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101 Theoretical High Energy Physics COO - 2271 - 101 THEORETICAL HIGH ENERGY PHYSICS Progress Report for the Period May 1, 1977-April 30, 1978 This report was prepared as an account of work sponsored by the United States Government. Neither the United States nor the United States Department of Energy, nor any of their employees, nor any of their contractors, subcontractors, or their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness or usefulness of any information, apparatus, product or process disclosed, or represents that its use would not infringe privately owned rights. Principal Investigator: T. D. Lee Department of Physics Columbia University New York/ N. Y. 10027 ,. <We .s no ob|*cffon from me potswr .ooJwr of view to the pubuco^o* or ditKttfMMtlon of the document) . BROOKHAVEN PATENT GROUP June 1978 -^/^-^7£ By C&Z Prepared for The U. S. Department of Energy under Contract EY-76-C-02-2271. DISTRIBUTION OF THIS DOCUMENT IS UNT.TWT*?ft DISCLAIMER This report was prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Government nor any agency Thereof, nor any of their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government or any agency thereof. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof. DISCLAIMER Portions of this document may be illegible in electronic image products. Images are produced from the best available original document. ' ' Notice : = - -- - ,- " i' ■* -—~ This report was prepared as* an account of work sponsored by the United States Government. Neither the United States nor the United States Department of Energy, nor any of their employees, nor any of their .contractors^ subcontractor or their employees, makes any warranty, express or implied, or assumes any lega liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product or process disclosed or represents that its use would not infringe privately owned rights. PUBLICATION LIST EY-76-C-02-2271 1. C. Bernard and E. J. Weinberg, "Interpretation of Pseudoparticles in Physical Gauges", Physical Review DJ_5, 3655 (1977). 2. C. Bernard, N. H. Christ, A. Guth and E. J. Weinberg, " Pseudoparticle Parameters for Arbitrary Gauge Groups", Physical Review D]6, 2967 (1977). 3. C. Bernard, A. Guth and E. J. Weinberg, "Note on the Atiyah-Singer Index Theorem", Physical Review D17, 1053 (1978). 4. C. Bernard, "Instanton Interactions at the One-Loop Level", to be published in -Physical Review D. 5. N. H. Christ, N. Stanton and E. J. Weinberg, "General Self-Dual Yang-Mills Solutions", submitted to Physical Review D. 6. B. Coffey and R. Friedberg, "Effect of Short-Range Coulomb Interaction on Cooperative Spontaneous Emission", Physical Review A17, 1033 (1978). 7. S. Cummins, "Confinement in Three Dimensions", to be published in Physical Review D. 8. A. Duncan, "Explicit Dimensional Renormalization of Quantum Field Theory in Curved Space-Time", Physical Review D^, 964 (1978). 9. A. Duncan, "Instanton Effects in Bound-State Dynamics", to be published in Physical Review D. 10. G. Feinberg, "Parity Nonconservation in Atoms", to be published in the Proceedings of the Ben Lee Memorial International Conference on Parity Nonconservation, Weak Neutral Currents and Gauge Theories, held at Fermilab in October 1977. 11. G. Feinberg, "Handedness of Atoms and Parity Nonconservation", Nature 271, 509 (1978). 12. G. Feinberg, "Lorentz Invariance of Tachyon Theories, Physical Review D17, 1651 (1978). 13. G. Feinberg, " Parity-Violating Electromagnetic Interactions of Nuclei", Transactions of the New York Academy of Sciences 38, 26 (1977). 14. G. Feinberg, M. Goldhaber and G. Steigman, "Multiplicative Baryon Conservation and the Oscillation of Hydrogen into Antihydrogen", to be published in Physical Review A. 2. 15. G. Feinberg, J. Hiller and J. Sucher, "New Techniques for Evaluating Parity Conserving and Parity Violating Contact Interactions", submitted to Physical Review A. 16. J. Finkelstein, "A Sum Rule for Kaon-Nucleon Scattering", to be published In Physical Review D. 17. J. Finkelstein, G. Chew, J.-P. Sursock and G. Weissman, "Ordered Hadron , S Matrix", submitted to Nuclear Physics. 18. R. Friedberg and T. D. Lee, "Fermion-Field Nontopological Solitons II. Models for Hadrons", Physical Review D16, 1016 (1977). 19. R. Friedberg and T. D. Lee, "QCD Corrections in a Soliton Model of Hadrons", to be published in Physical Review D. 20. Fl'Krausz, "Cancellations of Mass Singularities in Yang-Mills Theories", Nuclear Physics B]26, 340 (1977). 