Related papers: Presymplectic Geometry and the Problem of Time. Pa…
We establish the Hamiltonian formulation of the teleparallel equivalent of general relativity, without fixing the time gauge condition, by rigorously performing the Legendre transform. The time gauge condition, previously considered,…
The paper is devoted to the description of the reparametrization - invariant dynamics of general relativity obtained by resolving constraints and constructing equivalent unconstrained systems. The constraint-shell action reveals the "field…
This paper is concerned with basic geometric properties of the phase space of a classical general relativistic particle, regarded as the 1st jet space of motions, i.e. as the 1st jet space of timelike 1--dimensional submanifolds of…
One approach to defining dynamics for quantum gravity in a naturally timeless setting is to select a suitable matter degree of freedom as a 'clock' before quantisation. This idea of deparametrisation was recently introduced in group field…
Barbour's interpretation of Mach's principle led him to postulate that gravity should be formulated as a dynamical theory of spatial conformal geometry, or in his terminology, "shapes." Recently, it was shown that the dynamics of General…
We present the Dirac Hamiltonian formalism for a pair of $1$-form fields with a topological-like potential coupled to first-order gravity in three-dimensional spacetime. By considering the complete phase space, we derive the full structure…
Since the main open problem of contemporary physics is to find a unified description of the four interactions, we present a possible scenario which, till now only at the classical level, is able to englobe experiments ranging from…
In this article, we investigate the geometry of static perfect fluid space-time on compact manifolds with boundary. We use the generalized Reilly's formula to establish a geometric inequality for a static perfect fluid space-time involving…
In this paper we study the structure of the phase space in noncommutative geometry in the presence of a nontrivial frame. Our basic assumptions are that the underlying space is a symplectic and parallelizable manifold. Furthermore, we…
The Hamiltonian system of general relativity and its quantization without any matter or gauge fields are discussed on the basis of the symplectic geometrical theory. A symplectic geometry of classical general relativity is constructed using…
In this paper, we apply the geometric Hamilton--Jacobi theory to obtain solutions of Hamiltonian systems in Classical Mechanics, that are either compatible with a cosymplectic or a contact structure. As it is well known, the first structure…
It is well known that nonrelativistic quantum mechanics presents a clear asymmetry between space and time. Much of this asymmetry is attributed to the lack of Lorentz invariance of the theory. Nonetheless, a recent work [Phys. Rev. A…
The classical and quantum dynamics of simple time-reparametrization- invariant models containing two degrees of freedom are studied in detail. Elimination of one ``clock'' variable through the Hamiltonian constraint leads to a description…
The purpose of this paper is twofold: On the one hand, after a thorough review of the matter free case, we supplement the derivations in our companion paper on 'loop quantum gravity without the Hamiltonian constraint' with calculational…
In this paper we provide a complete characterisation of coisotropic embeddings of precosymplectic manifolds into cosymplectic manifolds. This result extends a theorem of Gotay about coisotropic embeddings of presymplectic manifolds. We also…
We exploit the reparametrization symmetry of a relativistic free particle to impose a gauge condition which upon quantization implies space-time noncommutativity. We show that there is an algebraic map from this gauge back to the standard…
We study a class of theories in which space-time is treated classically, while interacting with quantum fields. These circumvent various no-go theorems and the pathologies of semi-classical gravity, by being linear in the density matrix and…
Actions of Lie groups on presymplectic manifolds are analyzed, introducing the suitable comomentum and momentum maps. The subsequent theory of reduction of presymplectic dynamical systems with symmetry is studied. In this way, we give a…
Positive-energy solutions of the Klein-Gordon equation form a Hilbert space of holomorphic functions on the future tube. This domain is interpreted as an extended phase space for the associated classical particle, the extra dimensions being…
This manuscript introduces novel approaches to three phenomena. First, we extend the algebraic formulation of kinetic theory within the contact framework by making explicit the gauge freedom, thereby obtaining a formulation in which the…