BRST quantization of the massless minimally coupled scalar field in de Sitter space (zero modes, euclideanization and quantization)

Details BRST quantization of the massless minimally coupled scalar field in de Sitter space (zero modes, euclideanization and quantization) BRST quantization of the massless minimally coupled scalar field in de Sitter space (zero modes, euclideanization and quantization)

2009-11-11

arxiv.org/abs/0911.2064v1

Phys.Rev.D46:2553-2559,1992

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

This paper has been published under the title "Zero modes, euclideanization and quantization" [Phys. Rev. D46, 2553 (1992)]

Scientific paper

10.1103/PhysRevD.46.2553

We consider the massless scalar field on the four-dimensional sphere $S^4$. Its classical action $S={1\over 2}\int_{S^4} dV (\nabla \phi)^2$ is degenerate under the global invariance $\phi \to \phi + \hbox{constant}$. We then quantize the massless scalar field as a gauge theory by constructing a BRST-invariant quantum action. The corresponding gauge-breaking term is a non-local one of the form $S^{\rm GB}={1\over {2\alpha V}}\bigl(\int_{S^4} dV \phi \bigr)^2$ where $\alpha$ is a gauge parameter and $V$ is the volume of $S^4$. It allows us to correctly treat the zero mode problem. The quantum theory is invariant under SO(5), the symmetry group of $S^4$, and the associated two-point functions have no infrared divergence. The well-known infrared divergence which appears by taking the massless limit of the massive scalar field propagator is therefore a gauge artifact. By contrast, the massless scalar field theory on de Sitter space $dS^4$ - the lorentzian version of $S^4$ - is not invariant under the symmetry group of that spacetime SO(1,4). Here, the infrared divergence is real. Therefore, the massless scalar quantum field theories on $S^4$ and $dS^4$ cannot be linked by analytic continuation. In this case, because of zero modes, the euclidean approach to quantum field theory does not work. Similar considerations also apply to massive scalar field theories for exceptional values of the mass parameter (corresponding to the discrete series of the de Sitter group).

Affiliated with

Also associated with

No associations

Rating

BRST quantization of the massless minimally coupled scalar field in de Sitter space (zero modes, euclideanization and quantization) does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with BRST quantization of the massless minimally coupled scalar field in de Sitter space (zero modes, euclideanization and quantization), we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and BRST quantization of the massless minimally coupled scalar field in de Sitter space (zero modes, euclideanization and quantization) will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-533151