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1
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84927218933
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A canonical description of Maxwell's electrodynamics is given, e.g., in R. Arnowitt, S. Deser, and C. W. Misner, in Gravitation: An Introduction to Current Research, edited by L. Witten (Wiley, New York, 1962);
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3
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84927218932
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The canonical formulation for the Yang-Mills theories is developed, e.g., in A. J. Hanson, T. Regge, and C. Teitelboim, Constrained Hamiltonian Systems (Accademia Nazionale dei Lincei, Rome, 1976);
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5
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84927218931
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or in L. D. Faddeev and A. A. Slavnov, Gauge Fields: Introduction to Quantum Theory (Benjamin, London, 1980).
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6
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84927218930
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A classical account of the canonical formalism in general relativity is given by R. Arnowitt, S. Deser, and C. W. Misner, in Gravitation: An Introduction to Current Research (Ref. 1).
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9
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84927218929
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and Ref. 6.
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14
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0000211103
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A general approach to the systems whose constraints close with structure functions was developed, through the path integral formalism, by Faddeev, Popov, Batalin, Fradkin, and Vilkovisky. See, e.g.
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(1985)
J. Math. Phys.
, vol.26
, pp. 172
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Batalin, I.A.1
Vilkovisky, G.A.2
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16
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84927218928
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See, e.g., L. D. Faddeev and A. A. Slavnov, Gauge Fields: Introduction to Quantum Theory (Ref. 2).
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19
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36049055961
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The idea of projecting geometrical objects in general and the metric in particular with respect to a given congruence of lines or orbits recurs in different contexts in the general theory of relativity. Its simplest application is the split of the spacetime metric into the time interval and the spatial metric along the world lines of a family of observers [see, e.g., C. Moøller, The Theory of Relativity (Clarendon Press, Oxford, 1972)]. In the same spirit, the metric in higher-dimensional Kaluza-Klein-type theories is projected into the physical spacetime metric and matter field components [cf. P. G. Bergmann, Introduction to the Theory of Relativity (Prentice-Hall, Engelwood Cliffs, 1942)]., introduced the process by which the metric in the ``big space'' scrM induces a metric in the space of orbits of a group acting on scrM;
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(1967)
Phys. Rev.
, vol.160
, pp. 1113
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DeWitt, B.S.1
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20
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84927218927
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this idea is further developed in B. S. DeWitt, in Relativity: Proceedings of the Relativity Conference in the Midwest, edited by M. Carmeli, S. I. Fickler, and L. Witten (Plenum, New York, 1970).
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21
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84927218909
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Equations (9.6)–(9.8) generalize DeWitt's procedure of Ref. 12 in two respects: (1) The orbits are not necessarily those of a group and (2) the Poisson brackets (9.6) may vanish only weakly, modulo the constraints.
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22
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84927218907
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This property of the helical model is mentioned in the footnote on p. 729 of the article by B. S. DeWitt, in General Relativity: An Einstein Centenary Survey, edited by S. W. Hawking and W. Israel (Cambridge University Press, Cambridge, 1979).
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23
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84927218905
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The subtle points concerning the structure of the physical phase space at the origin r=0 will be discussed in a forthcoming paper by J. Arms and M. Gotay.
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