- Access by Xinjiang University
An introduction to the theory of dual models and strings
Rev. Mod. Phys. 47, 123 – Published 1 January, 1975
DOI: https://doi.org/10.1103/RevModPhys.47.123
Abstract
The theory of a free string is first presented classically and quantum mechanically both in a covariant and a nonexplicitly covariant treatment. Then the concepts and techniques obtained from the free string are used to build the operator formalism of dual models. Both the conventional Veneziano model and the Neveu-Schwarz-Ramond model are presented. The self-consistency of these models at the tree and loop levels is investigated, and the interpretation of the results obtained is given in terms of the string picture.
References (131)
- Alessandrini, V., D. Amati, M. Le Bellac and D. Olive, 1971, Phys. Report, Vol. 1C, No. 6
- Alessandrini, D. Amati and B. Morel, 1972, Nuovo Cimento, 7A, 797
- Amati, D., C. Bouchiat and J. L. Gervais, 1969, Nuovo Cimento Letters, 2, 399
- Bardakci, K., 1974, Nucl. Phys. B68, 331
- Bardakci, and M. B. Halpern, 1971, Phys. Rev. D3, 2493
- Bardakci and H. Ruegg, 1968, Phys. Letters 28B, 342
- Bardakci and H. Ruegg, 1969, Phys. Rev. 182, 1884
- Bardakci and S. Mandelstam, 1969 Phys. Rev. 184, 1640
- BardakciS. MandelstamBateman Manuscript project, Edited by A. Erdelyi, 1955, Vol. 1 (McGraw-Hill Book Co., Inc.)
- Berezin, F. A., 1966, The Method of Second Quantization (Academic, New York, London)
- Bogoliubov, N. and Shirkov, 1953, Introduction to the Theory of Quantized Fields (Interscience Publishers, London)
- Brink, L. and D. Olive, 1973a, Nucl. Phys. B56, 256
- Brink, L. and D. Olive, 1973b, CERN preprint TH 1620
- Brink, L., D. Olive and J. Scherk, 1973, Nucl. Phys. B61, 173
- Brink, L., D. Olive, C. Rebbi and J. Scherk, 1973, Phys. Letters 45B, 379
- Brower, R. C., 1972, Phys. Rev. D6, 1655
- Brower, and C. B. Thorn, 1971, Nucl. Phys. B31, 163
- Brower, R. C. and K. A. Friedman, 1973, Phys. Rev. D7, 535
- Caneschi, L., A. Schwimmer and G. Veneziano, 1969, Phys. Letters 30B, 351
- Case, K. M., 1956, Phys. Rev. 97, 810
- Casher, A. and L. Susskind, 1971, Phys. Letters 35B, 512
- Chan, H. M. 1968, Phys. Lett. 28B, 425
- Chang, L. N. and J. Mansouri, 1972, Phys. Rev. 5D, 2535
- Chew, G. F., 1962, "-Matrix Theory of Strong Interactions," (Benjamin, New York)
- Chodos, A. and C. B. Thorn, 1974, Nucl. Phys. B72, 509
- Clavelli, E. and J. A. Shapiro, 1973, Nucl. Phys. B57, 490
- Cornwall, J. M., D. N. Levin and G. Tiktopoulos, 1973, Phys. Rev. Letts. 30, 1268
- Corrigan, E. F., 1974, Nucl. Phys. B69, 325
- Corrigan, E. F., and P. Goddard, 1974, Nucl. Phys. B68, 189
- Corrigan, E. F., and P. Goddard, 1973, Nuovo Cimento 18A, 339
- Corrigan, E. F., P. Goddard, D. I. Olive and R. A. Smith, 1973, Nucl. Phys. B67, 477
- Corrigan, E. F., and D. I. Olive, 1972, Nuovo Cimento, Vol. 11, A.N. 3, 749
- Cremmer, E. and J. Scherk, 1972, Nucl. Phys. B50, 222
- Cremmer, E. and J. Scherk, 1974, Nucl. Phys. B72, 117
- De Tar, C. E., K. Kang, Chung-I-Tan, and J. H. Weis, 1971, Phys. Rev. D4, 425
- Dirac, P. A. M., 1950, Can. J. Phys. 2, 129
- Dirac, 1958, Proc. Roy. Soc. (London) A246, 326
- Di Vecchia, P., E. Del Giudice and S. Fubini, 1972, Ann. Phys. 70, 378
- Fadeev, L. D., 1969, Theor. Mat. Fiz. 1, 3 [Theor. and Math. Phys. 1, 1, 1970]
- Fadeev and V. N. Popov, 1967, Phys. Letters 25B, 29
- Fairlie, D. B. and D. Martin, 1973, Nuovo Cimento 18A; 373
- Feynman, R. P., 1972, "Magic Without Magic" edited by J. Klauder (W. H. Freeman, San Francisco), p. 355
- Frampton, P. H., P. Goddard and D. H. Wray, 1971, Nuovo Cimento 3A, 755
- Frautschi, S., 1971, Phys. Rev. D3, 282
- Fritzsch, H., M. Gell-Mann and H. Leutwyler, 1973, Phys. Letters 47B, 4, 365
