Abstract
The complexity of the field theoretic methods used for analyzing relativistic bound state problems has forced researchers to look for simpler computational methods. Simpler methods such as the relativistic harmonic oscillator method employed in the description of extended hadrons have been investigated. They are considered phenomenological, however, because they lack a theoretical basis. A probabilistic basis for these methods is presented here in terms of the four-space formulation of relativistic quantum mechanics (FSF). The single-particle FSF is reviewed and its physical meaning is examined. The many-body single-parameter formalism is then developed. Applications are presented to illustrate use of the many-body formalism and demonstrate the ease with which relativistic bound state problems can be handled. A multiple-parameter formalism is constructed in the Appendix.
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References
Particle Data Group,Rev. Mod. Phys. 52, Supplement (1980).
D. B. Lichtenberg,Unitary Symmetry and Elementary Particles (Academic Press, New York, 1978), 2nd ed.
J. R. Henley,Phys. Rev. D20, 2532 (1979);Phys. Rev. D22, 419 (1980).
R. P. Feynman, M. Kislinger, and F. Ravndal,Phys. Rev. D11, 2706 (1971); and their references.
Y. S. Kim and M. E. Noz,Prog. Theor. Phys. 60, 801 (1978), and their references; Y. S. Kim and M. E. Noz,Am. J. Phys. 46, 484 (1978).
K. Mita and M. L. Laursen, “Bilocal Field Model of Mesons and its Spectroscopy,” Research Note 107, Oklahoma State University (May 1980).
J. R. Fanchi and R. E. Collins,Found. Phys. 8, 851 (1978); R. E. Collins and J. R. Fanchi,Nuovo Cim. 48A, 314 (1978); J. R. Fanchi, Ph. D.Dissertation, University of Houston, 1977 (University of Michigan microfilm).
J. R. Fanchi,Am. J. Phys. 49, 850 (1981).
J. R. Fanchi,J. Math. Phys. 22, 794 (1981).
L. P. Horwitz and C. Piron,Helv. Phys. Acta,46, 316 (1973); L. P. Horwitz, C. Piron, and F. Reuse,Helv. Phys. Acta 48, 546 (1975); C. Piron and F. Reuse,Helv. Phys. Acta 51, 146 (1975); F. Reuse,Helv. Phys. Acta 51, 157 (1975); L. P. Horwitz, inOld and New Questions in Physics, Cosmology, Philosophy, and Theoretical Biology: Essays in Honor of Wolfgang Yourgrau, Alwyn van der Merwe, ed. (Plenum, New York, 1983).
J. R. Fanchi,Found. Phys. 11, 493 (1981).
J. R. Fanchi,Phys. Rev. D20, 3108 (1979).
H. Enatsu,Prog. Theor. Phys. 30, 236 (1963); H. Enatsu,Nuovo Cim. 58A, 891 (1968); H. Enatsu and S. Kawaguchi,Nuovo Cim. 27A, 458 (1975); H. Enatsu, A. Takenaka, and M. Okazaki,Nuovo Cim. 43A, 575 (1978).
L. Hostler,J. Math. Phys. 21, 2461 (1980).
L. P. Horwitz and Y. Lavie,Phys. Rev. D26, 819 (1982).
E. Schroedinger,Ann. Phys. 79, 361 (1926).
M. Born,Z. Phys. 37, 863 (1926).
R. E. Collins,J. Math. Phys., submitted for publication (1980).
W. Feller,An Introduction to Probability Theory and Its Applications (J. Wiley, New York, 1961).
R. E. Collins,Found. Phys. 7, 475 (1977);Nuovo Cim. Lett. 18, 581 (1977);Nuovo Cim. Lett. 25, 473 (1979).
J. G. Gilson,Proc. Camb. Phil. Soc. 64, 1061 (1968).
P. A. M. Dirac,Principles of Quantum Mechanics (Oxford U.P., Oxford, 1976), 4th ed.
L. I. Schiff,Quantum Mechanics (McGraw-Hill, New York, 1968), 3rd ed.
L. L. Foldy,Phys. Rev. 102, 568 (1956).
H. Goldstein,Classical Mechanics (Addison-Wesley, Reading, Mass., 1965).
V. Arunasalam,Am. J. Phys. 38, 1010 (1970).
P. A. M. Dirac,Proc. Roy. Soc. (London) A114, 243, 710 (1927).
W. Heisenberg,Z. Phys. 43, 172 (1927).
J. L. Cook,Aust. J. Phys. 25, 117, 141 (1972).
J. Schwinger,Phys. Rev. 82, 914 (1951).
N. Isgur,Phys. Rev. D12, 3770 (1975);13, 122 (1976).
J. H. Cooke,Phys. Rev. 166, 1293 (1968).
P. M. Pearle,Phys. Rev. 168, 1429 (1968).
D. M. Greenberger,J. Math. Phys. 15, 395 (1974); and references therein.
D. H. Perkins,An Introduction to High Energy Physics (Addison-Wesley, Reading, Mass., 1972).
A. O. Barut,Electrodynamics and Classical Theory of Fields and Particles (Dover, New York, 1980).
J. Rzewuski,Field Theory (Polish Science Publication, Warsaw, 1958).
F. Rohrlich,Ann. Phys. 117, 292 (1979); L. P. Horwitz and F. Rohrlich,Phys. Rev. D24, 1528 (1981).
P. Droz-Vincent,Phys. Rev. D19, 702 (1979).
I. T. Todorov, “Constraint Hamiltonian Mechanics of Directly Interacting Relativistic Particles,” inProceedings of the Barcelona Workshop on “Relativistic Action at a Distance: Classical and Quantum Aspects,” Barcelona, June 1981.
P. Droz-Vincent,Nuovo Cim. 58, 355 (1980).
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Fanchi, J.R., Wilson, W.J. Relativistic many-body systems: Evolution-parameter formalism. Found Phys 13, 571–605 (1983). https://doi.org/10.1007/BF00730099
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DOI: https://doi.org/10.1007/BF00730099