Massive Rarita-Schwinger field in de Sitter space

Abstract

We present a covariant quantization of the "massive" spin-3 2 Rarita-Schwinger field in de Sitter (dS) spacetime. The dS group representation theory and its Wigner interpretation combined with the Wightman-Gärding axiomatic and analyticity requirements in the complexified pseudo-Riemanian manifold constitute the basis of the quantization scheme, while the whole procedure is carried out in terms of coordinate-independent dS plane waves. We make explicit the correspondence between unitary irreducible representations (UIRs) of the dS group and the field theory in dS spacetime: by "massive" is meant a field that carries a particular principal series representation of the dS group. We drive the plane-wave representation of the dS massive Rarita-Schwinger field in a manifestly dS-invariant manner. We show that it exactly reduces to its Minkowskian counterpart when the curvature tends to zero as far as the analyticity domain conveniently chosen. We then present the Wightman two-point function fulfilling the minimal requirements of local anticommutativity, covariance, and normal analyticity. The Hilbert space structure and the unsmeared field operator are also defined. The analyticity properties of the waves and the two-point function that we discuss in this paper allow for a detailed study of the Hilbert space of the theory, and give rise to the thermal physical interpretation.

The de Sitter group and its representations: a window on the notion of de Sitterian elementary systems

“…These properties explicitly imply that W ν (x, z t ) is analytic in the strip S = t ∈ C ; 0 < Im(t) < 2πR , 90 and verifies the following condition:…”

“…[46], and finally for the massless spin-2 field (the dS 4 linear quantum gravity), Refs. [90][91][92][93][94][95][96]. Then, in this sense also, the choice of dS 4 scalar fields seems quite natural for our discussions.…”

“…[25], Dixmier defines p ∈ N/2 as the infimum (greatest lower bound) of the set of j l + j r : 45 p ≡ inf (j l ,jr)∈Γ U (j l + j r ) . (12.15) 45 Note that the parameter p by construction is the natural candidate for carrying the notion of spin in dS 4 relativity. Below, we clarify this point in two steps:…”

“…[42] and [43], for the massive and massless spin- 3 2 fields, Ref. [45], for the massive spin-2 field, Ref. [46], and finally for the massless spin-2 field (the dS 4 linear quantum gravity), Refs.…”

“…To see relevant arguments for higher spin fields in dS 4 spacetime, one can refer to Refs. [41][42][43][44][45][46]. By maximal type is meant that, with respect to the above set of postulates and without imposing very specific conditions (for instance, local commutativity at timelike separation), one cannot enlarge the (physical sheet) holomorphy domain of the corresponding two-point functions.…”