Feynman Integral and Random Dynamics in Quantum Physics: A Probabilistic Approach to Quantum Dynamics
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Dordrecht
Springer Netherlands
1999
|
| Schriftenreihe: | Mathematics and Its Applications
480 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | The Feynman integral is considered as an intuitive representation of quantum mechanics showing the complex quantum phenomena in a language comprehensible at a classical level. It suggests that the quantum transition amplitude arises from classical mechanics by an average over various interfering paths. The classical picture suggested by the Feynman integral may be illusory. By most physicists the path integral is usually treated as a convenient formal mathematical tool for a quick derivation of useful approximations in quantum mechanics. Results obtained in the formalism of Feynman integrals receive a mathematical justification by means of other (usually much harder) methods. In such a case the rigour is achieved at the cost of losing the intuitive classical insight. The aim of this book is to formulate a mathematical theory of the Feynman integral literally in the way it was expressed by Feynman, at the cost of complexifying the configuration space. In such a case the Feynman integral can be expressed by a probability measure. The equations of quantum mechanics can be formulated as equations of random classical mechanics on a complex configuration space. The opportunity of computer simulations shows an immediate advantage of such a formulation. A mathematical formulation of the Feynman integral should not be considered solely as an academic question of mathematical rigour in theoretical physics |
| Beschreibung: | 1 Online-Ressource (XX, 367 p) |
| ISBN: | 9789401147163 9789401059848 |
| DOI: | 10.1007/978-94-011-4716-3 |
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| 500 | |a The Feynman integral is considered as an intuitive representation of quantum mechanics showing the complex quantum phenomena in a language comprehensible at a classical level. It suggests that the quantum transition amplitude arises from classical mechanics by an average over various interfering paths. The classical picture suggested by the Feynman integral may be illusory. By most physicists the path integral is usually treated as a convenient formal mathematical tool for a quick derivation of useful approximations in quantum mechanics. Results obtained in the formalism of Feynman integrals receive a mathematical justification by means of other (usually much harder) methods. In such a case the rigour is achieved at the cost of losing the intuitive classical insight. The aim of this book is to formulate a mathematical theory of the Feynman integral literally in the way it was expressed by Feynman, at the cost of complexifying the configuration space. In such a case the Feynman integral can be expressed by a probability measure. The equations of quantum mechanics can be formulated as equations of random classical mechanics on a complex configuration space. The opportunity of computer simulations shows an immediate advantage of such a formulation. A mathematical formulation of the Feynman integral should not be considered solely as an academic question of mathematical rigour in theoretical physics | ||
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Datensatz im Suchindex
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| author | Haba, Zbigniew |
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| discipline | Physik Mathematik |
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| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:14Z |
| institution | BVB |
| isbn | 9789401147163 9789401059848 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027859375 |
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| publisher | Springer Netherlands |
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| series2 | Mathematics and Its Applications |
| spelling | Haba, Zbigniew Verfasser aut Feynman Integral and Random Dynamics in Quantum Physics A Probabilistic Approach to Quantum Dynamics by Zbigniew Haba Dordrecht Springer Netherlands 1999 1 Online-Ressource (XX, 367 p) txt rdacontent c rdamedia cr rdacarrier Mathematics and Its Applications 480 The Feynman integral is considered as an intuitive representation of quantum mechanics showing the complex quantum phenomena in a language comprehensible at a classical level. It suggests that the quantum transition amplitude arises from classical mechanics by an average over various interfering paths. The classical picture suggested by the Feynman integral may be illusory. By most physicists the path integral is usually treated as a convenient formal mathematical tool for a quick derivation of useful approximations in quantum mechanics. Results obtained in the formalism of Feynman integrals receive a mathematical justification by means of other (usually much harder) methods. In such a case the rigour is achieved at the cost of losing the intuitive classical insight. The aim of this book is to formulate a mathematical theory of the Feynman integral literally in the way it was expressed by Feynman, at the cost of complexifying the configuration space. In such a case the Feynman integral can be expressed by a probability measure. The equations of quantum mechanics can be formulated as equations of random classical mechanics on a complex configuration space. The opportunity of computer simulations shows an immediate advantage of such a formulation. A mathematical formulation of the Feynman integral should not be considered solely as an academic question of mathematical rigour in theoretical physics Physics Distribution (Probability theory) Quantum theory Quantum Physics Theoretical, Mathematical and Computational Physics Probability Theory and Stochastic Processes Elementary Particles, Quantum Field Theory Quantentheorie https://doi.org/10.1007/978-94-011-4716-3 Verlag Volltext |
| spellingShingle | Haba, Zbigniew Feynman Integral and Random Dynamics in Quantum Physics A Probabilistic Approach to Quantum Dynamics Physics Distribution (Probability theory) Quantum theory Quantum Physics Theoretical, Mathematical and Computational Physics Probability Theory and Stochastic Processes Elementary Particles, Quantum Field Theory Quantentheorie |
| title | Feynman Integral and Random Dynamics in Quantum Physics A Probabilistic Approach to Quantum Dynamics |
| title_auth | Feynman Integral and Random Dynamics in Quantum Physics A Probabilistic Approach to Quantum Dynamics |
| title_exact_search | Feynman Integral and Random Dynamics in Quantum Physics A Probabilistic Approach to Quantum Dynamics |
| title_full | Feynman Integral and Random Dynamics in Quantum Physics A Probabilistic Approach to Quantum Dynamics by Zbigniew Haba |
| title_fullStr | Feynman Integral and Random Dynamics in Quantum Physics A Probabilistic Approach to Quantum Dynamics by Zbigniew Haba |
| title_full_unstemmed | Feynman Integral and Random Dynamics in Quantum Physics A Probabilistic Approach to Quantum Dynamics by Zbigniew Haba |
| title_short | Feynman Integral and Random Dynamics in Quantum Physics |
| title_sort | feynman integral and random dynamics in quantum physics a probabilistic approach to quantum dynamics |
| title_sub | A Probabilistic Approach to Quantum Dynamics |
| topic | Physics Distribution (Probability theory) Quantum theory Quantum Physics Theoretical, Mathematical and Computational Physics Probability Theory and Stochastic Processes Elementary Particles, Quantum Field Theory Quantentheorie |
| topic_facet | Physics Distribution (Probability theory) Quantum theory Quantum Physics Theoretical, Mathematical and Computational Physics Probability Theory and Stochastic Processes Elementary Particles, Quantum Field Theory Quantentheorie |
| url | https://doi.org/10.1007/978-94-011-4716-3 |
| work_keys_str_mv | AT habazbigniew feynmanintegralandrandomdynamicsinquantumphysicsaprobabilisticapproachtoquantumdynamics |