Seminarium Teorii Względności i Grawitacji

Loop Quantum Gravity (LQG) is an attempt to quantize Einsteinian gravity, cast in terms of variable with SU(2) symmetry, deploying tools borrowed from lattice gauge theories. I will present a procedure to select a finite amount of degrees of freedom in LQG, which is called Quantum Reduced Loop Gravity (QRLG), and show that it can be applied to all gravitational models with diagonal metric tensor, including all the solutions of the Einstein equations relevant for cosmology and black holes physics. I will discuss the symplectic structure of the phase space of QRLG and comment on the quantization procedure applied to the Hamiltonian constraint for the Standard Model of matter fields. Next I will present results obtained, and show in particular that the Hamiltonian eigenvalues approach the classical Hamiltonian at the leading order in the continuum limit. The next-to-the-leading order corrections can be discussed in conjunction with their possible phenomenological implications. Finally I will discuss how the form of quantum-gravitational corrections are dependent on the chosen representation for matter fields.