Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2011-06-30
Physics
High Energy Physics
High Energy Physics - Theory
32 pages; title changed; discussion of supergravity moved to a forthcoming paper, cf. section 4.3.; result of proposition 5 im
Scientific paper
We first introduce a set of conditions which assure that a free spin $\frac32$ 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.
Hack Thomas-Paul
Makedonski Mathias
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