Related papers: Bracket relations for relativity groups

We write down the Poisson structure for a relativistic particle where the Lorentz group does not act canonically, but instead as a Poisson-Lie group. In so doing we obtain the classical limit of a particle moving on a noncommutative space…

We introduce a symmetric Poisson bracket that allows us to describe anticommuting fields on a classical level in the same way as commuting fields, without the use of Grassmann variables. By means of a simple example, we show how the Dirac…

We construct a Leibniz bracket on the space $\Omega^\bullet (J^k (\pi))$ of all differential forms over the finite-dimensional jet bundle $J^k (\pi)$. As an example, we write Maxwell equations with sources in the covariant…

The Hamiltonian description for a wide class of mechanical systems, having local symmetry transformations depending on time derivatives of the gauge parameters of arbitrary order, is constructed. The Poisson brackets of the Hamiltonian and…

In this note the notion of Poisson brackets in Kontsevich's "Lie World" is developed. These brackets can be thought of as "universally" defined classical Poisson structures, namely formal expressions only involving the structure maps of a…

In the presence of a cosmological constant, ordinary Poincare' special relativity is no longer valid and must be replaced by a de Sitter special relativity, in which Minkowski space is replaced by a de Sitter spacetime. In consequence, the…

Starting with the well-defined product of quantum fields at two spacetime points, we explore an associated Poisson structure for classical field theories within the deformation quantization formalism. We realize that the induced…

It is shown that the new formula for the field theory Poisson brackets arise naturally in the extension of the formal variational calculus incorporating divergences. The linear spaces of local functionals, evolutionary vector fields,…

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…

This paper introduces and investigates a class of noncommutative spacetimes that I will call ``T-Minkowski,'' whose quantum Poincar\'e group of isometries exhibits unique and physically motivated characteristics. Notably, the coordinates on…

In this paper we study the problem of Hamiltonization of nonholonomic systems from a geometric point of view. We use gauge transformations by 2-forms (in the sense of Severa and Weinstein [29]) to construct different almost Poisson…

We consider a general formalism for treating a Hamiltonian (canonical) field theory with a spatial boundary. In this formalism essentially all functionals are differentiable from the very beginning and hence no improvement terms are needed.…

Using a Lax pair based on twisted affine $sl(2,R)$ Kac-Moody and Virasoro algebras, we deduce a r-matrix formulation of two dimensional reduced vacuum Einstein's equations. Whereas the fundamental Poisson brackets are non-ultralocal, they…

This paper showed that Poisson brackets in quaternion variables can be obtained directly from canonical Poisson brackets on cotangent bundle of $SE(3)$ (or $SO(3)$) endowed by canonical symplectic geometry. Quaternion parameters in our case…

Poisson brackets provide the mathematical structure required to identify the reversible contribution to dynamic phenomena in nonequilibrium thermodynamics. This mathematical structure is deeply linked to Lie groups and their Lie algebras.…

The spin-statistics conection is obtained for classical point particles. The connection holds within pseudomechanics, a theory of particle motion that extends classical physics to include anticommuting Grassmann variables, and which…

Using the multisymplectic Hamiltonian formalism, we propose a Poisson bracket for the electromagnetic field that, in addition to satisfying the restricted principle of relativity, reproduces well-established results from the standard…

Using the method of canonical group quantization, we construct the angular momentum operators associated to configuration spaces with the topology of (i) a sphere and (ii) a projective plane. In the first case, the obtained angular momentum…

A fully relational quantum theory necessarily requires an account of changes of quantum reference frames, where quantum reference frames are quantum systems relative to which other systems are described. By introducing a relational…

In this paper, we study singular systems with complete sets of involutive constraints. The aim is to establish, within the Hamilton-Jacobi theory, the relationship between the Frobenius' theorem, the infinitesimal canonical transformations…