Related papers: First class functions in constrained second class …
It is shown that a Dirac bracket algebra is isomorphic to the original Poisson bracket algebra of first class functions subject to first class constraints. The isomorphic image of the Dirac bracket algebra in the star-product commutator…
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…
In the Dirac bracket approach to dynamical systems with second class constraints observables are represented by elements of a quotient Dirac bracket algebra. We describe families of new realizations of this algebra through quotients of the…
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 the Dirac approach to the generalized Hamiltonian formalism, dynamical systems with first- and second-class constraints are investigated. The classification and separation of constraints into the first- and second-class ones are…
Dirac's conjecture, that secondary first-class constraints generate transformations that do not change the physical system's state, has various counterexamples. Since no matching gauge conditions can be imposed, the Dirac bracket cannot be…
We show that a given set of first class constraints becomes abelian if one maps each constraint to the surface of other constraints. There is no assumption that first class constraints satisfy a closed algebra. The explicit form of the…
In a classical Hamiltonian theory with second class constraints the phase space functions on the constraint surface are observables. We give general formulas for extended observables, which are expressions representing the observables in…
The Dirac constraint formalism is used to analyze the first order form of the Einstein-Hilbert action in d > 2 dimensions. Unlike previous treatments, this is done without eliminating fields at the outset by solving equations of motion that…
A generalized version is proposed for the field-antifield formalism. The antibracket operation is defined in arbitrary field-antifield coordinates. The antisymplectic definitions are given for first- and second-class constraints. In the…
We show that after mapping each element of a set of second class constraints to the surface of the other ones, half of them form a subset of abelian first class constraints. The explicit form of the map is obtained considering the most…
The Dirac constraint formalism is applied to the d(d>2) dimensional Einstein-Hilbert action when written in first order form, using the metric density and affine connection as independent fields. Field equations not involving time…
A toy model (suggested by Klauder) is analyzed from the perspective of First Class and Second Class Dirac constrained systems. The comparison is made by turning a First Class into a Second Class system with the introduction of suitable…
Dynamical systems, described by Lagrangians with first- and second-class constraints, are investigated. In the Dirac approach to the generalized Hamiltonian formalism, the classification and separation of the first- and second-class…
The systematic method for the conversion of first class constraints to the equivalent set of Abelian one based on the Dirac equivalence transformation is developed. The representation for the corresponding matrix performing this…
In the framework of the generalized Hamiltonian formalism by Dirac, the local symmetries of dynamical systems with first- and second-class constraints are investigated. For theories with an algebra of constraints of special form (to which a…
Potential algebras can be used effectively in the analysis of the quantum systems. In the article, we focus on the systems described by a separable, 2x2 matrix Hamiltonian of the first order in derivatives. We find integrals of motion of…
Dirac formalism of Hamiltonian constraint systems is studied for the noncommutative Abelian Proca field. It is shown that the system of constraints are of second class in agreement with the fact that the Proca field is not guage invariant.…
The structure functions of the Lagrangian gauge algebra are given explicitly in terms of the hamiltonian constraints and the first order Hamiltonian structure functions and their derivatives.
First-class constraints constitute a potential obstacle to the computation of a Poisson bracket in Dirac's theory of constrained Hamiltonian systems. Using the pseudoinverse instead of the inverse of the matrix defined by the Poisson…