Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Gauge invariance and the vacuum state   Quantum field theory is assumed to be gauge invariant. It is shown that for a
Dirac field the assumption of gauge invariance impacts on the way the vacuum
state is defined. It is shown that the conventional definition of the vacuum
state must be modified to take into account the requirements of gauge
invariance.

17
The categories of this paper are: q-fin
16
The categories of this paper are: stat
23
The categories of this paper are: solv-int
19
The categories of this paper are: eess
8
The categories of this paper are: hep-ex
20
The categories of this paper are: acc-phys
10
The categories of this paper are: q-bio
28
The categories of this paper are: alg-geom
29
The categories of this paper are: funct-an
0
The categories of this paper are: hep-ph
18
The categories of this paper are: econ
37
The categories of this paper are: supr-con
4
The categories of this paper are: cond-mat
2
The categories of this paper are: math
31
The categories of this paper are: ao-sci
12
The categories of this paper are: nucl-th