Related papers: Canonical tensor models with local time
We present a detailed analysis of the Hamiltonian constraints of the d-dimensional tetrad-connection gravity where the non-dynamical part of the spatial connection is fixed to zero by an adequate guage transformation. This new action…
We derive the kinematic Hamiltonian for the so-called "new general relativity" class of teleparallel gravity theories, which is the most general class of theories whose Lagrangian is quadratic in the torsion tensor and does not contain…
We consider inclusion of interactions between 3d Einstein gravity and the third order extensions of Chern-Simons. Once the gravity is minimally included into the third order vector field equations, the theory is shown to admit a…
(3+1) (continuous time) Regge calculus is reduced to Hamiltonian form. The constraints are classified, classical and quantum consequences are discussed. As basic variables connection matrices and antisymmetric area tensors are used…
The main goal of these lectures is to introduce and review the Hamiltonian formalism for classical constrained systems and in particular gauge theories. Emphasis is put on the relation between local symmetries and constraints and on the…
Space-time non-commutative theories are non-local in time. We develop the Hamiltonian formalism for non-local field theories in d space-time dimensions by considering auxiliary d+1 dimensional field theories which are local with respect to…
This paper presents a Hamiltonian formulation of spinfoam-gravity, which leads to a straight-forward canonical quantisation. To begin with, we derive a continuum action adapted to the simplicial decomposition. The equations of motion admit…
In this paper explore the relation between covariant and canonical approaches to quantum gravity and $BF$ theory. We will focus on the dynamical triangulation and spin-foam models, which have in common that they can be defined in terms of…
A modification of the canonical quantization procedure for systems with time-dependent second-class constraints is discussed and applied to the quantization of the relativistic particle in a plane wave. The time dependence of constraints…
We consider the most general class of teleparallel gravitational {}{}theories quadratic in the torsion tensor, in three space-time dimensions, and carry out a detailed investigation of its Hamiltonian formulation in Schwinger's time gauge.…
A variety of local index formulas is constructed for quantum Hamiltonians with periodic boundary conditions. All dimensions of physical space as well as many symmetry constraints are covered, notably one-dimensional systems in Class DIII as…
The Hamiltonian formulation of the tetrad gravity in any dimension higher than two, using its first order form when tetrads and spin connections are treated as independent variables, is discussed and the complete solution of the three…
The standard geometrodynamics is transformed into a theory of conformal geometrodynamics by extending the ADM phase space for canonical general relativity to that consisting of York's mean exterior curvature time, conformal three-metric and…
We study constrained Hamiltonian systems by utilizing general forms of time discretization. We show that for explicit discretizations, the requirement of preserving the canonical Poisson bracket under discrete evolution imposes strong…
The importance of the first-class constraint algebra of general relativity is not limited just by its self-contained description of the gauge nature of spacetime, but it also provides conditions to properly evolve the geometry by selecting…
Essential to the description of a quantum system are its local degrees of freedom, which enable the interpretation of subsystems and dynamics in the Hilbert space. While a choice of local tensor factorization of the Hilbert space is often…
One of the hardest problems to tackle in the dynamics of canonical approaches to quantum gravity is that of the Hamiltonian constraint. We investigate said problem in the context of formal geometric quantization. We study the implications…
We construct a model of quantum gravity in which dimension, topology and geometry of spacetime are dynamical. The microscopic degree of freedom is a real rectangular matrix whose rows label internal flavours, and columns label spatial…
Only a severely restricted class of tensor fields can provide classical spacetime geometries, namely those that can carry matter field equations that are predictive, interpretable and quantizable. These three conditions on matter translate…
The total Hamiltonian in general relativity, which involves the first class Hamiltonian and momentum constraints, weakly vanishes. However, when the action is expanded around a classical solution as in the case of a single scalar field…