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Bilinear quantum field theories and their coherent states
1.Y. Takahashi and H. Umezawa, Prog. Theor. Phys. 9, 14 (1953);
1.Y. Takahashi and H. Umezawa, Nucl. Phys. 51, 193 (1964).
1.However, we especially recommend the monograph, Y. Takahashi, An Introduction to Field Quantization (Pergamon, London, 1969) which is much more complete.
2.C. L. Hammer and R. H. Tucker, J. Math. Phys. 12, 1327 (1971).
3.H. Reeh, Fortsch. Phys. 16, 687 (1968).
4.D. Kastler, D. W. Robinson, and J. A. Swieca, Commun. Math. Phys. 2, 108 (1966).
5.J. R. Klauder, J. Math. Phys. 11, 609 (1970).
6.J. R. Klauder, Commun. Math. Phys. 18, 307 (1970).
7.J. R. Klauder, Acta. Phys. Austriaca Suppl. 8, 227 (1971).
8.J. R. Klauder, “Heisenberg Equations of Motion,” Proc. Sym. Basic Question Elem. Part. Phys., Münich, June 8–18, (1971).
9.J. R. Klauder, in Lectures in Theoretical Physics, Mathematical Methods in Theoretical Physics, Vol. XIV. B. edited by W. Brittin (Colorado Associated Universities Press, Boulder, 1973), pp. 329–421.
10.J. R. Klauder, Ann. Phys. (NY) 79, 111 (1973).
11.R. H. Tucker and C. L. Hammer, Phys. Rev. D 3, 2448 (1971).
12.C. N. Yang and D. Feldman, Phys. Rev. 79, 972 (1950).
13.S. S. Schweber, An Introduction to Relativistic Field Theory, (Harper and Row, New York, 1961), See esp. Eq. (3.64), p. 211.
14.G. N. Fleming, Phys. Rev. 137, B188 (1965).
15.A. Sankaranarayanan and R. H. Good, Jr., Phys. Rev. 140, B509 (1965).
16.Ref. 9. See esp. pp. 350, 351.
17.J. Rzewuski, Field Theory, Vol. 2 (Iliffe Books, London, and PWN Polish Scientific Publishers, Warsaw, 1969). See esp. pp. 252–55. We thank Dr. Klauder for pointing this out.
18.Ref. 13. See esp. p. 250.
19.J. R. Klauder, J. Math. Phys. 4, 1055 (1963).
20.J. R. Klauder, J. McKenna, and D. G. Currie, J. Math. Phys. 6, 734 (1965).
21.B. Simon, The Euclidean (Quantum) Field Theory (Princeton U.P., Princeton, New Jersey, 1974). See esp. pp. 348–57.
22.R. J. Glauber, Phys. Rev. 131, 2766 (1963).
23.M. Reed and B. Simon, Methods of Modern Mathematical Physics, Vol. 1. Functional Analysis (Academic, New York, 1972). See esp. the discussion on pp. 249–317 for the best introductory discussion available on unbounded operators, essential self‐adjointness, and quadratic forms.
24.T. Kato, Trans. Am. Math. Soc. 70, 195 (1951).
25.W. Faris and R. B. Lavine, Commun. Math. Phys. 35, 39 (1974).
26.F. E. Schroeck, Jr., “Cores for Operators in Quantum Mechanics,” J. Math. Phys. (accepted for publication).
27.G. Goldin, J. Math. Phys. 12, 462 (1971).
28.L. Gross, Commun. Pure Appl. Math. 19, 1 (1966).
29.I. M. Gel’Fand and N. Ya. Vilenkin, Generalized Functions, Vol. 4, Applications of Harmonic Analysis (Translated by Amiel Feinstein) (Academic, New York, 1964). See esp. pp. 103 et seq.
30.For an infinite particle number operator the quantity z in Eq. (4.43) is reminescent of an infinite field strength renormalization constant. In this case, Eq. (4.53) gives a renormalized matrix element and for more general c‐number functions φ̂, only the most singular terms survive.
31.G. C. Hegerfeldt and J. R. Klauder, Nuovo Cimento A 10, 723 (1972).
32.See esp. p. 317 of Ref. 6.
33.R. F. Dashen, B. Hasslacher, and A. Neveu, Phys. Rev. D 10, 4114, 4130and 4138(1974);
33.and Princeton Institute for Advanced Study Preprint (to be published). These authors and other workers on quark confinement have studied the quantization of nonlinear classical systems in two‐dimensional space‐time.
34.H. Umezawa, in Renormalization and Invariance in Quantum Theory, edited by E. R. Caianiello (Plenum, New York, 1974).
35.L. Leplae, H. Umezawa, and F. Mancini, Phys. Rep. 10C, 152 (1974).
36.H. Matsumoto, N. J. Papastamatiou, and H. Umezawa, Infrared Effect of the Goldstone Boson and the Order Parameter (University of Wisconsin‐Milwaukee Preprint UWM‐4867‐75‐5, May 1975).
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