Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Sphaleron Barrier in the Presence of Fermions   We calculate the minimal energy path over the sphaleron barrier in the
pre\-sen\-ce of fermions, assuming that the fermions of a doublet are
degenerate in mass. This allows for spherically symmetric ans\"atze for the
fields, when the mixing angle dependence is neglected. While light fermions
have little influence on the barrier, the presence of heavy fermions ($M_F
\sim$ TeV) strongly deforms the barrier, giving rise to additional sphalerons
for very heavy fermions ($M_F \sim$ 10 TeV). Heavy fermions form
non-topological solitons in the vacuum sector.

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The categories of this paper are: astro-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: nlin
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The categories of this paper are: q-bio
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The categories of this paper are: math
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The categories of this paper are: adap-org
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The categories of this paper are: math-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: acc-phys
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The categories of this paper are: nucl-th
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The categories of this paper are: eess
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The categories of this paper are: chao-dyn
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The categories of this paper are: nucl-ex
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The categories of this paper are: gr-qc
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The categories of this paper are: q-alg
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The categories of this paper are: solv-int