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内容提要:
路径积分作为重要的量子化手段在规范场理论的发展中起着极为重要的作用,同时在量子力学、统计物理和高分子物理研究中也有着广泛的应用。本书是作者积多年教学和研究之经验而写成的,它讨论了路径积分的原理、性质、解法及其应用。本书初版于1990年,第2版对许多章节都作了较大的修改和补充,并新增加了“相对论性粒子轨道的路径积分“一章。
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Since this book first appeared three years ago,a number of important developments have taken place calling for various extensions to the text.
Chapter 4 now contains a discussion of the features of the xemiclassical quantization which are relevant for multidimensional chaotic systems. 本书为英文版。 目录:
1 Fundamentals
1.1 Classical Mechanics 1.2 Quantum Mechanics 1.3 Dirac's Bra-Ket Formalism 1.4 Boservables 1.5 Quantum Mechanics of General Lagrangian Systems 1.6 Particle on the Surface of a Sphere 1.7 Spinning Top 1.8 Time Evolution Operator 1.9 Properties of the Time Evolution Operator 1.10 Heisenberg Picture of Quantum Mechanics 1.11 Classical and Quantum Statistics Appendix 1A The Asymmetric Top Notes and References 2 Path Integrals-Elementary Properties and Simple Solutions 2.1 Path Integral Representation of Time Evolution Amplitudes 2.2 Exact Solution for a Free Particle 2.3 Finite-E Properties of the Free-Paticle Amplitued 2.4 Exact Solution for the Harmonic Oscillator 2.5 Useful Fluctuation Formulas 2.6 Oscillator Amplitude on a Finite Lattice 2.7 Gelfand-Yaglom Formula 2.8 Oscillator Wave Functions 2.9 Path Integrals and Quantum Statistics 2.10 Density Matrix 2.11 Quamtum Statstics of Harmonic Oscillator 2.12 Time-Dependent Harmonic Potential 3.13 Functional Measure in Fourier Space 3.14 Classical Limit 3.15 Calculation Techniques on a Finite Sliced Time Axis Poisson Formula …… 3 External Sources,Correlations,and Prturbation Theory 4 Semicalssical Time Evolution Amplitued 5 Variational Perturbaion Theory 6 Path Integrals with Topological Constraints 7 Many Particle Orbits-Statistics and Second Quantization 8 Path Integrals in Spherical Coordinates 9 Fixed-Energy Amplitude and Wave Functions 10 Short-Time Amplitude in Spaces with Curvature and Torsion 11 Schrodinger Equation in General Metric-Affine Sapces 12 New Path Integral Formula for Singular Potentials 13 Path Integral of the Coulomb System 14 Solution of Futher Path Ingerals by the Duru-Kleinert Method 15 Path Integrals in Polymer Physics 16 Polymers and Particle Orbits in Multiply Connected Spaces 17 Path Integrals and Tunneling 18 Path Integrals and Nonequilibrium Quantum Statistics 19 Path Integrals for Relativistic Particle Orbits Index |