Gravity in the presence of fermions as an SU(2) gauge theory

Journal Article · Mon Feb 15 04:00:00 EST 2010 · Physical Review. D, Particles Fields

DOI:https://doi.org/10.1103/PHYSREVD.81.044015· OSTI ID:21409303

Cianfrani, Francesco ^[1]; Montani, Giovanni ^[1]

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1. ICRA-International Center for Relativistic Astrophysics, Dipartimento di Fisica (G9), Universita di Roma, 'Sapienza', Piazzale Aldo Moro 5, 00185 Roma (Italy)

The Hamiltonian formulation of the Holst action in the presence of a massless fermion field with a nonminimal Lagrangian is performed without any restriction on the local Lorentz frame. It is outlined that the phase-space structure does not resemble that of a background-independent Lorentz gauge theory, as some additional constraints are present. Proper phase-space coordinates are introduced, such that SU(2) connections can be defined, and the vanishing of conjugate momenta to boost variables is predicted. Finally, it is demonstrated that for a particular value of the nonminimal parameter, the kinematics coincides with that of a background-independent SU(2) gauge theory, and the Immirzi parameter becomes the coupling constant of such an interaction between fermions and the gravitational field.

• OSTI ID: 21409303
• Journal Information: Physical Review. D, Particles Fields, Journal Name: Physical Review. D, Particles Fields Journal Issue: 4 Vol. 81; ISSN PRVDAQ; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
COUPLING CONSTANTS
FERMIONS
FUNCTIONS
GAUGE INVARIANCE
GRAVITATION
GRAVITATIONAL FIELDS
HAMILTONIANS
INTERACTIONS
INVARIANCE PRINCIPLES
LAGRANGIAN FUNCTION
LIE GROUPS
LORENTZ INVARIANCE
MATHEMATICAL OPERATORS
MATHEMATICAL SPACE
PHASE SPACE
QUANTUM OPERATORS
SPACE
SU GROUPS
SU-2 GROUPS
SYMMETRY GROUPS