Related papers: Generalized geometric commutator theory and quantu…
`How do our ideas about quantum mechanics affect our understanding of spacetime?' This familiar question leads to quantum gravity. The complementary question is also important: `How do our ideas about spacetime affect our understanding of…
Recent work has shown that two-dimensional non-linear $\sigma$-models on group manifolds with Poisson-Lie symmetry can be understood within generalised geometry as exemplars of generalised parallelisable spaces. Here we extend this idea to…
In this paper we relate the geometric Poisson brackets on the Grassmannian of 2-planes in R^4 and on the (2,2) Moebius sphere. We show that, when written in terms of local moving frames, the geometric Poisson bracket on the Moebius sphere…
The concept of quantum commutativity with respect to an action or coaction of a given Hopf algebra is used for the algebraic description of a system of particles and their interaction with certain quantum field. Graded commutativity and…
We look at generalized complex structures from the point of view of Poisson and Dirac geometry and we remark that the puzzling equations underlying the notion of generalized complex structure have miraculously simple meaning when passing to…
A new class of modified theory of gravity is introduced where the volume form becomes dynamical. This approach is motivated by unimodular gravity and can also be related to Brans-Dicke theory. On the level of the action, the only change…
We construct the commutative Poisson algebra of classical Hamiltonians in field theory. We pose the problem of quantization of this Poisson algebra. We also make some interesting computations in the known quadratic part of the quantum…
An algebraic formulation of general relativity is proposed. The formulation is applicable to quantum gravity and noncommutative space. To investigate quantum gravity we develop the canonical formalism of operator geometry, after…
We extend the covariant canonical formalism recently discussed in ref. [1] to geometric theories coupled to both bosonic and fermionic $p$-forms. This allows a covariant hamiltonian treatment of supergravity theories. As examples we present…
Classical Hamiltonian mechanics, characterized by a single conserved Hamiltonian (energy) and symplectic geometry, `hides' other invariants into symmetries of the Hamiltonian or into the kernel of the Poisson tensor. Nambu mechanics aims to…
We develop a Heisenberg-picture \emph{kinematical} framework in which (i) time is treated as a quantum observable, admitting both a relational POVM construction for semibounded spectra and a fully self-adjoint realization on an enlarged…
This paper reframes Riemannian geometry as a generalized Lie algebra allowing the equations of both RG and then General Relativity to be expressed as commutation relations among fundamental operators. We begin with an Abelian Lie algebra of…
Assuming that the Hamiltonian of a canonical field theory can be written in the form N H + N^i H_i, and using as the only input the actual choice of the canonical variables, we derive: (i) The algebra satisfied by H and H_i, (ii) any…
We address the issue of when generalized quantum dynamics, which is a classical symplectic dynamics for noncommuting operator phase space variables based on a graded total trace Hamiltonian ${\bf H}$, reduces to Heisenberg picture complex…
In a series of papers we proposed a model unifying general relativity and quantum mechanics. The idea was to deduce both general relativity and quantum mechanics from a noncommutative algebra ${\cal A}_{\Gamma}$ defined on a transformation…
The use of geometric methods has proved useful in the hamiltonian description of classical constrained systems. In this note we provide the first steps toward the description of the geometry of quantum constrained systems. We make use of…
In this work we take into consideration a generalization of Gauge Theories based on the analysis of the structural characteristics of Maxwell theory, which can be considered as the prototype of such kind of theories (Maxwell-like). Such…
It is well known that in a generally covariant gravitational theory the choice of spacetime scalars as coordinates yields phase-space observables (or "invariants"). However their relation to the symmetry group of diffeomorphism…
We introduce Hopf algebroid covariance on Woronowicz's differential calculus. Using it, we develop quite a general framework of noncommutative complex geometry that subsumes the one in [2]. We present transverse complex and K\"ahler…
How to give a natural geometric definition of a covariant Poisson bracket in classical field theory has for a long time been an open problem - as testified by the extensive literature on "multisymplectic Poisson brackets", together with the…