• DOI:10.1007/978-3-540-49186-6_8
• Corpus ID: 118628191

Path Integrals in Quantum Physics

@article{Rosenfelder2012PathII,
  title={Path Integrals in Quantum Physics},
  author={R. Rosenfelder},
  journal={arXiv: Nuclear Theory},
  year={2012}
}

• R. Rosenfelder
• Published 6 September 2012
• Physics
• arXiv: Nuclear Theory

These lectures aim at giving graduate students an introduction to and a working knowledge of path integral methods in a wide variety of fields in physics. Consequently, the lecture notes are organized in three main parts dealing with non-relativistic quantum mechanics, many-body physics and field theory. In the first part the basic concepts of path integrals are developed in the usual heuristic, non-mathematical way followed by the standard examples of quadratic Lagrangians for which the path integrals can be solved exactly. Applications include perturbation theory, semi-classical expansions, scattering problems, tunneling processes and the representation of Green functions as path integrals. It is shown how (euclidean) path integrals can be treated numerically by Monte-Carlo methods with a program for the anharmonic oscillator as an explicit example. The second part deals with the application of path integrals in statistical mechanics and manybody problems. Various chapters treat the partition function, the polaron problem as a non-relativistic field theory, dissipative quantum systems, path integrals over ordinary and Grassmannian coherent states and perturbation theory for both bosons and fermions. Again a simple Fortran program is included for illustrating the use of strong-coupling methods in the polaron problem. Finally, in the third part path integrals in relativistic quantum field theory are discussed. Standard topics like the generating functional for Green functions, perturbative expansions, effective actions and quantization of gauge theories are treated. Some special applications (the worldline formalism and spin in relativistic path integrals, the derivation of anomalies by path integral methods) are contained in additional chapters. The last section tries to give a simple introduction into lattice (gauge) field theory including a numerical example which can be run on a PC. The set of problems which accompanied the lectures is also included in the present notes.