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On charges of massless particles
1.C. M. Bender and B. M. McCoy, Phys. Rev. 148, 1375 (1966).
2.S. Weinberg and E. Witten, Phys. Lett. B 96, 59 (1980).
3.See, e.g., (a) E. C. G. Sudarshan, Phys. Rev. D 24, 1591 (1981);
3.(b) T. Kugo and S. Uehara, Prog. Theor. Phys. 66, 1044 (1981);
3.(c) T. Kugo, Phys. Lett. B 109, 205 (1982);
3.(d) M. Flato, D. Sternheimer, and C. Fronsdal, Commun. Math. Phys. 90, 563 (1983).
3.The author is thankful to Dr. C. H. Woo and Dr. J. Sucher for drawing his attention to (a) and (d).
4.See, e.g., R. F. Streater and A. S. Wightman, PCT, Spin and Statistics, and All That (Benjamin, New York, 1964).
5.The notation used in (1.1) is rather symbolic; what one really understands by (1.1) is a sesquilinear form extended then to an operator for denotes any localized state. See, e.g.,
5.C. Orzalesi, Ref. Mod. Phys. 42, 381 (1970) and the literature quoted therein. Of course, we are assuming that the symmetry corresponding to is not spontaneously broken.
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8.The author is grateful to the unknown referee of this paper for calling to his attention the existence of such expressions.
9.Notice that for any p with and as therefore, in any frame of reference; if then
10.This assertion can be made easily plausible for each charge B whose commutator with a certain set of field ψ is linear in these fields viz.
10. linear in components of ψ Taking into account this assumption it follows from and where Ω and are the vacuum and one‐particle state corresponding to the field, respectively, that This, however implies Thus B commutes with all fields of the chosen set.
11.See, e.g., P. Moussa and R. Stora, Methods in Subnuclear Physics (Gordon and Breach, New York, 1968), Vol. 2. S. Weinberg, Lectures on Particles and Field Theory, Brandeis Summer Institute in Theoretical Physics, 1964 (Prentice‐Hall, Englewood Cliffs, NJ, 1965), Vol. 2.
12.The author is grateful to the unknown referee of this paper for his remark concerning the nonlocal character of currents of type (3.4).
13.This is the case in free field theory. In general, it is only known that the massless one‐particle states are in the domain of the closure of BN.
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17.See, e.g., I. and Z. Bialynicki‐Birula, Quantum Electrodynamics (Pergamon, Oxford, 1975).
18.F. A. E. Pirani, [Introduction to Gravitational Radiation Theory,] in lectures on General Relativity edited by A. Trautman, F.A.E. Pirani, and H. Bondi (Prentice-Hall, Englewood Cliffs, NJ, 1965), Vol. I;
18.C. W. Misner, K. S. Thorne, and J. A. Wheeler, Gravitation (Freeman, San Francisco, 1973),Chaps, 18 and 41;
18.P. Van Niewuenhuizen, Phys. Rep. 68, 189 (1981).
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