Related papers: Simultaneous Quantization and Reduction of Constra…
We analyze constrained quantum systems where the dynamics do not preserve the constraints. This is done in particular for the restriction of a quantum particle in Euclidean n-space to a curved submanifold, and we propose a method of…
We use Dirac's method for the quantization of constrained systems in order to quantize a spatially flat Friedmann-Lema\^{i}tre-Robertson-Walker spacetime in the context of $f(Q)$ cosmology. When the coincident gauge is considered, the…
Starting with the first-order singular Lagrangian, the problem of the quantization of a dynamical system constrained to a submanifold embedded in the higher-dimensional Euclidean space is investigated within the framework of operatorial…
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…
Building towards a more covariant approach to canonical classical and quantum gravity we outline an approach to constrained dynamics that de-emphasizes the role of the Hamiltonian phase space and highlights the role of the Lagrangian phase…
Motivated by a similar approach for Born-Oppenheimer molecular dynamics, this paper proposes an extended "shadow" Lagrangian density for quantum states of superfluids. The extended Lagrangian contains an additional field variable that is…
We propose here a new symplectic quantization scheme, where quantum fluctuations of a scalar field theory stem from two main assumptions: relativistic invariance and equiprobability of the field configurations with identical value of the…
Motivated by certain concepts introduced by the Refined Algebraic Quantization formalism for constrained systems which has been successfully applied within the context of Loop Quantum Gravity, in this paper we propose a phase space…
Many theories are formulated as constrained systems. We provide a mechanism that explains the origin of physical states of a constrained system by a process of selection of noiseless subsystems when the system is coupled to an external…
I study the canonical formulation and quantization of some simple parametrized systems, including the non-relativistic parametrized particle and the relativistic parametrized particle. Using Dirac's formalism I construct for each case the…
We present a new method for the quantization of totally constrained systems including general relativity. The method consists in constructing discretized theories that have a well defined and controlled continuum limit. The discrete…
The Dirac method of canonical quantization of theories with second class constraints has to be modified if the constraints depend on time explicitly. A solution of the problem was given by Gitman and Tyutin. In the present work we propose…
Recently, there were works claiming that path integral quantisation of gauge theories necessarily requires relaxation of Lagrangian constraints. As has also been noted in the literature, it is of course wrong since there perfectly exist…
An effective formalism for quantum constrained systems is presented which allows manageable derivations of solutions and observables, including a treatment of physical reality conditions without requiring full knowledge of the physical…
This paper develops a unified framework for quantum wavelet shrinkage, extending classical denoising ideas into the quantum domain. Shrinkage is interpreted as a completely positive trace-preserving process, so attenuation of coefficients…
We consider quantum mechanics on constrained surfaces which have non-Euclidean metrics and variable Gaussian curvature. The old controversy about the ambiguities involving terms in the Hamiltonian of order hbar^2 multiplying the Gaussian…
In this paper a new approach is proposed to quantize mechanical systems whose equations of motion can not be put into Hamiltonian form. This approach is based on a new type of variational principle, which is adopted to a describe a…
In this paper, we present a detailed review/analysis of the Dirac quantisation of Hamiltonian systems with constraints. To this end, we use, as a guide, the physical example provided by the dynamics of a solid ball rolling, without…
From the point of view of canonical quantum gravity, it has become imperative to find a framework for quantization which provides a {\em general} prescription to find the physical inner product, and is flexible enough to accommodate…
With the advent of quantum technologies, control issues are becoming increasingly important. In this article, we address the control in phase space under a global constraint provided by a minimal energy-like cost function and a local (in…