Related papers: Quantization of Nonstandard Hamiltonian Systems
We consider the generalized rotor Hamiltonians capable of describing quantum systems invariant with respect to symmetry point-groups that go beyond the usual D_2-symmetry of a tri-axial rotor. We discuss the canonical de-quantisation…
In this article we discuss the geometric quantization on a certain type of infinite dimensional super-disc. Such systems are quite natural when we analyze coupled bosons and fermions. The large-N limit of a system like that corresponds to a…
Familiar formulations of classical and quantum mechanics are shown to follow from a general theory of mechanics based on pure states with an intrinsic probability structure. This theory is developed to the stage where theorems from quantum…
The nonlinear supersymmetry of one-dimensional systems is investigated in the context of the quantum anomaly problem. Any classical supersymmetric system characterized by the nonlinear in the Hamiltonian superalgebra is symplectomorphic to…
Three problems stand in the way of deriving classical theories from quantum mechanics: those of realist interpretation, of classical properties and of quantum measurement. Recently, we have identified some tacit assumptions that lie at the…
We give a comprehensive review of the quantization of midisuperspace models. Though the main focus of the paper is on quantum aspects, we also provide an introduction to several classical points related to the definition of these models. We…
We develop a new algorithm for the quantisation of systems with first-class constraints. Our approach lies within the (History Projection Operator) continuous-time histories quantisation programme. In particular, the Hamiltonian treatment…
Non-classical probability (along with its underlying logic) is a defining feature of quantum mechanics. A formulation that incorporates them, inherently and directly, would promise a unified description of seemingly different prescriptions…
In this paper we give examples of applications of general methods of quantization by symmetrization of classical integrable systems, which have been illustrated in two previous works by the same authors. We consider two classes of systems…
A generic procedure is proposed to construct many-body quantum Hamiltonians with partial dynamical symmetry. It is based on a tensor decomposition of the Hamiltonian and allows the construction of a hierarchy of interactions that have…
It is generally assumed that a Hamiltonian for a physically acceptable quantum system (one that has a positive-definite spectrum and obeys the requirement of unitarity) must be Hermitian. However, a PT-symmetric Hamiltonian can also define…
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 tenth paper of the series we aim at showing that our formalism, using the Wigner-Moyal Infinitesimal Transformation together with classical mechanics, endows us with the ways to quantize a system in any coordinate representation we…
It is demonstrated that the so-called "unavoidable quantum anomalies" can be avoided in the farmework of a special non-linear quantization scheme. A simple example is discussed in detail.
Precise rules are developed in order to formalize the reasoning processes involved in standard non-relativistic quantum mechanics, with the help of analogies from classical physics. A classical or quantum description of a mechanical system…
Classical dynamics is formulated as a Hamiltonian flow on phase space, while quantum mechanics is formulated as a unitary dynamics in Hilbert space. These different formulations have made it difficult to directly compare quantum and…
The Hamiltonian treatment of constrained systems in $G\ddot{u}ler's$ formalism leads us to the total differential equations in many variables. These equations are integrable if the corresponding system of partial differential equations is a…
Circuit quantization is an extraordinarily successful theory that describes the behavior of quantum circuits with high precision. The most widely used approach of circuit quantization relies on introducing a classical Lagrangian whose…
The formalism to treat quantization and evolution of cosmological perturbations of multiple fluids is described. We first construct the Lagrangian for both the gravitational and matter parts, providing the necessary relevant variables and…
We use a local scale invariance of a classical Hamiltonian and describe how to construct six different formulations of quantum mechanics in spaces with two time-like dimensions. All these six formulations have the same classical limit…