Related papers: On the Relation between Operator Constraint --, Ma…

Coherent states can be used for diverse applications in quantum physics including the construction of coherent state path integrals. Most definitions make use of a lattice regularization; however, recent definitions employ a continuous-time…

We introduce a master constraint operator on the kinematical Hilbert space of loop quantum gravity representing a set of gauge conditions which classically fix the densitized triad to be diagonal. We argue that the master constraint…

Unfortunately, the Hamiltonian mechanics of degenerate Lagrangian systems is usually presented as a mere recipe of Dirac, with no explanation as to how it works. Then it comes to discussing conjectures of whether all primary constraints…

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…

We show how to construct the measure of the path integral in lattice gauge theory. This measure contains a factor beyond the standard Haar measure. Such factor becomes relevant for the calculation of a single transition amplitude (in…

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…

A simple, often invoked, regularization scheme of quantum mechanical path integrals in curved space is mode regularization: one expands fields into a Fourier series, performs calculations with only the first $M$ modes, and at the end takes…

The path integral approach to quantum mechanics provides a method of quantization of dynamical systems directly from the Lagrange formalism. In field theory the method presents some advantages over Hamiltonian quantization. The Lagrange…

Starting with the first-order singular Lagrangian, the canonical structures of the noncommutative quantum system on a submanifold embedded in the higher-dimensional Euclidean space are investigated with the projection operator method (POM)…

Certain phase space path integrals can be evaluated exactly using equivariant cohomology and localization in the canonical loop space. Here we extend this to a general class of models. We consider hamiltonians which are {\it a priori}…

Exploiting our previous results on higher order controlled Lagrangians in [Nonlinear Anal. {\bf 207} (2021), 112263], we derive here an analogue of the classical first order Pontryagin Maximum Principle (PMP) for cost minimising problems…

We consider questions related to a quantization scheme in which a classical variable f:\Omega\to R on a phase space \Omega is associated with a semispectral measure E^f, such that the moment operators of E^f are required to be of the form…

The projectability of Poincar\'e-Cartan forms in a third-order jet bundle $J^3\pi$ onto a lower-order jet bundle is a consequence of the degenerate character of the corresponding Lagrangian. This fact is analyzed using the constraint…

Trough the systematic use of the Minlos theorem on the support of cylindrical measures on R infinity, we produce several mathematically rigorous path integrals in interacting euclidean quantum fields with Gaussian free measures defined by…

We investigate the structure of the constraints on three-point correlation functions emerging when conformal invariance is imposed in momentum space and in arbitrary space-time dimensions, presenting a derivation of their solutions for…

We explore the existence of a class of generalised Laplace maps for third order partial differential operators of the form…

Ambiguities arising in different approaches (canonical, quasiclassical, path integration) to quantization are discussed by an example of the mechanics of a point-like particle in the Riemannian space (the geodesic dynamics). A way to select…

We show how to systematically derive the exact form of local symmetries for the abelian Proca and CS models, which are converted into first class constrained systems by the BFT formalism, in the Lagrangian formalism. As results, without…

We propose a general method for deformation quantization of any second-class constrained system on a symplectic manifold. The constraints determining an arbitrary constraint surface are in general defined only locally and can be components…