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No-go results on the quantization of spin 3/2 fields in curved spacetimes

Thomas-Paul Hack
(DESY, Hamburg)
Fredag, 2 december, 2011, at 09:00-09:45, in Koll. G (1532-214)
 In flat spacetime, Poincare invariance and irreducibility conditions determine unique free field equations for given spin and mass. In curved spacetime, however, there is a large arbitrariness in selecting free field equations, usually restricted by the requirement of "simplicity". It is know that several "simple" field equations in curved spacetimes for spin 3/2 suffer from inconsistencies, either in the classical or in the quantum field theory.

We formulate four sufficient conditions for a spin 3/2 field equation to be a starting point for a consistent QFT on arbitrary curved spacetimes and prove that a large class of field equations does not satisfy these conditions. As spin 3/2 fields appear naturally in supergravity theories, we investigate whether these theories satisfy at least weaker conditions, and prove that spin 3/2 field excitations do not propagate causally in the usually employed unitary gauge.

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