dorsal/arxiv
View SchemaPath Integral Methods and Applications
| Authors | Richard MacKenzie |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0004090 |
| URL | https://arxiv.org/abs/quant-ph/0004090 |
Abstract
These lectures are intended as an introduction to the technique of path integrals and their applications in physics. The audience is mainly first-year graduate students, and it is assumed that the reader has a good foundation in quantum mechanics. No prior exposure to path integrals is assumed, however. The path integral is a formulation of quantum mechanics equivalent to the standard formulations, offering a new way of looking at the subject which is, arguably, more intuitive than the usual approaches. Applications of path integrals are as vast as those of quantum mechanics itself, including the quantum mechanics of a single particle, statistical mechanics, condensed matter physics and quantum field theory. After an introduction including a very brief historical overview of the subject, we derive a path integral expression for the propagator in quantum mechanics, including the free particle and harmonic oscillator as examples. We then discuss a variety of applications, including path integrals in multiply-connected spaces, Euclidean path integrals and statistical mechanics, perturbation theory in quantum mechanics and in quantum field theory, and instantons via path integrals. For the most part, the emphasis is on explicit calculations in the familiar setting of quantum mechanics, with some discussion (often brief and schematic) of how these ideas can be applied to more complicated situations such as field theory.
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"abstract": "These lectures are intended as an introduction to the technique of path\nintegrals and their applications in physics. The audience is mainly first-year\ngraduate students, and it is assumed that the reader has a good foundation in\nquantum mechanics. No prior exposure to path integrals is assumed, however.\n The path integral is a formulation of quantum mechanics equivalent to the\nstandard formulations, offering a new way of looking at the subject which is,\narguably, more intuitive than the usual approaches. Applications of path\nintegrals are as vast as those of quantum mechanics itself, including the\nquantum mechanics of a single particle, statistical mechanics, condensed matter\nphysics and quantum field theory.\n After an introduction including a very brief historical overview of the\nsubject, we derive a path integral expression for the propagator in quantum\nmechanics, including the free particle and harmonic oscillator as examples. We\nthen discuss a variety of applications, including path integrals in\nmultiply-connected spaces, Euclidean path integrals and statistical mechanics,\nperturbation theory in quantum mechanics and in quantum field theory, and\ninstantons via path integrals.\n For the most part, the emphasis is on explicit calculations in the familiar\nsetting of quantum mechanics, with some discussion (often brief and schematic)\nof how these ideas can be applied to more complicated situations such as field\ntheory.",
"arxiv_id": "quant-ph/0004090",
"authors": [
"Richard MacKenzie"
],
"categories": [
"quant-ph",
"hep-th"
],
"title": "Path Integral Methods and Applications",
"url": "https://arxiv.org/abs/quant-ph/0004090"
},
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