Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Time reversal, fermion doubling, and the masses of lattice Dirac
  fermions in three dimensions   Motivated by recent examples of three-dimensional lattice Hamiltonians with
massless Dirac fermions in their (bulk) spectrum, I revisit the problem of
fermion doubling on bipartite lattices. The number of components of the Dirac
fermion in a time-reversal and parity invariant d-dimensional lattice system is
determined by the minimal representation of the Clifford algebra of $d+1$
Hermitian Dirac matrices that allows a construction of the time-reversal
operator with the square of unity, and it equals $2^d$ for $d=2,3$. Possible
mass-terms for (spinless) Dirac fermions are listed and discussed. In three
dimensions there are altogether eight independent masses, out of which four are
even, and four are odd under time reversal. A specific violation of
time-reversal symmetry that leads to (minimal) four-component massless Dirac
fermion in three dimensions at low energies is constructed.

33
The categories of this paper are: plasm-ph
25
The categories of this paper are: patt-sol
3
The categories of this paper are: physics
26
The categories of this paper are: bayes-an
21
The categories of this paper are: adap-org
19
The categories of this paper are: eess
35
The categories of this paper are: mtrl-th
32
The categories of this paper are: atom-ph
0
The categories of this paper are: hep-ph
30
The categories of this paper are: q-alg
13
The categories of this paper are: quant-ph
27
The categories of this paper are: comp-gas
1
The categories of this paper are: cs
9
The categories of this paper are: nlin
18
The categories of this paper are: econ
17
The categories of this paper are: q-fin