Related papers: Quantization of counterexamples to Dirac's conject…

First class constraints in a canonical formalism of a gauge theory might generate transformations which map a state to its physically equivalent state. This is called Dirac's conjecture. There are two examples which may be candidates of…

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…

A standard tenet of canonical quantum gravity is that evolution generated by a Hamiltonian constraint is just a gauge transformation on the phase space and therefore does not change the physical state. The basis for this belief is a theorem…

We show that an unambiguous and correct quantization of the second-class constrained system of a free particle on a sphere in $D$ dimensions is possible only by converting the constraints to abelian gauge constraints, which are of first…

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.…

Another counter-example to Dirac's Conjecture is presented, which resembles the Cawley model but is so modified as to include second class constraints. The arbitrary function in the general solution to the defining equations of momenta…

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…

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…

In Dirac-Bergmann constrained dynamics, a first-class constraint typically does not _alone_ generate a gauge transformation. Each first-class constraint in Maxwell's theory generates a change in the electric field E by an arbitrary…

In order to quantize systems involving second-class constraints, one should use Dirac bracket instead of Poisson bracket. Furthermore, one can specify a star product in which the term linear in $\hbar$ is proportional to the Dirac bracket.…

Dirac's quantization of the Maxwell theory on non-commutative spaces has been considered. First class constraints were found which are the same as in classical electrodynamics. The gauge covariant quantization of the non-linear equations of…

In this article we show that boundary conditions can be treated as Lagrangian and Hamiltonian constraints. Using the Dirac method, we find that boundary conditions are equivalent to an infinite chain of second class constraints which is a…

The constrained Hamiltonian systems admitting no gauge conditions are considered. The methods to deal with such systems are discussed and developed. As a concrete application, the relationship between the Dirac and reduced phase space…

In this paper, I consider a recent controversy about whether first-class constraints generate gauge transformations in the case of electromagnetism. I argue that there is a notion of gauge transformation, the extended notion, which is…

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 relationship between the Dirac and reduced phase space quantizations is investigated for spin models belonging to the class of Hamiltonian systems having no gauge conditions. It is traced out that the two quantization methods may give…

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…

We provide a simultaneous derivation of the Dirac bracket and of the equations of motion for second-class constrained systems when the constraints are time-dependent. The necessity of time-dependent gauge-fixing conditions is shown in the…

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…

In the paper "Constraint Quantization of Open String in Background $B$ field and Noncommutative D-brane", it is claimed that the boundary conditions lead to an infinite set of secondary constraints and Dirac brackets result in a…