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.