Related papers: Quantum Canonical Transformations revisited
The Hamilton-Jacobi method of constrained systems is discussed. The equations of motion of a singular system with time dependent constraints are obtained as total differential equations in many variables. The integrability conditions for…
These lectures are intended as an introduction to the technique of path integrals and their applications in physics. The audience is mainly first-year graduate students, and it is assumed that the reader has a good foundation in quantum…
We developed a path integral formalism for the quantum mechanics in a rotating reference of frame, and proposed a spin path integral description for the spin degrees of freedom in it. We have also give some examples for the applications of…
Quantum mechanics in conical space is studied by the path integral method. It is shown that the curvature effect gives rise to an effective potential in the radial path integral. It is further shown that the radial path integral in conical…
A quantum bit encoding converter between qubits of different forms is experimentally demonstrated, paving the way to efficient networks for optical quantum computing and communication.
We describe a new viewpoint on canonical quantization of linear fields on a general curved background that encompasses and generalizes the standard treatment of canonical QFT given in textbooks. Our method permits the construction of pure…
Quantum canonical transformations are used to derive the integral representations and Kummer solutions of the confluent hypergeometric and hypergeometric equations. Integral representations of the solutions of the non-periodic three body…
In this paper, we investigate the quantum field theory in Klein space that has two time directions. To study the canonical quantization, we select the ``length of time" $q$ as the evolution direction of the system. In our novel…
Path integration is a respected form of quantization that all theoretical quantum physicists should welcome. This elaboration begins with simple examples of three different versions of path integration. After an important clarification of…
In this paper we develop the alternative path-integral approach to quantum mechanics. We present a resolvent of a Hamiltonian (which is Laplace transform of a evolution operator) in a form which has a sense of ``the sum over paths'' but it…
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…
The present paper is a short review of different path integral representations of the partition function of quantum spin systems. To begin with, I consider coherent states for SU(2) algebra. Different parameterizations of the coherent…
We derive the first order canonical formulation of cosmological perturbation theory in a Universe filled by a few scalar fields. This theory is quantized via well-defined Hamiltonian path integral. The propagator which describes the…
Review of the most basic issues appearing in the most conservative approaches to quantum theory of gravity is given. The most part of the review is devoted to issues of perturbative quantization based on functional integral technique.…
Following Dirac, the rules of canonical quantization include classical and quantum contact transformations of classical and quantum phase space variables. While arbitrary classical canonical coordinate transformations exist that is not the…
Quantum computation is based on implementing selected unitary transformations which represent algorithms. A generalized optimal control theory is used to find the driving field that generates a prespecified unitary transformation. The…
The Feynman path integral representation of quantum theory is used in a non--parametric Bayesian approach to determine quantum potentials from measurements on a canonical ensemble. This representation allows to study explicitly the…
Coherent states path integral formalism for the simplest quantum algebras, q-oscillator, SU_q(2) and SU_q(1,1) is introduced. In the classical limit canonical structure is derived with modified symplectic and Riemannian metric. Non-constant…
Fourier transforms are ubiquitous mathematical tools in basic and applied sciences. We here report classical and quantum optical realizations of the discrete fractional Fourier transform, a generalization of the Fourier transform. In the…
We consider the form of the path integral that follows from canonical quantization and apply it to the first order form of the Einstein-Hilbert action in $d > 2$ dimensions. We show that this is inequivalent to what is obtained from…