Related papers: Weak Dirac bracket construction and the superparti…
The Barnich--Troessaert bracket is a proposal for a modified Poisson bracket on the covariant phase space for general relativity. The new bracket allows us to compute charges, which are otherwise not integrable. Yet there is a catch. There…
The jet bundle description of time-dependent mechanics is revisited. The constraint algorithm for singular Lagrangians is discussed and an exhaustive description of the constraint functions is given. By means of auxiliary connections we…
We consider (2+1)-gravity with vanishing cosmological constant as a constrained dynamical system. By applying Dirac's gauge fixing procedure, we implement the constraints and determine the Dirac bracket on the gauge-invariant phase space.…
In this paper, we present a detailed review/analysis of the Dirac quantisation of Hamiltonian systems with constraints. To this end, we use, as a guide, the physical example provided by the dynamics of a solid ball rolling, without…
In her recent work, Dittrich generalized Rovelli's idea of partial observables to construct Dirac observables for constrained systems to the general case of an arbitrary first class constraint algebra with structure functions rather than…
Generators of the algebra of first class functions in a system with second class constraints are found. It is shown that first class functions form algebras with respect to the Dirac bracket and pointwise multiplication.The subspace of…
We propose a systematic procedure that solves the Dirac bracket commutators. The method is based on the Gauge Unfixing formalism, a procedure that converts second class systems into first class ones without the enlargement of the original…
We present a reduction procedure for gauge theories based on quotienting out the kernel of the presymplectic form in configuration-velocity space. Local expressions for a basis of this kernel are obtained using phase space procedures; the…
An extension of the Dirac procedure for the quantization of constrained systems is necessary to address certain issues that are left open in Dirac's original proposal. These issues play an important role especially in the context of…
In this work we study some symplectic submanifolds in the cotangent bundle of a factorizable Lie group defined by second class constraints. By applying the Dirac method, we study many issues of these spaces as fundamental Dirac brackets,…
Covariant quantization of the Nambu-Goto spinning particle in 2+1-dimensions is studied. The model is relevant in the context of recent activities in non-commutative space-time. From a technical point of view also covariant quantization of…
In this work, we investigate a Lagrangian model describing a particle constrained to move along non-degenerate conic sections, parameterized by the orbital eccentricity \( e \). In the non-relativistic regime, we apply the Dirac--Bergmann…
We present the Dirac Hamiltonian formalism for a pair of $1$-form fields with a topological-like potential coupled to first-order gravity in three-dimensional spacetime. By considering the complete phase space, we derive the full structure…
In this work, a conformable singular system with second-class constraints is discussed. The conformable Poisson bracket (CDB) of two functions is defined. and, the Dirac theory is developed to be applicable to conformable singular systems.…
Central issues of the Dirac constraint formalism are discussed in relation to the algorithmic methods of commutative algebra based on the Groebner basis techniques. For a wide class of finite dimensional polynomial degenerate Lagrangian…
The necessary and sufficient conditions are established for the second-class constraint surface to be (an almost) K\"ahler manifold. The deformation quantisation for such systems is scetched resulting in the Wick-type symbols for the…
Adopting the omni-Lie algebroid approach to Dirac-Jacobi structures, we propose and investigate a notion of weak dual pairs in Dirac-Jacobi geometry. Their main motivating examples arise from the theory of multiplicative precontact…
This work is dedicated to the quantization of the light-front Yukawa model in D=1+3 dimensions with higher order derivatives of the scalar field. The problem of the computing Dirac brackets and the (anti-) commutator algebra of interacting…
We analyze the canonical treatment of classical constrained mechanical systems formulated with a discrete time. We prove that under very general conditions, it is possible to introduce nonsingular canonical transformations that preserve the…
In a Hamiltonian system with first class constraints observables can be defined as elements of a quotient Poisson bracket algebra. In the gauge fixing method observables form a quotient Dirac bracket algebra. We show that these two algebras…