相关论文: (Constrained) Quantization Without Tears
We give an overview of the two different methods that have been introduced in order to describe the dynamics of constrained quantum systems; the symplectic formulation and the metric formulation. The symplectic method extends the work of…
The procedure of nonperturbative quantization \`a la Heisenberg is considered. A few applications, features, perspectives, problems, and so on are considered. The comparison with turbulence modeling is performed.
So far, it is not well known how to deal with dissipative systems. There are many paths of investigation in the literature and none of them present a systematic and general procedure to tackle the problem. On the other hand, it is well…
A new framework for deriving equations of motion for constrained quantum systems is introduced, and a procedure for its implementation is outlined. In special cases the framework reduces to a quantum analogue of the Dirac theory of…
In this paper we discuss two approaches to anomaly-free quantization of a two-dimensional string. The first approach is based on the canonical Dirac prescription of quantization of degenerated systems. At the second approach we "weaken" the…
We give an explicit operator realization of Dirac quantization of free particle motion on a surface of codimension 1. It is shown that the Dirac recipe is ambiguous and a natural way of fixing this problem is proposed. We also introduce a…
A new method is introduced to create artificial time sequences that fulfil given constraints but are random otherwise. Constraints are usually derived from a measured signal for which surrogate data are to be generated. They are fulfilled…
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…
(some errors corrected, slightly extended)
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.…
Exact procedures that follow Dirac's constraint quantization of gauge theories are usually technically involved and often difficult to implement in practice. We overview an "effective" scheme for obtaining the leading order semiclassical…
Constrained quantization for a Borel probability measure refers to the idea of estimating a given probability by a discrete probability with a finite number of supporting points lying on a specific set. The specific set is known as the…
Randomized (dithered) quantization is a method capable of achieving white reconstruction error independent of the source. Dithered quantizers have traditionally been considered within their natural setting of uniform quantization. In this…
We present a novel method for neural network quantization that emulates a non-uniform $k$-quantile quantizer, which adapts to the distribution of the quantized parameters. Our approach provides a novel alternative to the existing uniform…
We study the reduced phase space quantization of a closed Friedmann Universe, where matter content is constituted by two (no-interacting) fluids, namely dust (or cold dark matter) and radiation. It is shown that, for this particular model,…
Quantum annealing is an emerging metaheuristic used for solving combinatorial optimisation problems. However, hardware based physical quantum annealers are primarily limited to a single vendor. As an alternative, we can discretise the…
It is shown that the Dirac approach to Hamiltonization of singular theories can be slightly modified in such a way that primary Dirac constraints do not appear in the process. According to the modified scheme, Hamiltonian formulation of…
We propose a method of quantization based on Hamilton-Jacobi theory in the presence of a random constraint due to the fluctuations of a set of hidden random variables. Given a Lagrangian, it reproduces the results of canonical quantization…
An extension of the Legendre transform to non-convex functions with vanishing Hessian as a mix of envelope and general solutions of the Clairaut equation is proposed. Applying this to systems with constraints, the procedure of finding a…
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…