Related papers: Conservation Laws in Poincar\'e Gauge Theory
The Hamiltonian formulation of Horava gravity is derived. In a closed universe the Hamiltonian is a sum of generators of gauge symmetries, the foliation-preserving diffeomorphisms, and vanishes on shell. The scalar constraint is second…
We investigate $n$-component systems of conservation laws that possess third-order Hamiltonian structures of differential-geometric type. The classification of such systems is reduced to the projective classification of linear congruences…
The gauge symmetries of a general dynamical system can be systematically obtained following either a Hamiltonean or a Lagrangean approach. In the former case, these symmetries are generated, according to Dirac's conjecture, by the first…
The relativistic conservation law involving the center of energy is reviewed and illustrated using simple examples from classical electromagnetic theory. It is emphasized that this conservation law is parallel to the conservation laws for…
Within a strong coupling expansion, we construct local quasi-conserved operators for a class of Hamiltonians that includes both integrable and non-integrable models. We explicitly show that at the lowest orders of perturbation theory the…
This work presents a general geometric framework for simulating and learning the dynamics of Hamiltonian systems that are invariant under a Lie group of transformations. This means that a group of symmetries is known to act on the system…
A new, general, field theoretic approach to the derivation of asymptotic conservation laws is presented. In this approach asymptotic conservation laws are constructed directly from the field equations according to a universal prescription…
We initiate the construction of the global Poincar\'e algebra generators in the context of the post-Minkowskian Hamiltonian formulation of gravitating binary dynamics in isotropic coordinates that is partly inspired by scattering…
A new quasigroup approach to conservation laws in general relativity is applied to study asymptotically flat at future null infinity spacetime. The infinite-parametric Newman-Unti group of asymptotic symmetries is reduced to the Poincar\'e…
A new formalism for lattice gauge theory is developed that preserves Poincar\'e symmetry in a discrete universe. We define the $\mathbb{1}$-loop, a generalization of the Wilson loop that reformulates classical differential equations of…
Using a Poisson bracket representation, in 3D, of the Lie algebra $\mathfrak{sl}(2)$, we first use highest weight representations to embed this into larger Lie algebras. These are then interpreted as symmetry and conformal symmetry algebras…
We present a Lagrangian description of the $SU(2)/U(1)$ coset model perturbed by its first thermal operator. This is the simplest perturbation that changes sign under Krammers--Wannier duality. The resulting theory, which is a 2--component…
A method to construct Hamiltonian theories for systems of both ordinary and partial differential equations is presented. The knowledge of a Lagrangian is not at all necessary to achieve the result. The only ingredients required for the…
The semiclassical limit of full non-commutative gauge theory is known as Poisson gauge theory. In this work we revise the construction of Poisson gauge theory paying attention to the geometric meaning of the structures involved and advance…
We present AI Poincar\'e, a machine learning algorithm for auto-discovering conserved quantities using trajectory data from unknown dynamical systems. We test it on five Hamiltonian systems, including the gravitational 3-body problem, and…
Starting from the most general formulation of stochastic thermodynamics---i.e. a thermodynamically consistent nonautonomous stochastic dynamics describing systems in contact with several reservoirs---, we define a procedure to identify the…
We obtain the Poincare group generators by proper choice of arbitrary functions present in the Relativistic Theory of Gravitation (RTG) Hamiltonian. Their Dirac brackets give the Poincare algebra in accordance with the fact that RTG has 10…
We perform the full Hamiltonian analysis of the topological BFCG action based on the Poincare 2-group. The Hamiltonian of the theory is constructed, and the algebra of constraints is computed. The Dirac brackets are evaluated, and the…
Starting from matter lagrangean containing higher order derivative than the first, we construct the Poincare gauge theory by localising the Poincare symmetry of the matter theory. The construction is shown to follow the usual geometric…
The Dirac-Bergmann algorithm for the Hamiltonian analysis of constrained systems is a nice and powerful tool, widely used for quantization and non-perturbative counting of degrees of freedom. However, certain aspects of its application to…