Abstract
Recent experimental and theoretical advances have provided some additional insight into the value of local field theories for the description of actual phenomena. It is suggested, on the basis of some of these results, that there is evidence that the concept of the position of an elementary system may have phenomenological importance.
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This question was discussed for a first-quantized non-Abelian gauge theory by L.P. Horwitz, Helv. Phys. Acta 32, 144 (1966). The one-particle Hamiltonian was shown not to be an observable since its expectation value is not gauge invariant under gauge transformations of the first kind. A similar phenomenon occurs in electromagnetism under gauge transformations of the second kind; in this case it is clear that the energy of the field must be included (since it carries momentum). This mechanism is also responsible for the non-invariance of the Hamiltonian of a particle in a non-Abelian gauge field; the canonical momentum is altered by a gauge transformation of the first kind. Hence it is difficult to define the “particle” independently of the field. I wish to thank Dr.A. Casher for a recent discussion of this point.
A Chodos, R.L. Jaffe, K. Johnson, C.B. Thorn and V.F.Weisskopf, M.I.T. preprint CTP, 387, Nov. 1973.
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© 1974 D. Reidel Publishing Company, Dordrecht, Holland
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Horwitz, L. (1974). Phenomenological Aspects of Localizability. In: Enz, C.P., Mehra, J. (eds) Physical Reality and Mathematical Description. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-2274-3_21
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