Super-gauge field in de Sitter universe

Abstract

The Gupta-Bleuler triplet for vector-spinor gauge field is presented in de Sitter ambient space formalism. The invariant space of field equation solutions is obtained with respect to an indecomposable representation of the de Sitter group. By using the general solution of the massless spin-3 2 field equation, the vector-spinor quantum field operator and its corresponding Fock space is constructed. The quantum field operator can be written in terms of the vector-spinor polarization states and a quantum conformally coupled massless scalar field, which is constructed on Bunch-Davies vacuum state. The two-point function is also presented, which is de Sitter covariant and analytic. * Electronic address: sajad.parsamehr@srbiau.ac.ir

General Solution of Massless Spin- 3 2 $\frac {3}{2}$ Field in de Sitter Universe

“…the choice of the gauge fixing parameter restrict the space of gauge solutions [16]. We want to find the general solution without any condition.…”

“…Since the conformally coupled scalar field are explicitly constructed [9], so, the field operator, the quantum states and the two-point function for the massless spin-3 2 field can be constructed in terms of a vector-spinor polarization state D α U and a massless conformally coupled scalar field φ c [16].…”

“…In the previous paper [16], the general solution of the massless spin-3 2 field was introduced. In this paper, we calculate explicitly this solution in more details and show that all the solutions can be extracted by applying various conditions.…”

Conjugate spinor field equation for massless spin-$\frac{3}{2}$ field in de Sitter ambient space

“…Since the simplest curved space-time that corresponds to these observations is de Sitter space-time and this space-time has maximal symmetry, the group of ten parametric SO (1,4) is the kinematic group of the de Sitter space. Therefore, quantum field theory, gauge theory and quantum cosmology are investigated in this space-time [7][8][9][10][11][12][13][14][15][16].…”

“…According to this method, the quantum field affects the space including all states with positive and negative norm. In this formalism, of all the degrees of freedom, only two are physical [12,13].…”