Quantum gravity, torsion, parity violation, and all that

Journal Article · Tue Nov 15 04:00:00 EST 2005 · Physical Review. D, Particles Fields

DOI:https://doi.org/10.1103/PhysRevD.72.104002· OSTI ID:20711555

Freidel, Laurent ^[1]; Minic, Djordje; Takeuchi, Tatsu ^[2]

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1. Perimeter Institute for Theoretical Physics, 31 Caroline St. N. Waterloo, N2L 2Y5, Ontario (Canada)
2. Institute for Particle Physics and Astrophysics, Department of Physics, Virginia Tech, Blacksburg, Virginia 24061 (United States)

We discuss the issue of parity violation in quantum gravity. In particular, we study the coupling of fermionic degrees of freedom in the presence of torsion and the physical meaning of the Immirzi parameter from the viewpoint of effective field theory. We derive the low-energy effective Lagrangian which turns out to involve two parameters: one measuring the nonminimal coupling of fermions in the presence of torsion, the other being the Immirzi parameter. In the case of nonminimal coupling the effective Lagrangian contains an axial-vector interaction leading to parity violation. Alternatively, in the case of minimal coupling there is no parity violation and the effective Lagrangian contains only the usual axial-axial interaction. In this situation the real values of the Immirzi parameter are not at all constrained. On the other hand, purely imaginary values of the Immirzi parameter lead to violations of unitarity for the case of nonminimal coupling. Finally, the effective Lagrangian blows up for the positive and negative unit imaginary values of the Immirzi parameter.

• OSTI ID: 20711555
• Journal Information: Physical Review. D, Particles Fields, Journal Name: Physical Review. D, Particles Fields Journal Issue: 10 Vol. 72; ISSN PRVDAQ; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
COUPLING
DEGREES OF FREEDOM
FERMIONS
LAGRANGIAN FIELD THEORY
LAGRANGIAN FUNCTION
P INVARIANCE
PARITY
PARTICLE INTERACTIONS
QUANTUM GRAVITY
UNITARITY
VECTORS