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Dynamics of tensor fields in hyperspace. III
1.K. Kuchař, J. Math. Phys. 17, 777 (1976). Our notation is explained in Sec. 2 of that paper. The equations from it are quoted by prefixing the Roman numeral I before their section and equations numbers.
2.K. Kuchař, J. Math. Phys. 17, 792 (1976). The equations from it are quoted by prefixing the Roman numeral II before their section and equation numbers.
3.See P. A. M. Dirac, Lectures on Quantum Mechanics (Academic, New York, 1965), and the papers quoted there.
4.The parametrized scalar field is discussed by R. Arnowitt, S. Deser, and C. W. Misner, Phys. Rev. 116, 1322 (1959).
4.The constraints, however, are not projected into directions ⊥ and ‖ to the hypersurface. The electromagnetic field is discussed in R. Arnowitt, S. Deser, and C. W. Misner, The Dynamics of General Relativity, in: Gravitation: An Introduction to Current Research, edited by L. Witten (Wiley, New York, 1962).
4.See also P. A. M. Dirac, Can. J. Math. 3, 1 (1951).
5.F. Belinfante, Phys. 7, 449 (1940).
6.L. Rosenfeld, Mem. Acad. R. Belg. Sci. 18, No. 6 (1940).
7.W. Pauli, Rev. Mod. Phys. 13, 203 (1941).
8.See, e.g., S. W. Hawking and G. F. R. Ellis, The Large Scale Structure of Space—Time (Cambridge U.P., Cambridge, 1973), p. 67.
9.The use of the term “derivative gravitational coupling” is not entirely uniform. Sometimes, people refer by it to the theories in which the source and geometry are coupled through the terms containing the Riemann curvature tensor (the second derivatives of the metric).
10.For the importance of the boundary terms in asymptotically flat spacetimes, see, e.g., B. S. DeWitt, Phys. Rev. 160, 113 (1967),
10.or T. Regge and C. Teitelboim, Ann. Phys. 88, 286 (1974).
11.K. Kuchař, Phys. Rev. D 4, 955 (1971);
11.K. Kuchař, J. Math. Phys. 13, 768 (1972).
12.K. Kuchař, “Canonical Quantization of Gravity,” in Relativity, Astrophysics and Cosmology, edited by W. Israel (Reidel, Dordrecht 1973).
13.C. Lanczos, The Variational Principles of Mechanics (University of Toronto Press, Toronto, 1970), 4th ed., Chaps. VI. 10, IX. 6–IX. 10.
14.F. B. Estabrook and H. D. Wahlquist, SIAM Rev. 17, 201 (1975).
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