scholarly journals On asymptotic perturbation theory for quantum mechanics: Almost invariant subspaces and gauge invariant magnetic perturbation theory

2002 ◽  
Vol 43 (3) ◽  
pp. 1273-1298 ◽  
Author(s):  
G. Nenciu
Keyword(s):  
Perturbation Theory ◽  
Quantum Mechanics ◽  
Invariant Subspaces ◽  
Gauge Invariant ◽  
Magnetic Perturbation ◽  
Asymptotic Perturbation

scholarly journals Gauge Explicit Quantum Mechanics and Perturbation Theory

1997 ◽  
Vol 50 (5) ◽  
pp. 869
Author(s):  
A. M. Stewart
Keyword(s):  
Perturbation Theory ◽  
Quantum Mechanics ◽  
Wave Equation ◽  
Statistical Mechanics ◽  
Gauge Invariant

A version of quantum and statistical mechanics, including perturbation theory, is described in which explicit electromagnetic gauge arbitrariness is maintained at every stage. Any gauge may be used for a calculation provided that the wave equation operator is gauge invariant.

scholarly journals A MANIFESTLY GAUGE INVARIANT AND UNIVERSAL CALCULUS FORSU(N) YANG–MILLS

2006 ◽  
Vol 21 (23n24) ◽  
pp. 4627-4761 ◽  
Author(s):  
OLIVER J. ROSTEN
Keyword(s):  
Perturbation Theory ◽  
Renormalization Group ◽  
Explicit Dependence ◽  
Gauge Invariant ◽  
Yang Mills ◽  
Group A ◽  
Β Function ◽  
Exact Renormalization Group

Within the framework of the Exact Renormalization Group, a manifestly gauge invariant calculus is constructed for SU (N) Yang–Mills. The methodology is comprehensively illustrated with a proof, to all orders in perturbation theory, that the β function has no explicit dependence on either the seed action or details of the covariantization of the cutoff. The cancellation of these nonuniversal contributions is done in an entirely diagrammatic fashion.

Successive approximation; perturbation theory in quantum mechanics

2021 ◽  
pp. 130-148
Author(s):  
Geoffrey Brooker
Keyword(s):  
Perturbation Theory ◽  
Quantum Mechanics ◽  
Successive Approximation ◽  
Iterative Procedure ◽  
Approximation Problems

“Successive approximation; perturbation theory in quantum mechanics” introduces a toolbox for handling successive-approximation problems in any context. An iterative procedure is presented with examples. Newton's approximation is also an iterative procedure, but often other methods are better. Perturbation theory is presented, organized as an application of the toolbox.

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