2005/07/31 by Laurent Freidel, Djordje Minić, Djordje Minic +1 · 6 citations
Physics and Astronomy · #Black Holes and Theoretical Physics #Classical mechanics #Cosmology and Gravitation Theories #Fermion #Immirzi parameter #Loop quantum gravity #Noncommutative and Quantum Gravity Theories #Parity (physics) #Physics #Quantum #Quantum gravity #Quantum mechanics #Theoretical physics #Torsion (gastropod) #Unitarity #gr-qc #hep-ph #hep-th
paper · pdf · doi:10.1103/physrevd.72.104002
published as Phys.Rev.D72:104002,2005 · 11 pages, LaTeX; (two footnotes, acknowledgements and references added, typos corrected)
arxiv created 2005/09/16 · openalex publication_date 2005/11/01 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.