On the Quantum Theory of Massless Spin-3/2 Field in Minkowski Spacetime

Abstract

From the modern viewpoint and by the geometric method, this paper provides a concise foundation for the quantum theory of massless spin-3/2 field in Minkowski spacetime, which includes both the one-particle's quantum mechanics and the many-particle's quantum field theory. The explicit result presented here is useful for the investigation of spin-3/2 field in various circumstances such as supergravity, twistor programme, Casimir effect, and quantum inequality.

Casimir Effect for a Massless Spin-3/2 Field in Minkowski Spacetime

“…Especially, different from neutrino and electromagnetic fields, there is no gauge invariant local energy momentum tensor for massless spin-3/2 field, which is also shared by linear gravitational field indeed. However, fortunately, as is shown in [46], the integral of energy momentum tensor over the whole space is gauge independent, which justifies our present work and makes it acquire particular interest.…”

“…where the identity σ aCB ′ σ bD B ′ + σ bCB ′ σ aD B ′ = η ab ǫ CD has been employed [46]. Taking into account Rarita-Schwinger constraint condition, i.e.,…”

“…It is worth noting that Rarita-Schwinger field equations are invariant under the following gauge transformation [46,47] …”

“…For later progress in the subsequent section, a consistent massless spin-3/2 quantum field can be constructed by the plane wave basis in Coulomb gauge as [46] ψ a B (x) = 1…”

“…Notations and conventions follow those in [46]. Especially, the metric signature takes (+, −, −, −), and {σ µ Σ ′ Σ = 1…”