Related papers: Perturbation theory in covariant canonical quantiz…
Problems concerning with application of quantum rules on classical phenomena have been widely studied, for which lifted up the idea about quantization and uncertainty principle. Energy quantization on classical example of simple harmonic…
We have recently introduced an approach for studying perturbatively classical and quantum canonical general relativity. The perturbative technique appears to preserve many of the attractive features of the non-perturbative quantization…
This article lays out a complete framework for an effective theory of cosmological perturbations with corrections from canonical quantum gravity. Since several examples exist for quantum-gravity effects that change the structure of…
An approximation method which combines the perturbation theory with the variational calculation is constructed for quantum mechanical problems. Using the anharmonic oscillator and the He atom as examples, we show that the present method…
It is shown how cosmological perturbation theory arises from a fully quantized perturbative theory of quantum gravity. Central for the derivation is a non-perturbative concept of gauge-invariant local observables by means of which…
We take a qualitative comparative look at quantum and classical quartic anharmonic oscillators. It has been shown that the behavior of the quantum anharmonic oscillator mimics that of the classical anharmonic oscillators with the…
The method, proposed in the given work, allows the application of well developed standard methods used in quantum mechanics for approximate solution of the systems of ordinary linear differential equations with periodical coefficients.
We argue that to solve the foundational problems of quantum theory one has to first understand what it means to quantize a classical system. We then propose a quantization method based on replacement of deterministic c-numbers by…
We develop a new analytical method for solving real time evolution problems of quantum many-body systems. Our approach is a direct generalization of the well-known canonical perturbation theory for classical systems. Similar to canonical…
We study a quantum mechanical toy model that mimics some features of a quenched phase transition. Both by virtue of a time-dependent Hamiltonian or by changing the temperature of the bath we are able to show that even after classicalization…
Here a special case of perturbation in quantum harmonic oscillator is studied. Here we assume the perturbed potential to be a Harmonic Oscillator that has been shifted in the position space.We construct the new creation and annihilation…
A careful study of the classical/quantum connection with the aid of coherent states offers new insights into various technical problems. This analysis includes both canonical as well as closely related affine quantization procedures. The…
Perturbation theory in quantum mechanics studies how quantum systems interact with their environmental perturbations. Harmonic perturbation is a rare special case of time-dependent perturbations in which exact analysis exists. Some…
We develop an alternative approach to time independent perturbation theory in non-relativistic quantum mechanics. The method developed has the advantage to provide in one operation the correction to the energy and to the wave function,…
A new method of approximation scheme with potential application to a general interacting quantum system is presented. The method is non-perturbative, self- consistent, systematically improvable and uniformly applicable for arbitrary…
Recently, we presented a unified way of analysing classical cosmological perturbation in generalized gravity theories. In this paper, we derive the perturbation spectrums generated from quantum fluctuations again in unified forms. We…
We propose a system of equations to describe the interaction of a quasiclassical variable $X$ with a set of quantum variables $x$ that goes beyond the usual mean field approximation. The idea is to regard the quantum system as continuously…
We study spectral parametric correlations in quantum chaotic systems and introduce the number covariance as a measure of such correlations. We derive analytic results for the classical random matrix ensembles using the binary correlation…
The relationship between the perturbation theory in light-front coordinates and Lorentz-covariant perturbation theory is investigated. A method for finding the difference between separate terms of the corresponding series without their…
In this paper we show how Feynman diagrams, which are used as a tool to implement perturbation theory in quantum field theory, can be very useful also in classical mechanics, provided we introduce also at the classical level concepts like…