Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Stability of Covariant Relativistic Quantum Theory   In this paper we study the relativistic quantum mechanical interpretation of
the solution of the inhomogeneous Euclidean Bethe-Salpeter equation. Our goal
is to determine conditions on the input to the Euclidean Bethe-Salpeter
equation so the solution can be used to construct a model Hilbert space and a
dynamical unitary representation of the Poincar\'e group. We prove three
theorems that relate the stability of this construction to properties of the
kernel and driving term of the Bethe-Salpeter equation. The most interesting
result is that the positivity of the Hilbert space norm in the non-interacting
theory is not stable with respect to Euclidean covariant perturbations defined
by Bethe-Salpeter kernels. The long-term goal of this work is to understand
which model Euclidean Green functions preserve the underlying relativistic
quantum theory of the original field theory. Understanding the constraints
imposed on the Green functions by the existence of an underlying relativistic
quantum theory is an important consideration for formulating field-theory
motivated relativistic quantum models.

5
The categories of this paper are: gr-qc
37
The categories of this paper are: supr-con
16
The categories of this paper are: stat
19
The categories of this paper are: eess
30
The categories of this paper are: q-alg
8
The categories of this paper are: hep-ex
32
The categories of this paper are: atom-ph
4
The categories of this paper are: cond-mat
35
The categories of this paper are: mtrl-th
21
The categories of this paper are: adap-org
9
The categories of this paper are: nlin
3
The categories of this paper are: physics
20
The categories of this paper are: acc-phys
33
The categories of this paper are: plasm-ph
36
The categories of this paper are: cmp-lg
18
The categories of this paper are: econ