Related papers: Conservation Laws in Poincar\'e Gauge Theory
We investigate the tension between symplecticity and gauge covariance in classical Hamiltonian mechanics. The pursuit of manifest covariance over manifest symplecticity results in a unique geometric formulation. Firstly, covariant yet…
A new gauge invariant formulation of the relativistic scalar field interacting with Chern-Simons gauge fields is considered. This formulation is consistent with the gauge fixed formulation. Furthermore we find that canonical (Noether)…
The fact that the conserved current of a gauge symmetry is reduced to a superpotential is proved in a very general setting.
How can we relate the constraint structure and constraint dynamics of the general gauge theory in the Hamiltonian formulation with specific features of the theory in the Lagrangian formulation, especially relate the constraint structure…
Poincar\'e Gauge Theories are a class of Metric-Affine Gravity theories with a metric-compatible (i.e. Lorentz) connection and with an action quadratic in curvature and torsion. We perform an explicit one-loop calculation starting with a…
We aim to analyze the consistency of the deformation of the Heisenberg algebra in the setting of constrained Hamiltonian systems, providing a procedure to induce the deformation on the Poisson algebra after symplectic reduction. We…
We introduce a method to construct conservation laws for a large class of linear partial differential equations. In contrast to the classical result of Noether, the conserved currents are generated by any symmetry of the operator, including…
In this work we study a generalized variable-coefficient Gardner equation from the point of view of Lie symmetries in partial differential equations. We find conservation laws by using the multipliers method of Anco and Bluman which does…
A systematic procedure is proposed for deriving all the gauge symmetries of the general, not necessarily variational, equations of motion. For the variational equations, this procedure reduces to the Dirac-Bergmann algorithm for the…
The Hamiltonian approach to the General Relativity is formulated as a joint nonlinear realization of conformal and affine symmetries by means of the Dirac scalar dilaton and the Maurer-Cartan forms. The dominance of the Casimir vacuum…
Many important physical systems can be described as the evolution of a Hamiltonian system, which has the important property of being conservative, that is, energy is conserved throughout the evolution. Physics Informed Neural Networks and…
We construct a modification of the Poisson bracket which is suitable for a canonical analysis of space-time noncommutative field theories. We show that this bracket satisfies the Jacobi identities and generates equations of motion. In this…
This paper investigates Hamiltonian properties of the algebro-geometric discretization of KP hierarchy introduced in \cite{Gie1}. A Poisson bracket is introduced. The system is related to the periodic band matrix system of \cite{vM-M}. It…
We present a pseudoclassical mechanics model which exhibits gauge symmetry and time-reparametrization invariance. As such, first- and second-class constraints restrict the phase space, and the Hamiltonian weakly vanishes. We show that the…
In this paper we study the infinitesimal symmetries, Newtonoid vector fields, infinitesimal Noether symmetries and conservation laws of Hamiltonian systems. Using the dynamical covariant derivative and Jacobi endomorphism on the cotangent…
We treat energy-momentum conservation laws as particular gauge conservation laws when generators of gauge transformations are horizontal vector fields on fibre bundles. In particular, the generators of general covariant transformations are…
The neat formulation that describes the gauge interactions associated with internal symmetries is extended to the case of a simple, yet non-trivial, symmetry group structure which mixes gravity and electromagnetism by associating a gauge…
Exotic General Massive Gravity is the next-to-simplest gravitational theory fulfilling the so-called third-way consistency, the simplest being Minimal Massive Gravity. We investigate the canonical structure of the first-order formulation of…
Symmetry properties of conservation laws of partial differential equations are developed by using the general method of conservation law multipliers. As main results, simple conditions are given for characterizing when a conservation law…
We discuss in detail how string-inspired lineal gravity can be formulated as a gauge theory based on the centrally extended Poincar\'e group in $(1+1)$ dimensions. Matter couplings are constructed in a gauge invariant fashion, both for…