Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Implications of $Tr\gamma_{5}=0$ in Lattice Gauge Theory   We analyze the implications of the relation $Tr\gamma_{5}=0$, which is
customarily assumed in practical lattice calculations. On the basis of the
finite dimensional representations of the Ginsparg-Wilson algebra, it is shown
that this relation reflects the species doubling in lattice theory; topological
excitations associated with species doublers, which have eigenvalue $2/a$,
contribute to $Tr\gamma_{5}$ without any suppression. In this sense, the
relation $Tr\gamma_{5}=0$ is valid only when we allow the presence of
unphysical states in the Hilbert space; this statement is also valid in the
Pauli-Villars regularization. If one eliminates the contributions of the
unphysical states, the trace $Tr\gamma_{5}$ is replaced by $Tr\Gamma_{5}\equiv
Tr \gamma_{5}(1 -{1/2}aD)$ which gives rise to the Pontryagin index, to be
consistent with the continuum analysis.

16
The categories of this paper are: stat
1
The categories of this paper are: cs
36
The categories of this paper are: cmp-lg
27
The categories of this paper are: comp-gas
7
The categories of this paper are: hep-th
18
The categories of this paper are: econ
19
The categories of this paper are: eess
25
The categories of this paper are: patt-sol
37
The categories of this paper are: supr-con
17
The categories of this paper are: q-fin
12
The categories of this paper are: nucl-th
4
The categories of this paper are: cond-mat
30
The categories of this paper are: q-alg
31
The categories of this paper are: ao-sci
14
The categories of this paper are: math-ph
10
The categories of this paper are: q-bio