Related papers: Riemann surface and quantization
The new emerging quantum physics - quantum computing conceptual bridge, mandates a ``grand unification'' of space-time-matter and quantum information (all quantized), with deep implications for science in general. The major physics…
The Feynman path integral does not allow a "one real path" interpretation, because amplitudes contribute to probabilities in a non-separable manner. The opposite extreme, "all paths happen", is not a useful or informative account. In this…
Dirac particle dynamics is encoded as a unitary path summation rule and implemented on a qubit array, where the qubit array represents both spacetime and the fermions contained therein. The unitary path summation rule gives a quantum…
A "minimal" generalization of Quantum Mechanics is proposed, where the Lagrangian or the action functional is a mapping from the (classical) states of a system to the Lie algebra of a general compact Lie group, and the wave function takes…
{}From Feynman's path integral, we derive quasi-classical quantization rules in supersymmetric quantum mechanics (SUSY-QM). First, we derive a SUSY counterpart of Gutzwiller's formula, from which we obtain the quantization rule of Comtet,…
It is shown that the equations of relativistic Bohmian mechanics for multiple bosonic particles have a dual description in terms of a classical theory of conformally "curved" space-time. This shows that it is possible to formulate quantum…
Starting with the generally well accepted opinion that quantizing an arbitrary Hamiltonian system involves picking out some additional structure on the classical phase space (the {\sl shadow} of quantum mechanics in the classical theory),…
We review equivariant localization techniques for the evaluation of Feynman path integrals. We develop systematic geometric methods for studying the semi-classical properties of phase space path integrals for dynamical systems, emphasizing…
We have studied the quantum Liouville theory on the Riemann sphere with n>3 punctures. While considering the theory on the Riemann surfaces with n=4 punctures, the quantum theory near an arbitrary but fixed puncture can be obtained via…
The possibility of extending the canonical formulation of quantum mechanics (QM) to a space-time symmetric form has recently attracted wide interest. In this context, a recent proposal has shown that a spacetime symmetric many-body…
Through a very careful analysis of Dirac's 1932 paper on the Lagrangian in Quantum Mechanics as well as the second and third editions of his classic book {\it The Principles of Quantum Mechanics}, I show that Dirac's contributions to the…
It is the goal of this article to extend the notion of quantization from the standard interpretation focused on non-commuting observables defined starting from classical analogues, to the topological equivalents defined in terms of…
According to loop quantum gravity, matter fields must be quantized in a background independent manner. For scalar fields, such a background independent quantization is called polymer quantization and is inequivalent to the standard…
By parametrizing the action integral for the standard Schrodinger equation we present a derivation of the recently proposed method for quantizing a parametrized theory. The reformulation suggests a natural extension from conventional to…
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…
We explore the quantization of classical models with position-dependent mass (PDM) terms constrained to a bounded interval in the canonical position. This is achieved through the Weyl-Heisenberg covariant integral quantization by properly…
A diagram approach to classical nonlinear stochastic field theory is introduced. This approach is intended to serve as a link between quantum and classical field theories, resulting in an independent constructive characterisation of the…
We continue in this paper our program of rederiving all quantum mechanical formalism from the classical one. We now turn our attention to the derivation of the second quantized equations, both for integral and half-integral spins. We then…
Scalar field systems containing higher derivatives are studied and quantized by Hamiltonian path integral formalism. A new point to previous quantization methods is that field functions and their derivatives with time are considered as…
A theoretical scheme, based on a probabilistic generalization of the Hamilton's principle, is elaborated to obtain an unified description of more general dynamical behaviors determined both from a lagrangian function and by mechanisms not…