Hendrik Grundling, Fernando Lledo
Local quantum constraints
(163K, latex)
ABSTRACT. We analyze the situation of a local quantum field theory with constraints
which are also local. In particular we find "weak" Haag-Kastler axioms
which will ensure that the final constrained theory satisfies the usual
Haag-Kastler axioms. We develop in detail Gupta-Bleuler electromagnetism
as an example of such a theory which satisfies the "weak" Haag-Kastler
axioms but not the usual ones.
We conclude the analysis by a comparison of the final algebra produced
by a system of local constrainings to the one obtained from a single
global constraining, and also consider the issue of reduction by stages.
For the usual spectral condition on the generators of the translation
group, we also find a "weak" version, and show that the Gupta-Bleuler
example satisfies it, using a representation of the physical algebra
coming from the usual indefinite metric Fock representation of the
original algebra.