A No-Go Theorem for the Consistent Quantization of Spin 3/2 Fields onThomas-Paul Hack, Mathias Makedonski
General Curved Spacetimes [PDF]
We first introduce a set of conditions which assure that a free spinView original: http://arxiv.org/abs/1106.6327
$\frac32$ field with $m\ge 0$ can be consistently ('unitarily') quantized on
all four-dimensional curved spacetimes, i.e. also on spacetimes which are not
assumed to be solutions of the Einstein equations. We discuss a large -- and,
as we argue, exhaustive -- class of spin $\frac32$ field equations obtained
from the Rarita-Schwinger equation by the addition of non-minimal couplings and
prove that no equation in this class fulfils all sufficient conditions.
In supergravity theories, the curved background is usually assumed to satisfy
the Einstein equations and thus detailed knowledge on the spacetime curvature
is available. Hence, our no-go theorem does not cover supergravity theories,
but rather complements previous results indicating that they may be the only
consistent field-theoretic models which contain spin $\frac32$ fields.
Particularly, our no-go theorem seems to imply that composite systems with spin
$\frac32$ can not be stable in curved spacetimes.