Related papers: Planar Carrollean dynamics, and the Carroll quantu…
Quantum theory can be formulated as a theory of operations, more specific, of complex represented operations from real Lie groups. Hilbert space eigenvectors of acting Lie operations are used as states or particles. The simplest simple Lie…
Standard particle theory is based on quantized matter embedded in a classical geometry. Here, a complementary model is proposed, based on classical matter -- massive bodies, without quantum properties -- embedded in a quantum geometry. It…
Expansions of Lie algebras are the opposite process of contractions. Starting from a Lie algebra, the expansion process goes to another one, non-isomorphic and less abelian. We propose an expansion method based in the Casimir invariants of…
The symplectic geometry of the phase space associated with a charged particle is determined by the addition of the Faraday 2-form to the standard structure on the Euclidean phase space. In this paper we describe the corresponding algebra of…
Covariant classical particle dynamics is described, and the associated covariant relativistic particle quantum mechanics is derived. The invariant symmetric bracket is defined on the space of quantum amplitudes, and its relation to a…
Quadratic algebras are generalizations of Lie algebras; they include the symmetry algebras of 2nd order superintegrable systems in 2 dimensions as special cases. The superintegrable systems are exactly solvable physical systems in classical…
Classical relativistic system of point particles coupled with an electromagnetic field is considered in the three-dimensional representation. The gauge freedom connected with the chronometrical invariance of the four-dimensional description…
A study of fundamental geometrical interactions shows that the Dirac electron can be represented as a conformal wave. A Riemannian space is used, having coordinates that transform locally as spinors. The wave function becomes a gradient.…
These notes are a didactic overview of the non perturbative and background independent approach to a quantum theory of gravity known as loop quantum gravity. The definition of real connection variables for general relativity, used as a…
We show that the classical mechanics of an algebraic model are implied by its quantizations. An algebraic model is defined, and the corresponding classical and quantum realizations are given in terms of a spectrum generating algebra.…
Extended particles are considered in terms of the fields on the Poincar\'{e} group. Dirac like wave equations for extended particles of any spin are defined on the various homogeneous spaces of the Poincar\'{e} group. Free fields of the…
We derive the dynamics of (isotropic) scalar perturbations from the mean-field hydrodynamics of full Lorentzian quantum gravity, as described by a two-sector (timelike and spacelike) Barrett-Crane group field theory (GFT) model. The rich…
A reconciliation of gravitation and electromagnetism has eluded physics for neearly a century. It is argued here that this is because both quantum physics and classical physics are set in differentiable space time manifolds with point…
A general noncommutative-geometric theory of principal bundles is presented. Quantum groups play the role of structure groups. General quantum spaces play the role of base manifolds. A differential calculus on quantum principal bundles is…
This is an introduction for nonspecialists to the noncommutative geometric approach to Planck scale physics coming out of quantum groups. The canonical role of the `Planck scale quantum group' $C[x]\bicross C[p]$ and its observable-state…
We show how to take the first step in the conformal program for constructing general matter couplings to Carroll gravity. In particular, we couple a single massless electric/magnetic scalar to conformal Carroll gravity with isotropic…
Following the idea of a field quantization of gravity as realized in group field theory, we construct a minisuperspace model where the wavefunction of canonical quantum cosmology (either Wheeler-DeWitt or loop quantum cosmology) is promoted…
It is postulated that quantum gravity is a sum over causal structures coupled to matter via scale evolution. Quantized causal structures can be described by studying simple matrix models where matrices are replaced by an algebra of quantum…
Dynamics has been generalized to a noncommutative phase space. The noncommuting phase space is taken to be invariant under the quantum group $GL_{q,p}(2)$. The $q$-deformed differential calculus on the phase space is formulated and using…
If there exists a formulation of quantum mechanics which does not refer to a background classical spacetime manifold, it then follows as a consequence, (upon making one plausible assumption), that a quantum description of gravity should be…