By J. Alfaro, L. F. Urrutia, J. D. Vergara (auth.), Claudio Teitelboim, Jorge Zanelli (eds.)

ISBN-10: 1461280877

ISBN-13: 9781461280873

ISBN-10: 146130797X

ISBN-13: 9781461307976

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More 21 String Phenomenology surprisingly the ratio of SU2 and SU3 "fine structure constants" is always a rational number. This can happen in Kaluza-Klein theory [13], but as far as I know, it is not guaranteed. Note also that the possibility of a color singlet hypercharge 1/6 particle is not ruled out at this point. In GUT containing SUeS), such a particle is not allowed. It may be that world sheet locality provides the same constraint in string theory, though we know too little of the structure of quark and lepton vertex operators to prove this.

We find that as the lattice spacing tends to zero Uf = e 2iJLQ [ 1 - ~ (H Â± P) + D(a provided the weights band c behave for a b = e iJL [1 --i> 2) ] 0 as [16] + D(a 2 )] a->O C i . (24) 2 = -- e'JL moa [1 + D(a )] a->O 2 (23) H. J. de Vega 50 where f-t and rno are fixed parameters. We find for Hand P those of the massive Thirring model (MTM). P=-i H= f dXI/I+axl/l g 2J f dx [ -il/l + Y axl/l+rnol/ll/l+"2(l/Iy/-,l/I) S (25) with g = -2cotan(f-t - f-to), Equation (25) gives the bare operators and equation (24) defines the bare scaling limit.

Friedan, A. Kent, S. Shenker, and E. Witten, unpublished; A. Sen, Nuc/. Phys. B 278, 289 (1986); L. Dixon, D. Friedan, E. Martinec, and S. Shenker, Nuc/. Phys. B 282,13 (1987). 9. T. Banks, L. Dixon, D. Friedan, and E. Martinec, SLAC-Pub-4377 (1987), Nuc/. Phys. B (in press); T. Banks and L. Dixon, SCIPP Preprint 88/05 (1988). 10. V. Kaplunovsky, Phys. Rev. Lett. 55, 1033 (1985); M. Dine and N. Seiberg, Phys. Rev. Lett. 55, 366 (1985). 1l. D. Friedan and S. Shenker, unpublished. 12. H. Georgi, H.

### Quantum Mechanics of Fundamental Systems 2 by J. Alfaro, L. F. Urrutia, J. D. Vergara (auth.), Claudio Teitelboim, Jorge Zanelli (eds.)

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