440 research outputs found
The kinematical Hilbert space of Loop Quantum Gravity from BF theories
In this work, it is demonstrated how the kinematical Hilbert space of Loop
Quantum Gravity (LQG) can be inferred from the configuration space of BF
theories via the imposition of the Hamiltonian constraints. In particular, it
is outlined how the projection to the representations associated with
Ashtekar-Barbero connections provides the correct procedure to implement
second-class constraints and the corresponding nontrivial induced symplectic
structure. Then, the reduction to SU(2) invariant intertwiners is analyzed and
the properties of LQG states under Lorentz transformations is discussed.Comment: 13 page
Gravity in presence of fermions as a SU(2) gauge theory
The Hamiltonian formulation of the Holst action in presence of a massless
fermion field with a non-minimal Lagrangian is performed without any
restriction on the local Lorentz frame. It is outlined that the phase space
structure does not resemble that one 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 non-minimal parameter the
kinematics coincides with that one 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.Comment: 5 pages, accepted for publication in Phys. Rev.
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