
1
The categories of this paper are: cs
20
The categories of this paper are: acc-phys
13
The categories of this paper are: quant-ph
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The categories of this paper are: math-ph
11
The categories of this paper are: hep-lat