Abstract
The basic laws of classical physics are usually expressed as ordinary or partial differential equations. Although the form of the equations varies from law to law, there is a common characteristic shared by most of them: they are all derivable from a principle of stationary action. Let us begin by examining this principle in the context of the oldest established laws of physics: the laws of motion. We consider the simple example of a point particle moving in a one-dimensional space.
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Notes and References
The best exposition of the subject of path integrals can be found in: Feynman, R. P., and Hibbs, A. R.: 1965, Quantum Mechanics and Path Integrals, McGraw-Hill, New York.
A discussion of topics which are somewhat more ‘modern’ can be found in: Schulman, L. S.: 1981, Techniques and Applications of Path Integration, Wiley, New York.
We assume that the reader is familiar with the concepts of mechanics at the level of: Landau, L. D., and Lifshitz, E. M.: 1973, Mechanics, Pergamon, London.
and quantum mechanics at the level of: Schiff, L.: 1968, Quantum Mechanics, McGraw-Hill, New York.
A more mathematical discussion of functional integrals, measure, etc., can be found in: Albeverio, S. A., and Hough-Kohn R. J.: 1976, ‘Mathematical theory of Feynman Path Integrals’, Lecture Notes in Math. 523 (Springer-Verlag, Heidelberg).
More detailed discussion of the connection between probability theory and path integrals can be found in: Kac, M.: 1959, Probability and Related Topics in the Physical Sciences, Interscience, New York.
The evaluation of F in (34) is given in Schulman (1981) (see Note 1 above). Further details of the harmonic oscillator can also be found in the books cited in Note 1 above.
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© 1986 D. Reidel Publishing Company, Dordrecht, Holland
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Narlikar, J.V., Padmanabhan, T. (1986). Path Integrals. In: Gravity, Gauge Theories and Quantum Cosmology. Fundamental Theories of Physics, vol 11. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-4508-1_2
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DOI: https://doi.org/10.1007/978-94-009-4508-1_2
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