Local Quantum Constraints
Abstract
We analyze the situation of a local quantum field theory with constraints, both indexed by the same set of spacetime regions. In particular we find ``weak'' HaagKastler axioms which will ensure that the final constrained theory satisfies the usual HaagKastler axioms. GuptaBleuler electromagnetism is developed in detail as an example of a theory which satisfies the ``weak'' HaagKastler axioms but not the usual ones. This analysis is done by pure C*algebraic means without employing any indefinite metric representations, and we obtain the same physical algebra and positive energy representation for it than by the usual means. The price for avoiding the indefinite metric, is the use of nonregular representations and complex valued test functions. We also exhibit the precise connection with the usual indefinite metric representation. We conclude the analysis by comparing the final physical algebra produced by a system of local constrainings with 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 GuptaBleuler example satisfies it.
 Publication:

Reviews in Mathematical Physics
 Pub Date:
 2000
 DOI:
 10.1142/S0129055X00000459
 Bibcode:
 2000RvMaP..12.1159G