Abstract
A simple mathematical extension of quantum theory is presented. As well as opening the possibility of alternative methods of calculation, the additional formalism implies a new physical interpretation of the standard theory by providing a picture of an external reality. The new formalism, developed first for the single-particle case, has the advantage of generalizing immediately to quantum field theory and to the description of relativistic phenomena such as particle creation and annihilation.
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REFERENCES
J. S. Bell, Physics 1, 195 (1964).
J. F. Clauser and A. Shimony, Rep. Prog. Phys. 41, 1881 (1978).
A. Aspect, J. Dalibard, and G. Roger, Phys. Rev. Lett. 49, 1804 (1982).
O. Costa de Beauregard, Compt. Rend. 236, 1632 (1953); Nuovo Cimento B 42, 41 (1977); 51, 267 (1979); Found. Phys. 17, 775 (1987).
J. G. Cramer, Phys. Rev. D 22, 362 (1980); Rev. Mod. Phys. 58, 647 (1986); Int. J. Theor. Phys. 27, 227 (1988).
W. C. Davidon, Nuovo Cimento B 36, 34 (1976).
J. Rayski, in Symposium on the Foundations of Modern Physics, P. Lahti and P. Mittelstaedt, eds. (World Scientific, Singapore, 1985).
C. W. Rietdijk, Found. Phys. 8, 615 (1978); 10, 403 (1980); 17, 297 (1987); Nuovo Cimento B 97, 111 (1987).
H. P. Stapp, Nuovo Cimento B 29, 270 (1975).
R. I. Sutherland, Int. J. Theor. Phys. 22, 377 (1983).
W. Greiner, Quantum Mechanics—An Introduction, 3rd edn. (Springer, Berlin, 1994).
W. Greiner, Relativistic Quantum Mechanics—Wave Equations, 2nd edn. (Springer, Berlin, 1994).
R. P. Feynman, Phys. Rev. 76, 749 (1949).
S. Kochen and E. P. Specker, J. Math. Mech. 17, 59 (1967).
F. J. Belinfante, A Survey of Hidden-Variables Theories (Pergamon, Oxford, 1973).
S. S. Schweber, H. A. Bethe, and F. de Hoffmann, Meson and Fields. Vol. 1. Fields (Row & Peterson, Illinois, 1955).
W. Heitler, The Quantum Theory of Radiation, 3rd edn. (Oxford University Press, Oxford, 1954).
D. Bohm, Phys. Rev. 85, 166, 180 (1952).
L. de Broglie, Non-Linear Wave Mechanics (Elsevier, Amsterdam, 1960).
L. Cohen, J. Math. Phys. 7, 781 (1966). See also L. Cohen, in Frontiers of Nonequilibrium Statistical Physics, G. T. Moore and M. O. Scully, eds. (Plenum, New York, 1986).
E. P. Wigner, in Perspectives in Quantum Theory, W. Yourgrau and A. van der Merwe, eds. (Dover, New York, 1979).
H. Price, Time's Arrow and Archimedes' Point (Oxford University Press, Oxford, 1996).
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Sutherland, R.I. Density Formalism for Quantum Theory. Foundations of Physics 28, 1157–1190 (1998). https://doi.org/10.1023/A:1018850120826
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DOI: https://doi.org/10.1023/A:1018850120826