Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2004-06-22
Phys.Rev. D70 (2004) 044028
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
(14 pages) Accepted for publication in Physical Review D
Scientific paper
10.1103/PhysRevD.70.044028
We discuss the connection between the Fock space introduced by Ashtekar and Pierri for Einstein-Rosen waves and its perturbative counterpart based on the concept of particle that arises in linearized gravity with a de Donder gauge. We show that the gauge adopted by Ashtekar and Pierri is a generalization of the de Donder gauge to full (i.e. non-linearized) cylindrical gravity. This fact allows us to relate the two descriptions of the Einstein-Rosen waves analyzed here by means of a simple field redefinition. Employing this redefinition, we find the highly non-linear relation that exists between the annihilation and creation-like variables of the two approaches. We next represent the particle-like variables of the perturbative approach as regularized operators, introducing a cut-off. These can be expanded in powers of the annihilation and creation operators of the Ashtekar and Pierri quantization, each additional power being multiplied by an extra square-root of the three-dimensional gravitational constant, $\sqrt{G}$. In principle, the perturbative vacuum may be reached as the limit of a state annihilated by these regularized operators when the cut-off is removed. This state can be written as the vacuum of the Ashtekar and Pierri quantization corrected by a perturbative series in $\sqrt{G}$ with no contributions from particles with energies above the cut-off. We show that the first-order correction is in fact a state of infinite norm. This result is interpreted as indicating that the Fock quantizations in the two approaches are unitarily inequivalent and, in any case, proves that the perturbative vacuum is not analytic in the interaction constant. Therefore a standard perturbative quantum analysis fails.
Barbero Fernando J. G.
Mena Marugan Guillermo A.
Villaseñor Eduardo J. S.
No associations
LandOfFree
Particles and vacuum for perturbative and non-perturbative Einstein-Rosen gravity 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 Particles and vacuum for perturbative and non-perturbative Einstein-Rosen gravity, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Particles and vacuum for perturbative and non-perturbative Einstein-Rosen gravity will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-669482