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References
S. Weinberg:Phys. Rev.,18, 507 (1967).
SeeR. J. Oakes:Phys. Rev. Lett.,20, 513 (1968) and alsoS. P. de Alwis:Nuovo Cimento,51 A, 846 (1967);J. J. Sakurai:Phys. Rev. Lett.,19, 803 (1967); see also ref. (5,13).J. Das, V. S. Mathur andS. Okubo:Phys. Rev. Lett.,19, 470 (1967).H. T. Nieh:Phys. Rev.,163, 1769 (1967).
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J. Das, V. S. Mathur andS. Okubo:Phys. Rev. Lett.,19, 470 (1967).
J. Das, V. S. Mathur andS. Okubo:Phys. Rev. Lett.,19, 1067 (1967).
Our notations are as inJ. D. Bjorken andS. D. Drell:Relativistic Quantum Mechanics (New York, 1964).
We assume that once integrated Schwinger terms vanish.
Asymptotic means that the symmetry becomes exact in the limitq 2→∞,q being the momentum carried out by the currents. The generators of the algebra are not, of course, conserved charges. The possibility of obtaining an algebra of nonconserved charges that leaves the vacuum invariant has been discussed byH. Leutwyler (Bern preprint, May 1968).
Seee.g. S. Fubini, G. Segrè andJ. D. Walecka:Ann. of Phys.,39, 381 (1966).
S. L. Glashow, H. J. Schnitzer andS. Weinberg:Phys. Rev. Lett.,19, 139 (1967).
H. T. Nieh:Phys. Rev.,163, 1769 (1967).
K. Kawarabayashi andM. Suzuki:Phys. Rev. Lett.,16, 255 (1966).
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While this work was under completion we received a preprint byP. A. Cook andG. C. Joshi where the same result of eq. (30) is obtained. These authors, however, do not discuss the ambiguities underlying eq. (20).
We may observe that, even without making use of PCTC, eq. (27) is consistent with (20). In fact, using for ρ and B the experimental masses, we findf′=1.09f, which tends to confirm our scheme.
J. D. Bjorken:Phys. Rev.,148, 1467 (1966).
A. H. Rosenfeld et al.: UCRL 8030 January 1968.
R. F. Dashen andD. H. Sharp:Phys. Rev.,133, B 1585 (1964).
S. L. Adler:Phys. Rev.,139, B 1638 (1965).
This would be true in a field algebra model, seeT. D. Lee, S. Weinberg andB. Zumiko:Phys. Rev. Lett.,18, 1029 (1967).
L. Maiani:Phys. Lett. 26 B, 538 (1968).
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Work supported in part by the U.S. Office of Naval Research under contract Nonr.-1866(55) and by the U.S. Air Force under contract No. 49(638)-1380.
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Ademollo, M., Longhi, G. & Veneziano, G. Spectral-function sum rules for tensor currents. Nuovo Cimento A (1965-1970) 58, 540–546 (1968). https://doi.org/10.1007/BF02819155
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DOI: https://doi.org/10.1007/BF02819155