Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Anomaly and Anomaly-Free Treatment of QFTs Based on Symmetry-preserving
  Loop Regularization   The triangle anomaly in massless and massive QED is investigated by adopting
the symmetry-preserving loop regularization method proposed recently in
\cite{LR}. The method is realized in the initial dimension of theory without
modifying the original lagrangian, it preserves symmetries under non-Abelian
gauge and Poincare transformations in spite of the existence of two intrinsic
mass scales $M_c$ and $\mu_s$ which actually play the roles of UV- and IR-cut
off respectively. The axialvector-vector-vector (AVV) triangle diagrams in
massless and massive QED are evaluated explicitly by using the loop
regularization. It is shown that when the momentum $k$ of external state is
soft with $k^2 \ll \mu_s^2, m^2 $ ($m$ is the mass of loop fermions) and $ M_c
\to \infty$, both massless and massive QED become anomaly free. The triangle
anomaly is found to appear as quantum corrections in the case that $ m^2,
\mu_s^2 \ll k^2 $ and $M_c \to \infty$. Especially, it is justified that in the
massless QED with $\mu_s =0$ and $M_c\to \infty$, the triangle anomaly
naturally exists as quantum effects in the axial-vector current when the
ambiguity caused by the trace of gamma matrices with $\gamma_5$ is eliminated
by simply using the definition of $\gamma_5$. It is explicitly demonstrated how
the Ward identity anomaly of currents depends on the treatment for the trace of
gamma matrices, which enables us to make a clarification whether the ambiguity
of triangle anomaly is caused by the regularization scheme in the perturbation
calculations or by the trace of gamma matrices with $\gamma_5$.

30
The categories of this paper are: q-alg
6
The categories of this paper are: astro-ph
8
The categories of this paper are: hep-ex
10
The categories of this paper are: q-bio
24
The categories of this paper are: dg-ga
23
The categories of this paper are: solv-int
12
The categories of this paper are: nucl-th
5
The categories of this paper are: gr-qc
37
The categories of this paper are: supr-con
36
The categories of this paper are: cmp-lg
18
The categories of this paper are: econ
28
The categories of this paper are: alg-geom
1
The categories of this paper are: cs
26
The categories of this paper are: bayes-an
14
The categories of this paper are: math-ph
35
The categories of this paper are: mtrl-th