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. © 2010 The American Physical Society.
|Journal||Physical Review D - Particles, Fields, Gravitation and Cosmology|
|Publication status||Published - 10 Feb 2010|
All Science Journal Classification (ASJC) codes
- Nuclear and High Energy Physics
Cianfrani, F., & Montani, G. (2010). Gravity in the presence of fermions as an SU(2) gauge theory. Physical Review D - Particles, Fields, Gravitation and Cosmology, 81(4), -. . https://doi.org/10.1103/PhysRevD.81.044015