data i miejsce: 18.10.2022 godz. 11:15, sala 106 bud A-29
temat: A new perspective towards the general-relativistic canonical quantization of lattice gravity and the comparison of its phase space-reduced results with loop quantum cosmology
prelegent: mgr Jakub Bilski (Instytut Matematyki UZ)

Abstrakt: To construct a general-relativistic quantum field theory, background-independent quantum gravity is needed. By assuming the ADM decomposition of spacetime, it is possible to define the metric-independent discrete analog of a Fock space for quantum gravity on a lattice. This space, known as the spin network, is invariant under the SU(2) symmetry and the spatial diffeomorphism transformations. It is the states space for loop quantum gravity.
 I will describe an improved construction of the lattice regularization and cosmological reduction of the canonical formulation of loop quantum gravity. The application of this procedure to the Hamiltonian constraint provides its lattice analog, the domain of which has a natural structure of a sum over elementary cells. As a result, the related scalar constraint operator can be defined as a sum of the Hamiltonians restricted to different Euclidean cells. Hence, its spectrum will be independent of intertwiners. In this case, the SU(2) invariance should be implemented classically, determining the structure of the lattice before quantization.
 I will also discuss the cosmological phase space reduction of introduced lattice gravity. It is determined by a rigorous application of gauge-fixing conditions. Unlike in the case of loop quantum cosmology, the obtained Hamiltonian constraint is finite (without any cut-off introduction) and exact (with the holonomy expansion around the unit element of SU(2), known from QFT methods). Moreover, it describes a simple structure of inhomogeneities and anisotropies, which is also absent in the cae of loop quantum cosmology (unless added by a hand). Consequently, in the formalism that I am proposing, the construction of the quantum evolution of the Universe in terms of transition amplitudes (instead of using perturbative approximations) appears to be possible.