35 Lagrangian Methods and the Path Integral
In this chapter we’ll give a rapid survey of a diferent starting point for developing quantum mechanics, based on the Lagrangian rather than Hamiltonian classical formalism. The Lagrangian point of view is the one taken in most modern physics textbooks, and we will refer to these for more detail, concentrating here on explaining the relation to the Hamiltonian approach. Lagrangian methods have quite diferent strengths and weaknesses than those of the Hamiltonian formalism, and we’ll try and point these out,
The Lagrangian formalism leads naturally to an apparently very diferent notion of quantization, one based upon formulating quantum theory in terms of infinite dimensional integrals known as path integrals. A serious investigation of these would require another and very diferent volume, so we’ll have to restrict ourselves to a quick outline of how path integrals work, giving references to standard texts for the details. We will try and provide some indication of both the advantages of the path integral method, as well as the significant problems it entails.
Chapter contents
- 35.1 Lagrangian mechanics
- 35.2 Noether’s theorem and symmetries in the Lagrangian formalism
- 35.3 Quantization and path integrals
- 35.4 Advantages and disadvantages of the path integral
- 35.5 For further reading
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正文：英文 · OCR 机器稿 · 待校对
核对状态：OCR 机器稿 · 待校对
原书 PDF · 印刷页 368、369、370、371、372、373、374、375、376、377、378
来源版本：2025-10-20
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