scholarly journals Erratum: Geometrical perturbation theory: action‐principle surface terms in homogeneous cosmology [J. Math. Phys. 23, 2151 (1982)]

1983 ◽  
Vol 24 (4) ◽  
pp. 1013-1013
Author(s):  
Robert H. Gowdy
Keyword(s):  
Perturbation Theory ◽  
Action Principle ◽  
Homogeneous Cosmology ◽  
Math Phys

Renormalization issues for a whole abelian model

2015 ◽  
Vol 10 (2) ◽  
pp. 2715-2722
Author(s):  
Renato Doria ◽  
J. Chauca
Keyword(s):  
Perturbation Theory ◽  
Lorentz Force ◽  
Collective Behavior ◽  
Power Counting ◽  
Action Principle ◽  
Group A ◽  
The Common ◽  
Renormalization Constants

Considering that nature acts as a group, a whole abelian model is being developed. Classically, new aspects were observed as elds collective behavior and elds interacting among themselves and with mass through a global Lorentz force. This work analyzes some quantic aspects. Perturbation theory means that we know about 1-PI graphs. In a previous work, we have studied the quantum action principle, power-counting, primitively divergent graphs, Ward-Takahashi identities. This work concerns the study of counterterms and physical perturbation theory. It introduces a whole renormalization programme which informations are obtained from the common gauge parameter which establishes the elds set. It derives relationships between renormalization constants and on perturbative persistence on one masslessness eld in the fAIg set. It also argues on nitude possibilities through a whole expansion for the graphs.

SYMMETRICAL TREATMENT OF ELECTRON AND NUCLEAR MOTIONS IN M. BORN’S THEORY OF IDEAL CRYSTALS

1989 ◽  
Vol 01 (04) ◽  
pp. 497-504
Author(s):  
OTTO BERGMANN ◽  
P.N. RAYCHOWDHURY
Keyword(s):  
Perturbation Theory ◽  
Differential Equations ◽  
Action Principle ◽  
Ideal Crystal ◽  
System Of Differential Equations ◽  
Max Born ◽  
Statistical Operator ◽  
Derivatives Of

The equilibrium positions of the nuclei in an ideal crystal can be determined by thermal averages, as suggested by Max Born many years ago. We derive these equations without appealing to Born’s second condition which relates the proper frequencies to the statistical operator. We obtain these frequencies directly from the action principle and develop a perturbation theory including all the parity-violating terms (under reflection of generalized, proper coordinates). The equation which determines the equilibrium positions allows us to derive a system of differential equations for the derivatives of these positions with respect to the temperature.

scholarly journals Cherry flow: physical measures and perturbation theory

2016 ◽  
Vol 37 (8) ◽  
pp. 2671-2688 ◽  
Author(s):  
JIAGANG YANG
Keyword(s):  
Perturbation Theory ◽  
Periodic Orbits ◽  
Invariant Measures ◽  
Saddle Connection ◽  
Physical Measure ◽  
Hyperbolic Flow ◽  
Physical Measures ◽  
Full Volume ◽  
Math Phys

In this article we consider Cherry flows on the torus which have two singularities, a source and a saddle, and no periodic orbits. We show that every Cherry flow admits a unique physical measure, whose basin has full volume. This proves a conjecture given by Saghin and Vargas [Invariant measures for Cherry flows.Comm. Math. Phys.317(1) (2013), 55–67]. We also show that the perturbation of Cherry flows depends on the divergence at the saddle: when the divergence is negative, this flow admits a neighborhood, such that any flow in this neighborhood belongs to one of the following three cases: it has a saddle connection; it is a Cherry flow; it is a Morse–Smale flow whose non-wandering set consists of two singularities and one periodic sink. In contrast, when the divergence is non-negative, this flow can be approximated by a non-hyperbolic flow with an arbitrarily large number of periodic sinks.

A Perturbation Theory for the Population of Atomic Energy Levels in Non-Lte Plasmas

1988 ◽  
Vol 102 ◽  
pp. 343-347
Author(s):  
M. Klapisch
Keyword(s):  
Perturbation Theory ◽  
Small Parameter ◽  
Classification Scheme ◽  
Sum Rules ◽  
Energy Levels ◽  
Natural Classification ◽  
Quantum Numbers ◽  
Formal Expansion ◽  
Atomic Energy Levels ◽  
As Effects

AbstractA formal expansion of the CRM in powers of a small parameter is presented. The terms of the expansion are products of matrices. Inverses are interpreted as effects of cascades.It will be shown that this allows for the separation of the different contributions to the populations, thus providing a natural classification scheme for processes involving atoms in plasmas. Sum rules can be formulated, allowing the population of the levels, in some simple cases, to be related in a transparent way to the quantum numbers.

Sign in / Sign up

Export Citation Format

Share Document