21. T. D. Lee, "Nontopological Solitons", in Proceedings of the Symposium on Frontier Problems in High Energy Physics, edited by L. Foa and L. A. Radicati, Scuola Normale Superiore, Pisa, 1976, p. 47. 22. T. D. Lee, "Nontopological Solitons and Applications to Hadrons", Comments on Nuclear and Particle Physics 7, 165 (1978). 23. T. D. Lee, "Solitons and Hadrons", in Problemes Theoriques Lie's Aux Nouvelles Particules, Centre National de la Recherche Scientifique, Montpellier, 1977, p. 413. 24. -T. D. Lee, "Recent Results on Nontopological Soliton Solutions", to be published in Science of Matter (Festschrift in honor of T. Y. Wu). 25. T. D. Lee, "Nontopological Solitons and Applications to Hadrons", to be published in the issue of Physica Scripta devoted to the Chalmers Symposium on Solitons, Gbteborg, Sweden, 1978. 26. E. Mottola, "Fermion Green's Functions in the Presence of Pseudoparticles", Physical Review D]7, 1103 (1978). 27. A. H. Mueller, "Lectures on Hadron-Nucleus Collisions at High Energies", in Many Degrees of Freedom in Particle Theory, edited by H. Satz (Proceedings of the 1976 International Summer Institute of Theoretical Physics held at the University of Bielefeld) (New York, Plenum Press, 1978), p. 417. 28. A. H. Mueller, "Classical Euclidean Field Configurations and Charge Confinement", Physical Review D17, 1605 (1978). 3. 29. S. Sheth, "Effective Potential between Hard Spheres with an Attractive Tail", to be submitted to Physical Review. 30. A. Sinha, "Lorentz Transformations for Gauge Theory Monopole Solutions", Physical Review D]6, 1828 (1977). Dissertations A. S. Blaer, "Renormalization and the Elimination of Overlapping Divergences", 1977 A. Sinha, "On Gauge Theory Monopole Solutions", 1978. \ EY-76-C-02-2271 Percentages of Time Devoted to Project by Investigators November 1, 1977- October 31, 1978 Name % of Time Period Professors N. H. Christ 100 3 summer months -16 9 academic months G. Feinberg 100 3 summer months H. M. Foley 100 1^ summer months R. Friedberg 100 2 summer months T. D. Lee 100 3 summer months A. H. Mueller 100 3 summer months -15 9 academic months G. C. Wick 100 3 summer months Assistant Professors J. Finkelstein 100 3 summer months 50 9 academic months N. Stanton 100 1 summer month ' E. J. Weinberg 100 2\ summer months 50 9 academic months Research Associates C. Bernard 100 10 months S. Dimopoulos 100 2 months A. Duncan 100 12 months Note: During the academic year, the average teaching load for our faculty members is one course. A considerable amount of research (in addition to that specified above) Is performed by the several Investigators during those nine months. Progress Report Dr. Claude Bernard During the past year, Dr. Bernard has worked mainly on various aspects of "instanton" solutions to Yang-Mills field theory. In the summer and fall, he com• pleted work with Norman Christ, Alan Guth and Erick Weinberg which applied the mathematical tool of Atiyah-Singer index theory to the problem of counting the number of such solutions for arbitrary topological charge and gauge group. Most of their results appeared in Physical Review D16, 2967 (1977); a calculation of the Atiyah-Singer index for the case of interest will be published shortly in Physical Review D. More recently, Dr. Bernard has been studying the relation between exact multi-instanton solutions and linear superposition of single instantons in singular gauge. He has been able to establish a precise connection—keeping terms up to a fairly high order in the ratio of instanton size to separation—between the topological charge two exact solution (which is completely known) and the superposition of two instantons with arbitrary position, scale and orientation. Aside from elucidating the properties of the exact solution, this connection provides a parameterization of the exact solution which proves useful in discussing the lowest order quantum corrections. He expects to complete this work in the near future. Progress Report Professor Norman H. Christ During the past year Professor Christ's research has concentrated on the mathe• matical properties and physical applications of non-abelian gauge theories. In col• laboration with Claude Bernard, Alan Guth and Erick Weinberg, he produced an ex• haustive analysis of the number of parameters entering classical, self-dual, Yang-Mills solutions for all the compact, simple Lie groups. In all cases
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