Marko Vojinovic

Effective action and semi-classical limit of spin-foam models

We define an effective action for spin-foam models of quantum gravity by adapting the background field method from quantum field theory. We show that the Regge action is the leading term in the semi-classical expansion of the spin-foam effective action if the vertex amplitude has the large-spin asymptotics which is proportional to an exponential function of the vertex Regge action. In the case of the known three-dimensional and four-dimensional spin-foam models, this amounts to modifying the vertex amplitude such that the exponential asymptotics is obtained. In particular, we show that the ELPR/FK model vertex amplitude can be modified such that the new model is finite and has the Einstein?Hilbert action as its classical limit. We also calculate the first-order and some of the second-order quantum corrections in the semi-classical expansion of the effective action.

Poincaré 2-group and quantum gravity

We show that general relativity can be formulated as a constrained topological theory for flat 2-connections associated with the Poincare 2-group. Matter can be consistently coupled to gravity in this formulation. We also show that the edge lengths of the spacetime manifold triangulation arise as the basic variables in the path-integral quantization, while the state-sum amplitude is an evaluation of a colored 3-complex, in agreement with the category theory results. A 3-complex amplitude for Euclidean quantum gravity is proposed.

A finiteness bound for the EPRL/FK spin foam model

We show that the EPRL/FK spin foam model of quantum gravity has an absolutely convergent partition function if the vertex amplitude is divided by an appropriate power p of the product of dimensions of the vertex spins. This power is independent of the spin foam 2-complex and we find that p > 2 ensures the convergence of the state sum. Determining the convergence of the state sum for the values 0 ≤ p ≤ 2 requires the knowledge of the large-spin asymptotics of the vertex amplitude in the cases when some of the vertex spins are large and other are small.

Effective action for EPRL/FK spin foam models

We show that a natural modification of the EPRL/FK vertex amplitude gives a finite spin foam model whose effective action gives the Einstein-Hilbert action in the limit of large spins and arbitrarily fine spacetime triangulations. The first-order quantum corrections can be easily computed and we show how to calculate the higher-order corrections.

Solution to the cosmological-constant problem in a Regge quantum gravity model

We show that it is possible to solve the cosmological constant (CC) problem in a discrete quantum gravity theory based on Regge calculus by using the effective action approach and a special path-integral measure. The effective cosmological constant is given as a sum of 3 terms: the classical CC, the quantum gravity CC and the matter CC. Since the observations can only measure the sum of these 3 terms, we can choose the classical CC to be equal to the negative value of the matter CC. Hence the effective CC is given only by the quantum gravity CC, which is determined by the path-integral measure. Since the path-integral measure depends on a free parameter, this parameter can be chosen such that the effective CC gives the observed value.

Large-spin asymptotics of Euclidean LQG flat-space wavefunctions

We analyze the large-spin asymptotics of a class of spin-network wavefunctions of Euclidean Loop Quantum Gravity, which corresponds to a flat spacetime. A wavefunction from this class can be represented as a sum over the spins of an amplitude for a spin network whose graph is a composition of the the wavefunction spin network graph with the dual one-complex graph and the tetrahedron graphs for a triangulation of the spatial 3-manifold. This spin-network amplitude can be represented as a product of 6j symbols, which is then used to find the large-spin asymptotics of the wavefunction. By using the Laplace method we show that the large-spin asymptotics is given by a sum of Gaussian functions. However, these Gaussian functions are not of the type which gives the correct graviton propagator.

Cosine problem in EPRL/FK spinfoam model

We calculate the classical limit effective action of the EPRL/FK spinfoam model of quantum gravity coupled to matter fields. By employing the standard QFT background field method adapted to the spinfoam setting, we find that the model has many different classical effective actions. Most notably, these include the ordinary Einstein–Hilbert action coupled to matter, but also an action which describes antigravity. All those multiple classical limits appear as a consequence of the fact that the EPRL/FK vertex amplitude has cosine-like large spin asymptotics. We discuss some possible ways to eliminate the unwanted classical limits.

Hamiltonian analysis of the BFCG theory for the Poincaré 2-group

We perform the full Hamiltonian analysis of the topological BFCG action based on the Poincare 2-group. The Hamiltonian of the theory is constructed, and the algebra of constraints is computed. The Dirac brackets are evaluated, and the second class constraints are then eliminated from the theory. The results are contrasted to those of the topological Poincare gauge theory, which is equivalent to the BFCG model at the level of the classical action, but has a very different Hamiltonian structure.

Categorical generalization of spinfoam models

We give a brief review of the problem of quantum gravity. After the discussion of the nonrenormalizability of general relativity, we briefly mention the main research directions which aim to resolve this problem. Our attention then focuses on the approach of Loop Quantum Gravity, specifically spinfoam models. These models have some issues concerning the semiclassical limit and coupling of matter fields. The recent developments in category theory provide us with the necessary formalism to introduce a new action for general relativity and perform covariant quantization so that the issues of spinfoam models are successfully resolved.