Related papers: Formal Geometric Quantization
Constrained symplectic quantization is a functional formulation of quantum field theory in which quantum fluctuations are sampled through a deterministic Hamiltonian flow in an auxiliary intrinsic time $\tau$. In this paper we extend the…
This paper expands some of the issues of the paper math.SG/0506449. We introduce a new technique to produce symplectic manifolds, by taking a symplectic non-free action of a finite group on a symplectic manifold and resolving symplectically…
In this paper we find connection between the Hofer's metric of the group of Hamiltonian diffeomorphisms of a closed symplectic manifold, with an integral symplectic form, and the geometry, defined in a paper by Eliashberg and Polterovich,…
Due to the emergence of symplectic geometry, the geometric treatment of mechanics underwent a great development during the last century. In this scenario the pressence of symmetries in Hamiltonian systems leads naturally to the existence of…
On the basis of the covariant description of the canonical formalism for quantization, we present the basic elements of the symplectic geometry for a restricted class of topological defects propagating on a curved background spacetime. We…
$\mathcal{H}-$holomorphic curves are solutions of a specific modification of the pseudoholomorphic curve equation in symplectizations involving a harmonic $1-$form as perturbation term. In this paper we compactify the moduli space of…
Hamiltonian Monte Carlo is typically based on the assumption of an underlying canonical symplectic structure. Numerical integrators designed for the canonical structure are incompatible with motion generated by non-canonical dynamics. These…
We describe an approach for characterizing the process of quantum gates using quantum process tomography, by first modeling them in an extended Hilbert space, which includes non-qubit degrees of freedom. To prevent unphysical processes from…
We review recent results and ongoing investigations of the symplectic and Poisson geometry of derived moduli spaces, and describe applications to deformation quantization of such spaces.
We present a new math-physics modeling approach, called canonical quantization with numerical mode-decomposition, for capturing the physics of how incoming photons interact with finite-sized dispersive media, which is not describable by the…
On a complex symplectic manifold, we construct the stack of quantization-deformation modules, that is, (twisted) modules of microdifferential operators with an extra central parameter, a substitute to the lack of homogeneity. We also…
Quantisation on spaces with properties of curvature, multiple connectedness and non orientablility is obtained. The geodesic length spectrum for the Laplacian operator is extended to solve the Schroedinger operator. Homotopy fundamental…
A geometric description is given for the Sp(2) covariant version of the field-antifield quantization of general constrained systems in the Lagrangian formalism. We develop differential geometry on manifolds in which a basic set of…
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…
I present a method of performing geometric quantization using cohomology groups extended via coefficient groups of different types. This is possible according to the Universal Coefficient Theorem (UTC). I also show that by using this method…
This paper is one of a series of papers on coherent spaces and their applications, defined in the recent book 'Coherent Quantum Mechanics' by the first author. The paper studies coherent quantization -- the way operators in the quantum…
The compatibility between the conformal symmetry and the closure of conformal algebras is discussed on the nonlinear sigma model. The present approach, above the basis of field redefinition employed in the Hamiltonian scheme, attempts the…
We introduce symplectic quantization, a novel functional approach to quantum field theory which allows to sample quantum fields fluctuations directly in Minkowski space-time, at variance with the traditional importance sampling protocols,…
We use geometric methods to study two natural two-component generalizations of the periodic Camassa-Holm and Degasperis-Procesi equations. We show that these generalizations can be regarded as geodesic equations on the semidirect product of…
The metric known to be relevant for standard quantization procedures receives a natural interpretation and its explicit use simultaneously gives both physical and mathematical meaning to a (coherent-state) phase-space path integral, and at…