Quantum Field Theory in de Sitter Universe: Ambient Space Formalism

Abstract

Quantum field theory in the $4$-dimensional de Sitter space-time is constructed in the ambient space formalism in a rigorous mathematical framework. This work is based on the group representation theory and the analyticity of the complexified pseudo-Riemannian manifolds. The unitary irreducible representations of de Sitter group and their corresponding Hilbert spaces are reformulated in the ambient space formalism. Defining the creation and annihilation operators, quantum field operators and their corresponding analytic two-point functions for various spin fields have been constructed. The various spin massless fields can be constructed in terms of the massless conformally coupled scalar field in this formalism. Then the quantum massless minimally coupled scalar field operator, for the first time, is also constructed on Bunch-Davies vacuum state which preserve the analyticity. We show that the massless fields with $s\ge 3$ cannot propagate in de Sitter ambient space formalism. The massless gauge invariant field equations for $s=1,\frac{3}{2},2$ are studied. The gauge spin-$\frac{3}{2}$ fields satisfy the Grassmannian algebra, and hence provoke one to couple them with the gauge spin-$2$ field and the super-algebra is naturally appeared.

75 pages, typos corrected, paper improved, V5 some errors corrected

References in corpus (7)

• Entropy evolution of universes with initial and final de Sitter eras
• Fourier analysis and holomorphic decomposition on the one-sheeted hyperboloid
• Super-gauge Field in de Sitter Universe
• Krein Spaces in de Sitter Quantum Theories
• Auxiliary "massless" spin-2 field in de Sitter universe
• Linear Gravity in de Sitter universe
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• Laplacian and codifferential operators on p-forms in (Anti)-de Sitter spaces: restriction and continuation
• De Sitter scalar-spinor interaction in Minkowski limit
• Photon decaying in de Sitter universe
• Conjugate spinor field equation for massless spin-$\frac{3}{2}$ field in de Sitter ambient space
• de Sitter-covariant Hamiltonian formalism of Einstein--Cartan gravity
• Gauge Theories on de Sitter Spacetime