Vacuum states for gravitons field in de Sitter space

Abstract

In this paper, considering the linearized Einstein equation with a two-parameter family of linear covariant gauges in de Sitter spacetime, we examine possible vacuum states for the gravitons field with respect to invariance under the de Sitter group SO0(1, 4). Our calculations explicitly reveal that there exists no natural de Sitter-invariant vacuum state (the Euclidean state) for the gravitons field. Indeed, on the foundation of a rigorous group theoretical reasoning, we prove that if one insists on full covariance as well as causality for the theory, has to give up the positivity requirement of the inner product. However, one may still look for states with as much symmetry as possible, more precisely, a restrictive version of covariance by considering the gravitons field and the associated vacuum state which are, respectively, covariant and invariant with respect to some maximal subgroup of the full de Sitter group. In this regard, we treat SO(4) case, and find a family of SO(4)-invariant states. The associated SO(4)-covariant quantum field is given, as well.

Introduction to the Dicke Model: From Equilibrium to Nonequilibrium, and Vice Versa

“…Several recent works discussed whether the Hamiltonian describing such a system should contain A 2 terms, and as such, whether it is subject to the no-go theorem. [51][52][53][54][55][56][57] For at least some designs of the circuit, if one starts from the classical Kirchoff equations (i.e., conditions on the currents and voltages) of the circuit, and proceeds to quantize these equations, the resulting Hamiltonian is not necessarily subject to the no-go theorem. That is, there are cases where either the A 2 term is absent, or where it is present, but with a weaker coupling strength than required to prevent the phase transition.…”

A small non-vanishing cosmological constant from the Krein–Gupta–Bleuler vacuum

“…Our aim in the present work, instead, will be to point out a potential relevance between the observable smallness of the cosmological constant and a choice of vacuum in the dS gravitational background of * bamba@sss.fukushima-u.ac.jp † Enayati@iauctb.ac.ir ‡ s.rahbardehghan@iauctb.ac.ir our expanding Universe, now known as the KGB vacuum. This vacuum, based on a new representation of the canonical commutation relations, was recently proposed as an alternative to the dS natural vacuum state (the Bunch-Davies state) that yields a fully covariant and coordinate-independent quantization (the KGB quantization) of linearized gravity in dS space [6][7][8][9][10][11][12]. [Due to the lack of the natural dS-invariant vacuum state for free gravitons, the fact that is now widely accepted in the physics community (see, for instance, [7,13,14]), the usual canonical quantization seems to break down for field theory of dS quantum gravity.]…”

“…This vacuum, based on a new representation of the canonical commutation relations, was recently proposed as an alternative to the dS natural vacuum state (the Bunch-Davies state) that yields a fully covariant and coordinate-independent quantization (the KGB quantization) of linearized gravity in dS space [6][7][8][9][10][11][12]. [Due to the lack of the natural dS-invariant vacuum state for free gravitons, the fact that is now widely accepted in the physics community (see, for instance, [7,13,14]), the usual canonical quantization seems to break down for field theory of dS quantum gravity.] Let us begin by summarizing the general properties of the KGB quantization method, while dS spacetime with the metric (1) covering the whole dS manifold is considered as the classical background.…”

“…On one hand, this shows that the KGB quantization respects the whole dS manifold symmetries which are basic for field dynamics in this space. More exactly, the KGB quantum field is causal and has all covariance properties of the classical field in a strong sense, even when the KGB method is applied to situations where the usual quantization method fails, such as the dS linearized gravity [6][7][8][9] and the dS minimally coupled scalar field [11,12]. [The crucial point about both cases is that the associated total space is indeed the smallest, complete and non-degenerate innerproduct space fulfilling all invariance properties of the theory.]…”

Massive Rarita-Schwinger field in de Sitter space

“…All of these developments plead in favour of setting up a model of QFT in dS spacetime with the same level of completeness and rigor as its Minkowskian counterpart. In this regard, we refer in particular to a promising formulation of such a theory and its subsequent thermic interpretation that was originally put forward for the "massive" scalar fields in dS spacetime in the 1990's [7][8][9], and during recent two decades, it has been subject to scrutiny in a number of works to make explicit the extra algebraic structure inherent to other dS elementary systems (see, for instance, [10][11][12][13][14][15][16][17][18][19][20][21]). Technically, this model of dS QFT enjoys a robust group theoretical content.…”