A Basic Discontinuity Equation

Kevin E. Cahill; Henry P. Stapp

doi:10.1103/PhysRevD.6.1007

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A Basic Discontinuity Equation

Kevin E. Cahill^*

Henry P. Stapp

Department of Physics, Wesleyan University, Middletown, Connecticut 06457

Lawrence Berkeley Laboratory, University of California, Berkeley, California 94720

^*Participating guest, LBL.

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Phys. Rev. D 6, 1007 – Published 15 August, 1972

DOI: https://doi.org/10.1103/PhysRevD.6.1007

Abstract

We derive from field theory a formula that expresses the discontinuity of any multiparticle scattering function across any normal threshold cut in terms of specified limits of scattering functions for other processes. The special case that expresses any inclusive cross section as a discontinuity has been used extensively in recent work on high-energy processes. Other cases of the general formula also appear to have important implications, which are briefly discussed.

References (15)

A. H. Mueller, Phys. Rev. D 2, 2963 (1970) H. P. Stapp, ibid. 3, 3177 (1971) Chung-I Tan, ibid. 5, 1476 (1972) C. E. DeTar, C. E. Jones, F. E. Low, J. H. Weis, J. E. Young, and Chung-I Tan, Phys. Rev. Letters 26, 675 (1971) H. M. Chan, C. S. Hsue, C. Quigg, and J. M. Wang, ibid. 26, 672 (1971) J. Ellis, J. Finkelstein, P. A. Frampton, and M. Jacob, Phys. Letters 35B, 227 (1971) G. Veneziano, ibid. 36B, 397 (1971) S.-H. H. Tye and G. Veneziano, ibid. 38B, 30 (1972) G. Veneziano, Phys. Rev. Letters 28, 578 (1972)
H. P. Stapp, Matscience Report No. 26, Madras, 1964, Chaps. XII and XIII (unpublished) ICTP Trieste Report No. IC/65/17, 1965 (unpublished) D. I. Olive, Nuovo Cimento 37, 1422 (1965) R. J. Eden, P. V. Landshoff, D. I. Olive, and J. C. Polkinghorne, The Analytic $S$ -Matrix (Cambridge Univ. Press, Cambridge, England, 1964), Chap. 4.7
H. Araki, J. Math. Phys. 2, 163 (1960)
J. Bros, H. Epstein, and V. Glaser, reported by J. Bros in High-Energy Physics and Elementary Particles, edited by A. Salam (IAEA, Vienna, 1965), p. 85
R. Hwa, Phys. Rev. 134, B1086 (1964)
R. Gunning and H. Rossi, Analytic Functions of Several Complex Variables (Prentice Hall, Englewood Cliffs, N. J., 1965), p. 15
J. C. Polkinghorne, Nuovo Cimento 7A, 555 (1971)
J. Bros and D. Iagolnitzer, Saclay Report No. DPh-T/71-33, 1971 (unpublished)
C. Chandler and H. P. Stapp, J. Math. Phys. 10, 826 (1969) C. Chandler, Helv. Phys. Acta 42, 759 (1969)
D. Iagolnitzer and H. P. Stapp, Commun. Math. Phys. 14, 15 (1969)
H. P. Stapp, J. Math. Phys. 9, 1548 (1968)
J. Coster and H. P. Stapp, J. Math. Phys. 11, 2743 (1970)
[4]
H. Lehmann, K. Symanzik, and W. Zimmermann, Nuovo Cimento 6, 319 (1957)
H. J. Bremermann, thesis, Schrift. Math. Inst., University of Munster, No. 5, 1951 (unpublished) J. Bros, H. Epstein, and V. Glaser, Nuovo Cimento 31, 1265 (1964), p. 1289

[c1] A. H. Mueller, Phys. Rev. D 2, 2963 (1970) H. P. Stapp, ibid. 3, 3177 (1971) Chung-I Tan, ibid. 5, 1476 (1972) C. E. DeTar, C. E. Jones, F. E. Low, J. H. Weis, J. E. Young, and Chung-I Tan, Phys. Rev. Letters 26, 675 (1971) H. M. Chan, C. S. Hsue, C. Quigg, and J. M. Wang, ibid. 26, 672 (1971) J. Ellis, J. Finkelstein, P. A. Frampton, and M. Jacob, Phys. Letters 35B, 227 (1971) G. Veneziano, ibid. 36B, 397 (1971) S.-H. H. Tye and G. Veneziano, ibid. 38B, 30 (1972) G. Veneziano, Phys. Rev. Letters 28, 578 (1972)

[c2] H. P. Stapp, Matscience Report No. 26, Madras, 1964, Chaps. XII and XIII (unpublished) ICTP Trieste Report No. IC/65/17, 1965 (unpublished) D. I. Olive, Nuovo Cimento 37, 1422 (1965) R. J. Eden, P. V. Landshoff, D. I. Olive, and J. C. Polkinghorne, The Analytic $S$ -Matrix (Cambridge Univ. Press, Cambridge, England, 1964), Chap. 4.7

[c3] H. Araki, J. Math. Phys. 2, 163 (1960)

[c4] J. Bros, H. Epstein, and V. Glaser, reported by J. Bros in High-Energy Physics and Elementary Particles, edited by A. Salam (IAEA, Vienna, 1965), p. 85

[c5] R. Hwa, Phys. Rev. 134, B1086 (1964)

[c6] R. Gunning and H. Rossi, Analytic Functions of Several Complex Variables (Prentice Hall, Englewood Cliffs, N. J., 1965), p. 15

[c7] J. C. Polkinghorne, Nuovo Cimento 7A, 555 (1971)

[c8] J. Bros and D. Iagolnitzer, Saclay Report No. DPh-T/71-33, 1971 (unpublished)

[c9] C. Chandler and H. P. Stapp, J. Math. Phys. 10, 826 (1969) C. Chandler, Helv. Phys. Acta 42, 759 (1969)

[c10] D. Iagolnitzer and H. P. Stapp, Commun. Math. Phys. 14, 15 (1969)

[c11] H. P. Stapp, J. Math. Phys. 9, 1548 (1968)

[c12] J. Coster and H. P. Stapp, J. Math. Phys. 11, 2743 (1970)

[c13] [4]

[c14] H. Lehmann, K. Symanzik, and W. Zimmermann, Nuovo Cimento 6, 319 (1957)

[c15] H. J. Bremermann, thesis, Schrift. Math. Inst., University of Munster, No. 5, 1951 (unpublished) J. Bros, H. Epstein, and V. Glaser, Nuovo Cimento 31, 1265 (1964), p. 1289

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A Basic Discontinuity Equation

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