Related papers: An algebraic extension of Dirac quantization: Exam…
Two Hamiltonian formulations of General Relativity, due to Pirani, Schild and Skinner (Phys. Rev. 87, 452, 1952) and Dirac (Proc. Roy. Soc. A 246, 333, 1958), are considered. Both formulations, despite having different expressions for…
We apply the covariant analytic mechanics with the differential forms to the Dirac field and the gravity with the Dirac field. The covariant analytic mechanics treats space and time on an equal footing regarding the differential forms as…
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…
The Dirac's formalism for constrained systems is applied to the analysis of time-dependent Hamiltonians in the extended phase space. We show that the Lewis invariant is a reparametrization invariant and we calculate the Feynman propagator…
In the study of alternative or extended theories of gravity, Dirac's Hamiltonian constraint algorithm is invaluable for enumerating the propagating modes and gauge symmetries. For gravity, this canonical approach is frequently applied as a…
We show that representations of the group of spacetime diffeomorphism and the Dirac algebra both arise in a phase-space histories version of canonical general relativity. This is the general-relativistic analogue of the novel time structure…
The effective approach to quantum dynamics allows a reformulation of the Dirac quantization procedure for constrained systems in terms of an infinite-dimensional constrained system of classical type. For semiclassical approximations, the…
The Dirac-Bergmann algorithm is a recipe for converting a theory with a singular Lagrangian into a constrained Hamiltonian system. Constrained Hamiltonian systems include gauge theories -- general relativity, electromagnetism, Yang Mills,…
A pure Dirac's canonical analysis, defined in the full phase space for the Husain-Kuchar model is discussed in detail. This approach allows us to determine the extended action, the extended Hamiltonian, the complete constraint algebra and…
This paper explores in some detail a recent proposal (the Rieffel induction/refined algebraic quantization scheme) for the quantization of constrained gauge systems. Below, the focus is on systems with a single constraint and, in this…
The methods of reduced phase space quantization and Dirac quantization are examined in a simple gauge theory. A condition for the possible equivalence of the two methods is discussed.
Applications of the Dirac equation with an anomalous magnetic moment are considered for description of characteristics of electrons, muons and quarks. The Dirac equation with four-dimensional scalar and vector potentials is reduced to a…
Several approaches to the dynamics of loop quantum gravity involve discretizing the equations of motion. The resulting discrete theories are known to be problematic since the first class algebra of constraints of the continuum theory…
A conventional wisdom often perpetuated in the literature states that: (i) a 3+1 decomposition of space-time into space and time is synonymous with the canonical treatment and this decomposition is essential for any Hamiltonian formulation…
Canonical quantization of gravity requires knowledge about the representation theory of its constraint algebra, which is physically equivalent to the algebra of arbitrary 4-diffeomorphisms. All interesting lowest-energy representations are…
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 use of geometric methods has proved useful in the hamiltonian description of classical constrained systems. In this note we provide the first steps toward the description of the geometry of quantum constrained systems. We make use of…
In most introductory courses on electrodynamics, one is taught the electric charge is quantised but no theoretical explanation related to this law of nature is offered. Such an explanation is postponed to graduate courses on…
The semiclassical solution of quantum Dirac constraints in generic constrained system is obtained by directly calculating in the one-loop approximation the gauge field path integral with relativistic gauge fixing procedure. The gauge…
We apply the Dirac procedure for constrained systems to the Arnowitt-Deser-Misner formalism linearized around the Friedmann-Lemaitre universe. We explain and employ some basic concepts such as Dirac observables, Dirac brackets, gauge-fixing…