Abstract
A relativistic one-particle, quantum theory for spin-zero particles is constructed uponL 2(x, ct), resulting in a positive definite spacetime probability density. A generalized Schrödinger equation having a Hermitian HamiltonianH onL 2(x, ct) for an arbitrary four-vector potential is derived. In this formalism the rest mass is an observable and a scalar particle is described by a wave packet that is a superposition of mass states. The requirements of macroscopic causality are shown to be satisfied by the most probable trajectory of a free tardyon and a nontrivial framework for charged and neutral particles is provided. The Klein paradox is resolved and a link to the free particle field operators of quantum field theory is established. A charged particle interacting with a static magnetic field is discussed as an example of the formalism.
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References
S. S. Schweber,An Introduction to Relativistic Quantum Field Theory, (Harper and Row, New York, 1962).
J. D. Bjorken and S. D. Drell,Relativistic Quantum Mechanics (McGraw-Hill, New York, 1964).
V. A. Fock,Physik Z. Sowjetunion 12, 404 (1937).
E. C. G. Stückelberg,Helv. Phys. Acta 14, 322 (1941);15, 23 (1942).
Y. Nambu,Prog. Theor. Phys. 5, 82 (1950).
J. Schwinger,Phys. Rev. 82, 664 (1951).
R. P. Feynman,Phys. Rev. 80, 440 (1950), App. A;84, 108 (1951), App. D.
J. H. Cooke,Phys. Rev. 166, 1293 (1968).
R. E. Collins,Found. Phys. 7, 475 (1977).
R. E. Collins,Nuovo Cim. Lett. 18, 581 (1977).
E. Schrödinger,Ann. Physik 81, 109 (1926).
W. Gordon,Z. Physik 40, 117 (1926).
O. Klein,Z. Physik 41, 407 (1927).
L. I. Schiff,Quantum Mechanics, 3rd ed. (McGraw-Hill, New York, 1968).
E. C. G. Stückelberg,Helv. Phys. Acta 14, 588 (1941).
R. P. Feynman,Phys. Rev. 76, 749, 769 (1949).
S. Weinberg,Phys. Rev. 133, B1318 (1964).
H. Feshbach and F. Villars,Rev. Mod. Phys. 30, 24 (1958).
O. Klein,Z. Physik 53, 157 (1929).
R. G. Winter,Am. J. Phys. 27, 355 (1959).
E. Majorana,Nuovo Cim. 9, 335 (1932).
D. M. Fredkin,Am. J. Phys. 34, 314 (1966).
E. P. Wigner,Ann. Math. 40, 149 (1939);
V. Bargmann,Ann. Math. 48, 568 (1947);
V. Bargmann and E. P. Wigner,Proc. Nat. Acad. Sci. (US) 34, 211 (1948).
L. L. Foldy,Phys. Rev. 102, 568 (1956).
R. F. Streater and A. S. Wightman,PCT, Spin and Statistics, and All That (W. A. Benjamin, New York, 1964).
R. E. Collins and J. R. Fanchi,Nuovo Clim., to be published (1979).
R. M. Kiehn,Int. J. Eng. Sci. 13, 941 (1975).
J. R. Fanchi, PhD Dissertation, University of Houston (1977).
Y. Aharonov and D. Bohm,Phys. Rev. 115, 485 (1959).
R. M. Kiehn,J. Math. Phys. 18, 614 (1977).
J. D. Jackson,Classical Electrodynamics (Wiley, New York (1962).
R. P. Feynman, M. Kislinger, and F. Ravndal,Phys. Rev. D 3, 2706 (1971).
L. L. Foldy and S. A. Wouthuysen,Phys. Rev. 78, 29 (1950).
P. Dennery and A. Krzywicki,Mathematics for Physicists (Harper and Row, New York 1967), p. 237.
V. B. Berestetskii, E. M. Lifshitz, and L. P. Pitaevskii,Relativistic Quantum Theory (Pergamon Press, New York, 1971), esp. pp. 33–34.
W. Pauli,Phys. Rev. 58, 716 (1940).
L. Lam,J. Math. Phys. 12, 299 (1971).
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Fanchi, J.R., Collins, R.E. Quantum mechanics of relativistic spinless particles. Found Phys 8, 851–877 (1978). https://doi.org/10.1007/BF00715059
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DOI: https://doi.org/10.1007/BF00715059