Particle dynamics on Snyder space

Abstract

We examine Hamiltonian formalism on Euclidean Snyder space. The latter corresponds to a lattice in the quantum theory. For any given dynamical system, it may not be possible to identify time with a real number parametrizing the evolution in the quantum theory. The alternative requires the introduction of a dynamical time operator. We obtain the dynamical time operator for the relativistic (nonrelativistic) particle, and use it to construct the generators of Poincaré (Galilei) group on Snyder space. *

Kinetic energy properties and weak equivalence principle in a space with generalized uncertainty principle

“…Different generalizations of the uncertainty principle or alternatively different deformations of commutation relations were proposed. Among well studied algebras are the Snyder algebra (see, for instance, [5,6,7,8,9,10]) which in the nonrelativistic case reads…”

Nonassociative Snyder ϕ4 quantum field theory

“…The Snyder model has been studied in a series of papers [30][31][32][33][34][35][36] and the associated Hopf algebra investigated in [30] and [36], where the model has been generalized and the star product, coproducts and antipodes have been calculated using the method of realizations. A different approach was used in [35], where the Snyder model was considered in a geometrical perspective as a coset in momentum space, and the results are equivalent to those of Refs.…”

Noncommutative spaces and covariant formulation of statistical mechanics

“…It is straightforward to show that the above commutation relations can be realized from the symplectic structure [42] ω…”

“…In this limit, the series in the relation (43) converges and one can use it to obtain all the minimal length (quantum gravity) corrections to the internal energy and specific heat. Substituting the relation (43) into (42) and then using the definition U ¼ T 2 ð ∂ ln Z ∂T Þ N , it is easy to show that the internal energy in the limit of Θ ≫ 1 will be…”