Related papers: Topology and perturbation theory
The fields nonlinear modes quantization scheme is discussed. New form of the perturbation theory achieved by unitary mapping the quantum dynamics in the space $W_G$ of (action, angle)-type collective variables. It is shown why the…
The paper contains successive description of the strong-coupling perturbation theory. Formal realization of the idea is based on observation that the path-integrals measure for absorption part of amplitudes $\R$ is Diracian ($\d$-like). New…
The unitary transformation of path-integral differential measure is described. The main properties of perturbation theory in the phase space of action-angle, energy-time variables are investigated. The measure in cylindrical coordinates is…
We study finite-dimensional integrals in a way that elucidates the mathematical meaning behind the formal manipulations of path integrals occurring in quantum field theory. This involves a proper understanding of how Wick's theorem allows…
We present a novel form of relativistic quantum mechanics and demonstrate how to solve it using a recently derived unitary perturbation theory, within partial wave analysis. The theory is tested on a relativistic problem, with two spinless,…
We use the homological perturbation lemma to produce explicit formulas computing the class in the twisted de Rham complex represented by an arbitrary polynomial. This is a non-asymptotic version of the method of Feynman diagrams. In…
We show how to construct path integrals for quantum mechanical systems where the space of configurations is a general non-compact symmetric space. Associated with this path integral is a perturbation theory which respects the global…
In the Schrodinger picture of the Dirac quantum mechanics, defined in charts with spatially flat Robertson-Walker metrics and Cartesian coordinates the perturbation theory is applied to the interacting part of the Hamiltonian operator…
We propose a path integral formulation for scale invariant quantum field theories. We do it by modifying the functional integration measure in such a way that the partition function is always exactly scale invariant, at the cost of having…
The variational formulation for Lie-transform Hamiltonian perturbation theory is presented in terms of an action functional defined on a two-dimensional parameter space. A fundamental equation in Hamiltonian perturbation theory is shown to…
The mechanism underlying the divergence of perturbation theory is exposed. This is done through a detailed study of the violation of the hypothesis of the Dominated Convergence Theorem of Lebesgue using familiar techniques of Quantum Field…
We study perturbation theory in certain quantum mechanics problems in which the perturbing potential diverges at some points, even though the energy eigenvalues are smooth functions of the coefficient of the potential. We discuss some of…
We consider a perturbation of an ``integrable'' Hamiltonian and give an expression for the canonical or unitary transformation which ``simplifies'' this perturbed system. The problem is to invert a functional defined on the Lie- algebra of…
We recast the action principle of four dimensional General Relativity so that it becomes amenable for perturbation theory which doesn't break general covariance. The coupling constant becomes dimensionless (G_{Newton} \Lambda) and extremely…
For a wide class of nonlinear equations a perturbative solution is constructed. This class includes equations of motion of field theories. The solution possesses a graphical representation in terms of diagrams. To illustrate the formalism…
The `strong-coupling' perturbation theory over the inverse interaction constant $1/g$ near the nontrivial solution of Lagrange equation is formulated. The ordinary `week-coupling' perturbation theory over $g$ is described also to compare…
The quantum theory of cosmological perturbations in single field inflation is formulated in terms of a path integral. Starting from a canonical formulation, we show how the free propagators can be obtained from the well known…
We show how kinetic theory, the statistics of classical particles obeying Newtonian dynamics, can be formulated as a field theory. The field theory can be organized to produce a self-consistent perturbation theory expansion in an effective…
This article aims to explain essential elements of perturbation theory and their conceptual underpinnings. It is not meant as a summary of popular perturbation methods, though some illustrative examples are given to underline the main…
A wide class of boundary problems in quantum mechanics is discussed by using path integrals. This includes motion in half-spaces, radial boxes, rings, and moving boundaries. As a preparation the formalism for the incorporation of…