Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Proper Time Formalism, Gauge Invariance and the Effects of a Finite
  World Sheet Cutoff in String Theory   We discuss the issue of going off-shell in the proper time formalism. This is
done by keeping a finite world sheet cutoff. We construct one example of an
off-shell covariant Klein Gordon type interaction. For a suitable choice of the
gauge transformation of the scalar field, gauge invariance is maintained off
mass shell. However at second order in the gauge field interaction, one finds
that (U(1)) gauge invariance is violated due to the finite cutoff.
Interestingly, we find, to lowest order, that by adding a massive mode with
appropriate gauge transformation laws to the sigma model background, one can
restore gauge invariance. The gauge transformation law is found to be
consistent, to the order calculated, with what one expects from the interacting
equation of motion of the massive field. We also extend some previous
discussion on applying the proper time formalism for propagating gauge
particles, to the interacting (i.e. Yang Mills) case.

23
The categories of this paper are: solv-int
3
The categories of this paper are: physics
0
The categories of this paper are: hep-ph
36
The categories of this paper are: cmp-lg
4
The categories of this paper are: cond-mat
27
The categories of this paper are: comp-gas
17
The categories of this paper are: q-fin
21
The categories of this paper are: adap-org
9
The categories of this paper are: nlin
29
The categories of this paper are: funct-an
12
The categories of this paper are: nucl-th
2
The categories of this paper are: math
25
The categories of this paper are: patt-sol
32
The categories of this paper are: atom-ph
35
The categories of this paper are: mtrl-th
28
The categories of this paper are: alg-geom