Related papers: Simplicity in simplicial phase space
The kinematical phase space of classical gravitational field is flat (affine) and unbounded. Because of this, field variables may tend to infinity leading to appearance of singularities, which plague Einstein's theory of gravity. The…
In this paper, we are going to discuss the gauge reduction with respect to the simplicity constraint in both classical and quantum theory of all dimensional loop quantum gravity. With the gauge reduction with respect to edge-simplicity…
The program of quantizing the gravitational field with the help of affine field variables is continued. For completeness, a review of the selection criteria that singles out the affine fields, the alternative treatment of constraints, and…
In this paper it is implemented how to make compatible the boundary conditions and the gauge fixing conditions for complex general relativity written in terms of Ashtekar variables using the Henneaux-Teitelboim-Vergara approach. Moreover,…
The Spin Foam approach to quantum gravity aims at providing a covariant path-integral formulation of canonical Loop Quantum Gravity. Since spin foam amplitudes are defined through discretisations of spacetime, understanding the continuum…
In a recent work, a dual formulation of group field theories as non-commutative quantum field theories has been proposed, providing an exact duality between spin foam models and non-commutative simplicial path integrals for constrained BF…
Gauge-invariant systems in unconstrained configuration and phase spaces, equivalent to second-class constraints systems upon a gauge-fixing, are discussed. A mathematical pendulum on an $n-1$-dimensional sphere $S^{n-1}$ as an example of a…
We review the classical formulation of general relativity as an SL(2,C) gauge theory in terms of Ashtekar's selfdual variables and reality conditions for the spatial metric (RCI) and its evolution (RCII), and we add some new observations…
The kinematic degrees of freedom of spinning particles are analyzed and an explicit construction of the phase space and the simplectic structure that accomodates them is presented. A Poincare invariant theory of classical spinning particles…
We give a short review of the spin foam models of quantum gravity, with an emphasis on the Barret-Crane model. After explaining the shortcomings of the Barret-Crane model, we briefly discuss two new approaches, one based on the 3d spin foam…
An idea of reality conditions in the context of spin foams (Barrett-Crane models) is developed. The square of areas are the most elementary observables in the case of spin foams. This observation implies that simplest reality conditions in…
Spin foam models for quantum gravity are derived from lattice path integrals. The setting involves variables from both lattice BF theory and Regge calculus. The action consists in a Regge action, which depends on areas, dihedral angles and…
Recently, two new spin-foam models have appeared in the literature, both motivated by a desire to modify the Barrett-Crane model in such a way that the imposition of certain second class constraints, called cross-simplicity constraints, are…
We study the implications of the simplicity constraint in the spincube model of quantum gravity. By relating the edge-lengths to the integer areas of triangles, the simplicity constraint imposes very strong restrictions between them,…
We describe a simple gauge-fixing that leads to a construction of a quantum Hilbert space for quantum gravity in an asymptotically Anti de Sitter spacetime, valid to all orders of perturbation theory. The construction is motivated by a…
We investigate a formulation of continuum 4d gravity in terms of a constrained BF theory, in the spirit of the Plebanski formulation, but involving only linear constraints, of the type used recently in the spin foam approach to quantum…
The Lagrangian formulation of classical field theories and in particular general relativity leads to a coordinate-free, fully covariant analysis of these constrained systems. This paper applies multisymplectic techniques to obtain the…
We develop a proposal for a theory of simplicial gravity with spinors as the fundamental configuration variables. The underlying action describes a mechanical system with finitely many degrees of freedom, the system has a Hamiltonian and…
Hilbert spaces in theories of gravity are notoriously subtle due to the Hamiltonian constraints, particularly regarding the inner product. To demystify this subject, we review and extend a collection of ideas in canonical gravity, and…
So far spin foam models are hardly understood beyond a few of their basic building blocks. To make progress on this question, we define analogue spin foam models, so called spin nets, for quantum groups $\text{SU}(2)_k$ and examine their…