Immirzi parameter in quantum general relativity

Journal Article · Thu Jan 01 04:00:00 EST 1998 · Physical Review, D

DOI:https://doi.org/10.1103/PhysRevD.57.1009· OSTI ID:567082

Rovelli, C ^[1]; Thiemann, T ^[2]

---

1. Physics Department, University of Pittsburgh, Pittsburgh, Pennsylvania 15260 (United States)
2. Physics Department, Harvard University, Cambridge, Massachusetts 02118 (United States)

Barbero has generalized the Ashtekar canonical transformation to a one-parameter scale transformation U({gamma}) on the phase space of general relativity. Immirzi has noticed that in loop quantum gravity this transformation alters the spectra of geometrical quantities. We show that U({gamma}) is a canonical transformation that cannot be implemented unitarily in quantum theory. This implies that there exists a one-parameter quantization ambiguity in quantum gravity, namely, a free parameter that enters the construction of the quantum theory. The purpose of this paper is to elucidate the origin and the role of this free parameter. {copyright} {ital 1997} {ital The American Physical Society}

• OSTI ID: 567082
• Journal Information: Physical Review, D, Journal Name: Physical Review, D Journal Issue: 2 Vol. 57; ISSN 0556-2821; ISSN PRVDAQ
• Country of Publication: United States
• Language: English

Related Subjects

66 PHYSICS
CANONICAL TRANSFORMATIONS
GENERAL RELATIVITY THEORY
PHASE SPACE
QUANTIZATION
QUANTUM GRAVITY