Jan 2007
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2007cqgra..24..253f&link_type=abstract
Classical and Quantum Gravity, Volume 24, Issue 1, pp. 253-254 (2007).
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Scientific paper
It is not usual for someone to write a book on someone else's Ph.D. thesis, but then Feynman was not a usual physicist. He was without doubt one of the most original physicists of the twentieth century, who has strongly influenced the developments in quantum field theory through his many ingenious contributions. Path integral approach to quantum theories is one such contribution which pervades almost all areas of physics. What is astonishing is that he developed this idea as a graduate student for his Ph.D. thesis which has been printed, for the first time, in the present book along with two other related articles.
The early developments in quantum theory, by Heisenberg and Schrödinger, were based on the Hamiltonian formulation, where one starts with the Hamiltonian description of a classical system and then promotes the classical observables to noncommuting quantum operators. However, Dirac had already stressed in an article in 1932 (this article is also reproduced in the present book) that the Lagrangian is more fundamental than the Hamiltonian, at least from the point of view of relativistic invariance and he wondered how the Lagrangian may enter into the quantum description. He had developed this idea through his 'transformation matrix' theory and had even hinted on how the action of the classical theory may enter such a description. However, although the brief paper by Dirac contained the basic essential ideas, it did not fully develop the idea of a Lagrangian description in detail in the functional language.
Feynman, on the other hand, was interested in the electromagnetic interactions of the electron from a completely different point of view rooted in a theory involving action-at-a-distance. His theory (along with John Wheeler) did not have a Hamiltonian description and, in order to quantize such a theory, he needed an alternative formulation of quantum mechanics. When the article by Dirac was brought to his attention, he immediately realized what he was looking for and developed fully what is known today as the path integral approach to quantum theories. Although his main motivation was in the study of theories involving the concept of action-at-a-distance, as he emphasizes in his thesis, his formulation of quantum theories applies to any theory in general.
The thesis develops quite systematically and in detail all the concepts of functionals necessary for this formulation. The motivation and the physical insights are described in the brilliant 'Feynman' style. It is incredible that even at that young age, the signs of his legendary teaching style were evident in his presentation of the material in the thesis.
The path integral approach is now something that every graduate student in theoretical physics is supposed to know. There are several books on the subject, even one by Feynman himself (and Hibbs). Nonetheless, the thesis provides a very good background for the way these ideas came about. The two companion articles, although available in print, also gives a complete picture of the development of this line of thinking. The helpful introductory remarks by the editor also puts things in the proper historical perspective. This book would be very helpful to anyone interested in the development of modern ideas in physics.
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