- Access by Xinjiang University
Arguments against Anomalous Dimensions
Phys. Rev. D 3, 2005 – Published 15 April, 1971
DOI: https://doi.org/10.1103/PhysRevD.3.2005
Abstract
Two-dimensional solvable field theories provide examples of anomalous dimensions and conserved dilatation current, while in four-dimensional calculations anomalous dimensions occur together with strongly broken dilatation invariance. We show that the situation in two dimensions arises from peculiar phase-space properties which do not generalize to four dimensions. It appears that two-dimensional physics is not a good "laboratory" for studying scale invariance: Even the free-field theory behaves anomalously. We argue that at the present time there is no theoretical or experimental evidence for the consistency of anomalous dimensions with conserved or weakly broken scale invariance in physically realistic models.
References (10)
- K. Wilson, Phys. Rev. 179, 1499 (1969) Phys. Rev. D 2, 1473 (1970) ibid.2, 1478 (1970)
- B. Schroer, the Conference on Special Topics in Quantum Field Theory, University of Missouri, St. Louis, Mo., 1970 (unpublished) Pittsburgh University Report No. NYO-3829-56, 1970 (unpublished) J. H. Lowenstein and B. Schroer, this issue, Phys. Rev. D 3, 1981 (1971)
- K. Wilson, Phys. Rev. D 2, 1478 (1970) S. Coleman and R. Jackiw, Ann. Phys. (N. Y.) (to be published) R. Jackiw, in Lectures in Theoretical Physics (Gordon and Breach, New York, to be published), Vol. XIII C. G. Callan, Jr., Phys. Rev. D 2, 1541 (1970) K. Symanzik, Commun. Math. Phys. 18, 227 (1970)
- J. S. Bell and R. Jackiw, Nuovo Cimento 60, 47 (1969) S. L. Adler, Phys. Rev. 177, 2426 (1969) R. Jackiw and K. Johnson, ibid. 182, 1459 (1969) S. L. Adler and D. G. Boulware, ibid. 184, 1740 (1968)
- K. Johnson, Nuovo Cimento 20, 773 (1961) B. Schroer, Fortschr. Physik 11, 1 (1963) C. R. Hagen, Nuovo Cimento 51B, 169 (1967)
- C. G. Callan, Jr., S. Coleman, and R. Jackiw, Ann. Phys. (N. Y.) 59, 42 (1970)
- ([3])
- E. D. Bloom et al., Phys. Rev. Letters 23, 930 (1969) Proceedings of the Fifteenth International Conference on High Energy Physics, Kiev, 1970 (Academy of Science, IUPAP, Moscow, 1971)
- [1] S. Ciccariello, R. Gatto, G. Sartori, and M. Tonin, Phys. Letters 30B, 546 (1969) G. Mack, Phys. Rev. Letters 25, 400 (1970) ICTP Report No. IC 70 95, 1970 (unpublished)
- R. Jackiw, Phys. Rev. D 3, 1351 (1971) G. Segrè, ibid. D 3, 1303 (1971)