Related papers: Quantization of Nonstandard Hamiltonian Systems
A recent notion in theoretical physics is that not all quantum theories arise from quantising a classical system. Also, a given quantum model may possess more than just one classical limit. These facts find strong evidence in string duality…
An integrable anharmonic oscillator is presumably simulable by a classical computer and therefore by a quantum computer. An integrable anharmonic oscillator whose Hamiltonian is of normal type and quartic in the canonical coordinates is not…
These lectures are an introduction to formal semiclassical quantization of classical field theory. First we develop the Hamiltonian formalism for classical field theories on space time with boundary. It does not have to be a cylinder as in…
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…
One classical theory, as determined by an equation of motion or set of classical trajectories, can correspond to many unitarily {\em in}equivalent quantum theories upon canonical quantization. This arises from a remarkable ambiguity, not…
This work is a generalization of \cite{baldiotti2021} to Grassmann algebras of arbitrary dimensions. Here we present a covariant quantization scheme for pseudoclassical theories focused on non-hermitian quantum mechanics. The quantization…
Constrained Hamiltonian description of the classical limit is utilized in order to derive consistent dynamical equations for hybrid quantum-classical systems. Starting with a compound quantum system in the Hamiltonian formulation conditions…
A significant part of quantum theory can be obtained from a single innovation relative to classical theories, namely, that there is a fundamental restriction on the sorts of statistical distributions over physical states that can be…
Geometric quantization is an attempt at using the differential-geometric ingredients of classical phase spaces regarded as symplectic manifolds in order to define a corresponding quantum theory. Generally, the process of geometric…
In this paper, we investigate the connection between Classical and Quantum Mechanics by dividing Quantum Theory in two parts: - General Quantum Axiomatics (a system is described by a state in a Hilbert space, observables are self-adjoint…
A generalization of classical mechanics is obtained from a complex parametrization of the phase space. The formalism supports complex Hamiltonian functions describing non-conservative classical mechanical systems. A quantization scheme that…
Classical limits of quantum systems are shown to lead to different conceptions of spaces different from the classical one underlying the process of quantization of such systems. The accent is put in situations where traces of…
Further properties of a recently proposed higher order infinite spin particle model are derived. Infinitely many classically equivalent but different Hamiltonian formulations are shown to exist. This leads to a condition of uniqueness in…
In complete analogy with the classical situation (which is briefly reviewed) it is possible to define bi-Hamiltonian descriptions for Quantum systems. We also analyze compatible Hermitian structures in full analogy with compatible Poisson…
A recent development of the studies on classical and quasi-classical properties of supersymmetric quantum mechanics in Witten's version is reviewed. First, classical mechanics of a supersymmetric system is considered. Solutions of the…
The process of canonical quantization is redefined so that the classical and quantum theories coexist when \hbar>0, just as they do in the real world. This analysis not only supports conventional procedures, it also reveals new quantization…
Quantization of field-theoretic models with gauge symmetries is often obstructed by quantum anomalies. It is commonly believed that the origin of these anomalies lies in the infinite number of degrees of freedom, which requires completing…
A phenomenon of classical quantization is discussed. This is revealed in the class of pseudoclassical gauge systems with nonlinear nilpotent constraints containing some free parameters. Variation of parameters does not change local (gauge)…
These notes give an introduction to the quantization procedure called geometric quantization. It gives a definition of the mathematical background for its understanding and introductions to classical and quantum mechanics, to differentiable…
In this note, we provide a unifying framework to investigate the computational complexity of classical spin models and give the full classification on spin models in terms of system dimensions, randomness, external magnetic fields and types…