因書籍出版日期年代久遠,廠商目前剩餘庫存皆不佳,如不介意在下訂,感謝~~

Description

This book provides an innovative and mathematically sound treatment of the foundations of analytical mechanics and the relation of classical mechanics to relativity and quantum theory. It is intended for use at the graduate level.

A distinguishing feature of the book is its integration of special relativity into the teaching of classical mechanics. Extended Lagrangian and Hamiltonian methods are introduced that treat time as a transformable coordinate rather than the fixed parameter of Newtonian physics. Advanced topics such as covariant Lagrangians and Hamiltonians, canonical transformations, and the Hamilton-Jacobi equation are developed using this extended theory. This permits the Lorentz transformation of special relativity to become a canonical transformation.

 

This is also a book for those who study analytical mechanics as a preliminary to a critical exploration of quantum mechanics. Comparisons to quantum mechanics appear throughout the text, and classical mechanics itself is presented in a way that will aid the reader in the study of quantum theory. A chapter is devoted to linear vector operators and dyadics, including a comparison to the bra-ket notation of quantum mechanics. Rotations are presented using an operator formalism similar to that used in quantum theory, and the definition of the Euler angles follows the quantum mechanical convention. The extended Hamiltonian theory with time as a coordinate is compared to Dirac's formalism of primary phase space constraints. The chapter on relativistic mechanics shows how to use covariant Hamiltonian theory to write the Klein-Gordon and Dirac equations. The chapter on Hamilton-Jacobi theory includes a discussion of the closely related Bohm hidden variable model of quantum mechanics.

 

The book provides a necessary bridge to carry graduate students from their previous undergraduate classical mechanics courses to the future study of advanced relativity and quantum theory. Several of the current fundamental problems in theoretical physics---the development of quantum information technology, and the problem of quantizing the gravitational field, to name two---require a rethinking of the quantum-classical connection. This text is intended to encourage the retention or restoration of introductory graduate analytical mechanics courses. It is written for the intellectually curious graduate student, and the teacher who values mathematical precision in addition to accessibility.

 

Table of contents

Part I: Introduction: The Traditional Theory

1. Basic Dynamics of Point Particles and Collections

2. Introduction to Lagrangian Mechanics

3. Lagrangian Theory of Constraints

4. Introduction to Hamiltonian Mechanics

5. The Calculus of Variations

6. Hamilton's Principle

7. Linear Operators and Dyadics

8. Kinematics of Rotation

9. Rotational Dynamics

10. Small Vibrations about Equilibrium

 

Part II: Mechanics with Time as a Coordinate

11. Lagrangian Mechanics with Time as a Coordinate

12. Hamiltonian Mechanics with Time as a Coordinate

13. Hamilton's Principle and Noether's Theorem

14. Relativity and Spacetime

15. Fourvectors and Operators

16. Relativistic Mechanics

17. Canonical Transformations

18. Generating Functions

19. Hamilton-Jacobi Theory

 

Part III: Mathematical Appendices

A. Vector Fundamentals

B. Matrices and Determinants

C. Eigenvalue Problem with General Metric

D. The Calculus of Many Variables

E. Geometry of Phase Space

因書籍出版日期年代久遠，廠商目前剩餘庫存皆不佳，如不介意在下訂，感謝~~

描述

這本書提供了一個創新且數學上嚴謹的分析力學基礎和古典力學與相對論和量子理論的關係。它適用於研究生級別的使用。

該書的一個獨特之處在於將特殊相對論融入到古典力學的教學中。引入了擴展的拉格朗日和哈密頓方法，將時間視為可變換的坐標，而不是牛頓物理學中的固定參數。使用這個擴展理論發展了高級主題，如共變拉格朗日和哈密頓，正準變換以及哈密頓-雅可比方程。這使得特殊相對論的洛倫茲變換成為一個正準變換。

這也是一本為那些將分析力學作為對量子力學進行批判性探索的預備的書籍。與量子力學的比較貫穿整個文本，並且以一種有助於讀者研究量子理論的方式呈現古典力學。一章專門介紹了線性向量運算符和雙矢量，包括與量子力學的bra-ket符號的比較。旋轉使用類似於量子理論中使用的算符形式主義進行介紹，並且歐拉角的定義遵循量子力學的慣例。將時間視為坐標的擴展哈密頓理論與Dirac的主相空間約束形式主義進行了比較。相對論力學的章節展示了如何使用共變哈密頓理論來寫出Klein-Gordon和Dirac方程。哈密頓-雅可比理論的章節包括了與量子力學的Bohm隱變量模型密切相關的討論。

這本書為研究生從之前的本科古典力學課程到未來的高級相對論和量子理論的研究提供了必要的橋樑。當前理論物理學中的一些基本問題，如量子信息技術的發展和量子化引力場的問題，需要重新思考量子-古典聯繫。本文旨在鼓勵保留或恢復入門研究生分析力學課程。它是為具有智識好奇心的研究生和重視數學精確性和易讀性的教師而寫的。