Abstract
Quantum mechanics is troubled by the problem of nonlocality inherent in the theory. In a series of papers we explore the possibility of an algebraic formulation of quantum mechanics based on local observables which would incorporate nonlocality when small distances are involved but would be separable at large distances. This paper reviews some of the basic ideas and theories developed recently. These include a unified localization scheme, the introduction of local comoving evolution, local comoving observables, and related conservation laws. Technical considerations and mathematical jargon are kept to a minimum to avoid obscuring physical reasoning.
Similar content being viewed by others
References
K. K. Wan and T. D. Jackson,Phys. Lett. 106A, 219 (1984).
K. K. Wan, T. D. Jackson, and I. H. McKenna,Nuovo Cimento 81B, 165 (1984).
K. K. Wan and R. G. D. McLean,J. Math. Phys. 26, 2540 (1985).
K. K. Wan and R. G. D. McLean,Phys. Lett. 94A, 198 (1983).
K. K. Wan and R. G. D. McLean,Phys. Lett. 95A, 76 (1983).
K. K. Wan and R. G. D. McLean,J. Phys. 17A, 825 (1984), Corrigenda17A, 2367 (1984).
K. K. Wan and R. G. D. McLean,J. Phys. 17A, 837 (1984), Corrigenda17A, 2367 (1984).
D. R. E. Timson and K. K. Wan, preprint, 1987.
D. R. E. Timson, PhD Thesis, St. Andrews University, 1986.
K. K. Wan and K. McFarlane,J. Phys. 13A, 2673 (1980).
K. K. Wan and K. McFarlane,J. Phys. 14A, 2595 (1981).
K. McFlarlane and K. K. Wan,J. Phys. 14A, L1 (1981).
K. McFarlane and K. K. Wan,Int. J. Theor. Phys. 22, 55 (1983).
K. K. Wan and I. H. McKenna,Algebras, Groups, and Geometries 1, 154 (1984).
W. O. Amrein,Nonrelativistic Quantum Dynamics (Reidel, Dordrecht, 1981).
W. O. Amrein, J. M. Jauch, and K. B. Sinha,Scattering Theory in Quantum Mechanics (Benjamin, Reading, Mass., 1971).
W. Thirring,Quantum Mechanics of Atoms and Molecules (Springer, New York, 1979).
P. Pfeifer,Helv. Phys. Acta. 53, 410 (1980).
R. Abraham and J. E. Marsden,Foundations of Mechanics (Benjamin/Cummings, Reading, Mass., 1978).
E. G. Beltrametti and G. Cassinelli,The Logic of Quantum Mechanics (Addison-Wesley, Reading, Mass., 1981), p. 3.
A. Messiah,Quantum Mechanics, Vol. I (North-Holland, Amsterdam, 1967), p. 145.
P. Roman,Advanced Quantum Theory (Addison-Wesley, Reading, Mass., 1965), p. 28.
K. K. Wan and C. Viasminsky,Prog. Theor. Phys. 58, 1030 (1977).
J. Weidmann,Linear Operators in Hilbert Spaces (Springer, New York, 1980), p. 85.
J. D. Dollard,Comm. Math. Phys. 12, 193 (1969).
R. R. Strichartz,J. Func. Anal. 40, 341 (1981).
V. Enss,Comm. Math. Phys. 89, 245 (1983).
E. Merzbacher,Quantum Mechanics (Wiley, New York, 1970), p. 140.
G. W. Mackey,Mathematical Foundations of Quantum Mechanics (Benjamin, New York, 1963).
J. M. Jauch,Foundations of Quantum Mechanics (Addison-Wesley, Reading, Mass., 1968).
P. Mittelstaedt,Quantum Logic (Reidel, Drodrecht, 1978).
R. Haag and D. Kastler,J. Math. Phys. 5, 848 (1964).
G. G. Emch,Algebraic Methods in Statistical Mechanics and Quantum Field Theory (Wiley, New York, 1972).
O. Bratteli and D. W. Robinson,Operator Alhebras and Quantum Statistical Mechanics, Vol. I (Springer, New York, 1979).
N. N. Bogolubov, A. A. Logunov, and I. T. Todorov,Introduction to Axiomatic Quantum Field Theory (Benjamin, Reading, Mass., 1975), Chap. 23.
E. Prugovecki,Quantum Mechanics in Hilbert Space (Academic Press, New York, 1981).
P. Roman,Some Modern Mathematics for Physicists and other Outsiders (Pergamon, New York, 1975).
K. K. Wan and R. G. D. McLean,Phys. Lett. 102A, 163 (1984).
K. K. Wan and T. D. Jackson,Phys. Lett. 111A, 223 (1985).
H. Primas and U. Muller-Herold,Adv. Chem. Phys. 38, (1978), Chap. 3.5.
K. Hepp,Helv. Phys. Acta. 45, 237 (1972).
G. G. Emch,Helv. Phys. Acta. 45, 1049 (1972).
B. Whitten-Wolfe and G. G. Emch,Helv. Phys. Acta. 49, 45 (1976).
M. A. Naimark,Linear Differential Operators, Vol. II (Harrap, London, 1968), p. 209.
W. Arveson,An Invitation to C*-Algebra (Springer, New York, 1976), p. 21.
F. Selleri and G. Tarozzi,Riv. Nuovo Cimento 4(2), (1981).
W. M. de Muynck,Found. Phys. 14, 199 (1984).
C. E. Lanford and D. Ruelle,Comm. Math. Phys. 13, 194 (1969).
K. K. Wan,Can. J. Phys. 58, 976 (1980).
W. H. Furry,Phys. Rev. 49, 393 (1936).
E. Schrödinger,Proc. Camb. Phil. Soc. 31, 555 (1939).
M. Mugur-Schachter, inQuantum Mechanics a Half Century Later, J. Leite Lopes and M. Paty, eds. (Reidel, Dordrecht, 1977).
G. C. Ghirardi, A. Rimini, and T. Weber,Nuovo Cimento 36B, 97 (1976).
G. C. Hegerfeldt,Phys. Rev. D10, 3320 (1974).
G. C. Hegerfeldt and S. N. M. Ruijsenaas,Phys. Rev. D22, 377 (1980).
F. W. Byron and R. W. Fuler,Mathematics of Classical and Quantum Physics, Vol. I (Addison-Wesley, Reading, Mass., 1–969), Chap. 5.11.
M. Reed and B. Simon,Methods of Modern Mathematical Physics, Vol. II (Academic Press, New York, 1975), p. 282.
K. K. Wan and D. R. E. Timson,Phys. Lett. 111A, 165 (1985).
A. Einstein, B. Podolsky, and N. Rosen,Phys. Rev. 47, 777 (1935).
D. Bohm,Quantum Theory (Prentice-Hall, Englewood Cliffs, New Jersey, 1951).
M. Vujicic and F. Herbut,J. Math. Phys. 25, 2253 (1984).
D. Bohm,Phys. Rev. 85, 166 (1952).
C. Philippidis, C. Dewdney, and B. J. Hiley,Nuovo Cimento 52B, 15 (1979).
Author information
Authors and Affiliations
Additional information
An invited paper in honour of David Bohm on the occasion of his 70th birthday.
Rights and permissions
About this article
Cite this article
Wan, K.K. Local observables, nonlocality, and asymptotically separable quantum mechanics. Found Phys 18, 887–911 (1988). https://doi.org/10.1007/BF01855941
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01855941