Abstract
Through the explicit introduction of hyperplane dependence as a form of relativistic dynamical evolution, we construct a manifestly covariant description of a single positive energy particle interacting with any one of a large class of “moving” external potentials. In1+1 dimensions, the simplified mathematics allows us to display a number of general properties of solutions to the equations of motion for evolution on hyperplanes.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References and notes
G. N. Fleming,J. Math. Phys. 7, 1959 (1966).
G. N. Fleming, “Hyperplane Dependent Quantized Fields and Lorentz Invariance” inFoundations of Quantum Field Theory, R. Harre and H. Brown, eds. (Oxford University Press Oxford, 1987).
Angular momentum and spatial localization were first discussed in this formalism in G. N. Fleming,Phys. Rev. 137, B188 (1964).
The consistency conditions in 3+1 dimensions are considered, in general terms, in G. N. Fleming,J. Math. Phys. 9, 193 (1968).
H. Bennett and G. N. Fleming, in preparation.
E. P. Wigner,Ann. Math. 40, 149 (1939).
T. D. Newton and E. P. Wigner,Rev. Mod. Phys. 21, 400 (1949); A. S. Wightmann,Rev. Mod. Phys. 34, 845 (1962).
A. O. Barut and S. Malin,Rev. Mod. Phys. 40, 632 (1968).
T. F. Jordan and N. Mukunda,Phy. Rev. 132, 1842 (1963); D. G. Currie, T. F. Jordan and E. C. G. Sudarshan,Rev. Mod. Phys. 35, 350 (1963).
This assignment of interactions is a consequence of the hyperplane formalism being a manifestly covariant generalization/version of Dirac's instant form of relativistic dynamics. See P. A. M. Dirac,Rev. Mod. Phy. 21, 392 (1949).
G, Arfken,Mathematical Methods of Physics, 3rd edn. (Academic Press, New York, 1985), p. 613.
Ibid., p. 615.
G. N. Fleming,Phys. Rev. 139, B963 (1965).
G. C. Hegerfeldt,Phys. Rev. Lett. 54, 2395 (1985);Phys. Rev. D91, 3320 (1974); G. C. Hegerfeldt and S. N. M. Ruijsenaars,Phys. Rev. D22, 377 (1980).
P. H. Eberhard,Il Nuovo Cimento 46, 392 (1978); W. K. Wooters and W. H. Zurek,Nature 299, 802 (1982); G. C. Ghirardi and T. Weber,Il Nuovo Cimento 78, 9 (1983); D. N. PagePhys. Lett. 91A, 57 (1982).
G. N. Fleming, “Lorentz invariant state reduction and the ontology of space-time,” in preparation. See also S. N. M. Ruijsenaars,Ann. Phys. (N.Y.)37, 33 (1981).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Fleming, G.N., Bennett, H. Hyperplane dependence in relativistic quantum mechanics. Found Phys 19, 231–267 (1989). https://doi.org/10.1007/BF00734559
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF00734559