Abstract
The study of many-Fermion systems is now known to be very difficult and of fundamental importance whether atoms, molecules, nuclei or quarks are the constituents of interest. Indeed, most activity in physics is many-body physics and many of yesterdays “fundamental problems” such as the determination of the nuclear potential from scattering data, and the determination of the hadronic S-matrix from vague pseudoprinciples have gone the way of the Dodo, forgotten and mostly unlamented.
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References
G. A. Baker, Jr., and J. L. Gammel, Eds., The Pade Approxi- mant in Theoretical Physics ( Academic Press, New York, 1970 ).
G. A. Baker, Jr., Essentials of Pade Approximants (Academic Press, New York, 1975); Rocky Mt. Math. J. 4, 141 (1974).
C. M. Bender and S. A. Orszag, Advanced Mathematical Methods for Scientists and Engineers ( McGraw-Hill, New York, 1978 ).
R. P. Feynman, Rev. Mod. Phys. 20, 367 (1948); R. P. Feynman and A. R. Hibbs, Quantum Mechanics and Path Integrals ( McGraw- Hill, New York, 1965 ).
J. R. Klauder, Ann. Phys. (N.Y.) 11, 123 (1960).
M. Kac, Probability and Related Topics in Physical Sciences ( Interscience Publishers, New York, 1964 ).
J. R. Klauder, J. Math. Phys. 11, 609 (1970).
J. R. Klauder, J. Math. Phys. 18, 1711 (1978).
J. R. Klauder, Phys. Rev. D14, 1952 (1976); ibid 15, 2830 (1978).
J. R. Klauder, Ann. Phys. (N.Y.) 117, 19 (1979).
J. R. Klauder, “Continuous Representations and Path Integrals Revisited,” in Path Integrals, edited by G. J. Papadopoulos and J. T. Devreese (Plenum, New York, 1978), pg. 5 et seq.
J. R. Klauder, “Nonrenormalizability and New Measures for Quantum Field Theory I and II,” Third School of Elementary Particles and High Energy Physics, Primorsko, Bulgaria, October 5-13, 1977 (Sofia, 1978 ).
C. L. Hammer, J. E. Schrauner and B. DeFacio, Phys. Rev. D18, 373 (1978); ibid D19, 667 (1979).
D. Bessis, P. Maussa and M. Villani, J. Math. Phys. 16, 11 (1975).
D. Bessis, this volume.
W. Feller, An Introduction to Probability Theory and its Applications, Volume I (3rd edition, 1968 ) and ibid Volume II (2nd edition, 1971 ), ( John Wiley, New York ).
J. N. Ginocchio, Phys. Rev. C8, 135 (1973).
J. P. Draayer, J. B. French and S. S. M. Wong, Ann. Phys. (N.Y.) 196, 476 (1977).
S. M. Grimes, C. H. Poppe, C. Wong and B. J. Dalton, Phys. Rev. C18, 1100 (1978).
S.M. Grimes, S.D. Bloom, R.F. Hausman and B.J. Dalton Phys. Rev. C19, 2378 (1979).
J. C. Wheeler and R. G. Gordon, “Bounds for Averages Using Moments,” in Ref. (2).
E. Ising, Z. Physik 31, 253 (1925).
L. Onsager, Phys. Rev. 65, 117 (1944).
B. Kaufman, Phys. Rev. 7J5, 1232 (1949).
B. Kaufman and L. Onsager, Phys. Rev. 76 1244 (1949).
T. D. Lee and C. N. Yang, Phys. Rev. 87, 410 (1952).
E. Montroll, R. B. Potts and J. C. Ward, J. Math. Phys. 4, 308 (1963).
T. D. Schultz, D. C. Mattis and E. Lieb, Rev. Mod. Phys. 36 856 (1964).
B. M. McCoy and T. T. Wu, The Two-Dimensional Ising Model, ( Harvard University Press, Cambridge, MA, 1973 ).
C. J. Thompson, Mathematical Statistical Mechanics ( McMillan, New York, 1972 ).
F. Guerra, L. Rosen and B. Simon, Ann. Math 101, 111 (1975).
J. Glimm and A. Jaffe, Probability Applied to Physics, ( University of Arkansas Press, Fayetteville, AR, 1978 ).
B. Simon, The P(cf))2 Euclidean (Quantum) Field Theory, ( Princeton University Press, Princeton, NJ, 1974 ).
F. Wegner, J. Math. Phys. 12, 2259 (1971); J. Kogut, Rev. Mod. Phys. 51, 659 (1979).
G. A. Baker, Jr., B. G. Nickel, M. S. Green and D. I. Meiron, Phys. Rev. Lett. 3j6, 1351 (1976).
G. A. Baker, Jr., and J. M. Kincaid, Phys. Rev. Lett. 42, 1431 (1979).
C. M. Newman, J. Stat. Phys. 15, 399 (1976).
S. Gustafson, SIAM, J. Numer. Anal. 343 (1970).
S. Gustafson, Rocky Mt. J. Math. 4, 227 (1974).
C. N. Yang, Phys. Rev. 85, 809 (1952).
S. Fisk and B. Widom, J. Chem. Phys. 50, 3219 (1969).
D. B. Abraham, Stud. Appl. Math 51, 179 (1972).
D. B. Abraham and P. Reed, Comm. Math. Phys. 49, 35 (1976).
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Defacio, B., Hammer, C.L., Shrauner, J.E. (1980). Spectral Methods Applied to Ising Models. In: Dalton, B.J., Grimes, S.M., Vary, J.P., Williams, S.A. (eds) Theory and Applications of Moment Methods in Many-Fermion Systems. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-3120-9_18
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DOI: https://doi.org/10.1007/978-1-4613-3120-9_18
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