Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Fermions in odd space-time dimensions: back to basics   It is a well known feature of odd space-time dimensions $d$ that there exist
two inequivalent fundamental representations $A$ and $B$ of the Dirac gamma
matrices. Moreover, the parity transformation swaps the fermion fields living
in $A$ and $B$. As a consequence, a parity invariant Lagrangian can only be
constructed by incorporating both the representations. Based upon these ideas
and contrary to long held belief, we show that in addition to a discrete
exchange symmetry for the massless case, we can also define chiral symmetry
provided the Lagrangian contains fields corresponding to both the inequivalent
representations. We also study the transformation properties of the
corresponding chiral currents under parity and charge conjugation operations.
We work explicitly in 2+1 dimensions and later show how some of these ideas
generalize to an arbitrary number of odd dimensions.

13
The categories of this paper are: quant-ph
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The categories of this paper are: solv-int
26
The categories of this paper are: bayes-an
6
The categories of this paper are: astro-ph
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The categories of this paper are: nlin
15
The categories of this paper are: nucl-ex
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The categories of this paper are: alg-geom
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The categories of this paper are: hep-lat
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The categories of this paper are: comp-gas
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The categories of this paper are: eess
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The categories of this paper are: hep-th
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The categories of this paper are: q-bio
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The categories of this paper are: nucl-th
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The categories of this paper are: q-fin
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The categories of this paper are: mtrl-th
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The categories of this paper are: stat