Quantum field theory on 1 + 3-de Sitter space: annihilation and creation operators

Abstract In this paper, we construct the annihilation and creation operators for massive scalar particles in 1 + 3 dimensional de Sitter space using Berezin’s integral quantization method. We begin by demonstrating that the phase space of a massive scalar particle in this curved spacetime is isomorphic to the complex four-dimensional sphere $$S_{\mathcal {C}}^3$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mi>S</mml:mi> <mml:mrow> <mml:mi>C</mml:mi> </mml:mrow> <mml:mn>3</mml:mn> </mml:msubsup> </mml:math> . Each point on this complex sphere is associated with a vector (or coherent state) in a corresponding Hilbert subspace. We emphasize the intrinsically four-dimensional nature of the annihilation and creation operators and examine their connection to the infinitesimal generators of time translations and Lorentz boosts.