Titlebook: Classical and Quantum Dynamics; From Classical Paths Walter Dittrich,Martin Reuter Textbook 2020Latest edition The Editor(s) (if applicable

CHASM

https://doi.org/10.1007/978-3-030-93186-5We extend the perturbation theory of the previous chapter by going one order further and permitting several degrees of freedom. So let the unperturbed problem . be solved.

needle

祝賀

Dora Luise Münster,Sander MünsterHere we are dealing with an especially fast converging perturbation series, which is of particular importance for the proof of the KAM theorem (cf. below).

十字架

Sander Münster,Aaron Pattee,Florian NieblingThis theorem guarantees that, under certain assumptions, in the case of a perturbation ..(., .) with small enough ., the iterated series for the generator . converges (according to Newton’s procedure) and thus the invariant tori are not destroyed.

抵消

https://doi.org/10.1007/978-3-031-38871-2We shall favor the first method, which Feynman followed. Feynman, on his part, was put on the right track by—none other, of course, than—Dirac.

文藝

Sander Münster,Aaron Pattee,Florian NieblingWe now want to compute the kernel .(., .) for a few simple Lagrangians.

殺蟲劑

豐富

The Action Principles in Mechanics,We begin this chapter with the definition of the action functional as time integral over the Lagrangian . of a dynamical system: . Here, .., .?=?1, 2, …, ., are points in .-dimensional configuration space.

flamboyant

The Action Principle in Classical Electrodynamics,The main purpose of this chapter is to consider the formulation of a relativistic point particle in classical electrodynamics from the viewpoint of Lagrangian mechanics. Here, the utility of Schwinger’s action principle is illustrated by employing three different kinds of action to derive the equations of motion and the associated surface terms.

keloid