- Frye, G. and L. Susskind, 1970, Phys. Letters 31B, 537
- Fubini, S., D. Gordon and G. Veneziano, 1969, Phys. Letters 29B, 679
- Fubini, S. and G. Veneziano, 1969, Nuovo Cimento 64A, 811
- Fubini, S. and G. Veneziano, 1970, Nuovo Cimento 67A, 29
- Gato, T., 1971, Progr. Theor. Phys. 46, 1560
- Gell-Mann, M., 1964, Phys. Letters, 8, 214
- Gervais, J. L. and A. Neveu, 1972, Nucl. Phys. B46, 381
- Gervais and B. Sakita, 1971, Phys. Rev. D4, 2291
- Gervais and B. Sakita, 1971, Nucl. Phys. B34, 477
- Gervais and B. Sakita, 1973, Phys. Rev. Letters, 30, 716
- Goddard, P., 1971, Nuovo Cimento 4A, 343
- Goddard, P., J. Goldstone, C. Rebbi and C. B. Thorn, 1973, Nucl. Phys. B56, 109
- Goddard, P., C. Rebbi and C. B. Thorn, 1972, Nuovo Cimento 12, 425
- Goddard, P., and C. B. Thorn, 1972, Phys. Letters 40B, 2, 235
- Goddard, P., and R. E. Waltz, 1971, Nucl. Phys. B34, 99
- Goebel, C. G. and B. Sakita, 1969, Phys. Rev. Letters 22, 259
- Gross, D. J., A. Neveu, J. Scherk and J. H. Schwarz, 1970a, Phys. Letters, 31B, 9, 592
- Gross, D. J., A. Neveu, J. Scherk and J. H. Schwarz, 1970b, Phys. Rev. D2, 692
- Gross, D. J. and J. H. Schwarz, 1970, Nucl. Phys. B23, 333
- Green, M. B., 1973, Phys. Letters 46B, 392
- Grisaru, M. T., H. J. Schnitzer and H. S. Tsao, 1973, Phys. Rev. Lett. 30, 811
- Hagedorn, R. 1968, Nuovo Cimento 56A, 1027
- Hara, O., 1971, Progr. Theor. Phys. 46, 1549
- Harari, H., 1969, Phys. Rev. Letters, 562
- Hardy, G. H. and S. Ramanujan, 1917, Proc. Roy. Math. Soc. 17, 75
- Hopkinson, J. F. L. and R. W. Tucker, 1974 Phys. Rev. D10, 558
- Hsue, C. S., B. Sakita and M. A. Virasoro, 1970, Phys. Rev. D, 2, 2587
- Iwasaki, Y. and K. Kikkawa, 1973, Phys. Rev. D, 8, 440
- Jacob, M., 1970, Brandeis Summer Institute, edited by S. Deser, M. Grisaru and M. Pendleton (MIT press,) Vol. I
- Kaku, M. and K. Kikkawa, 1974, Phys. Rev. D10, 1110
- Kalb, M. and P. Ramond, 1974, Phys. Rev. D9, 2273
- Kikkawa, K., S. Klein, B. Sakita and M. A. Virasoro, 1970, Phys. Rev. D1, 3258
- Kikkawa, K., B. Sakita and M. A. Virasoro, 1969, Phys. Rev. 184, 1701
- Lovelace, C., 1968, Phys. Letters, 28B, 265
- Lovelace, C., 1971, Phys. Letters, 34B, 500
- Mandelstam, S., 1973a, Nucl. Phys. B64, 205
- Mandelstam, S., 1973b, Phys. Letters 46B, 447
- Mandelstam, S., 1974, Nucl. Phys. B69, 77
- Mansouri, J. and Y. Nambu, 1972, Phys. Letters 38B, 375
- Minami, M., 1972, Progr. Theor. Phys. 48, 1308
- Montonen, C., 1973, D.A.M.T.P. preprint (Cambridge)
- Nakanishi, N., 1971, Progr. Phys. 45, 436
- Nakanishi, N., 1972, Progr. Theor. Phys. 48, 355
- Nambu, Y., 1969, Proc. Intl. Conf. on Symmetries and Quark Models, (Wayne State University)
- Nambu, Y., 1970, Lectures at the Copenhagen Symposium
- Neveu, A. and J. Scherk, 1970, Phys. Rev. D, 1, 2355
- Neveu, A. and J. Scherk, 1972a, Nucl. Phys. B36, 155
- Neveu, A. and J. Scherk, 1972b, Nucl. Phys. B36, 317
- Neveu, A., and J. H. Schwarz, 1971a, Nucl. Phys. B31, 86
- Neveu, A., and J. H. Schwarz, 1971b, Phys. Rev. D4, 1109
- Neveu, A., J. H. Schwarz and C. B. Thorn, 1971, Phys. Letters 35B, 529
- Nielsen, H., 1970, 15th Conf. on High Energy Physics, Kiev Conference
- Nielsen, H., and P. Olesen, 1973, Nucl. Phys. B57, 367
- Olive, D. and J. Scherk, 1973a, Phys. Lettl 44B, 296
- Olive, D., and J. Scherk, 1973b, Nucl. Phys. B64, 335
- Paton, J. E. and Chan Hong-Mo, 1969, Nucl. Phys. B10, 519
- Ramond, P., 1971, Phys. Rev. D3, 2415
- Ramond, P., 1974, Yale Univ. preprint 3075-56
- Ramond, P., 1974, Yale Univ. Preprint, 3075-63
- Rebbi, C., 1974, Phys. Reports, 12C, No. 1
- Rosner, J. L., 1969, Phys. Rev. Lett. 22, 689
- Sakita, B. and M. A. Virasoro, 1970, Phys. Rev. Letters 24, 1146
- Scherk, J., 1971, Nucl. Phys. B31, 222
- Schnitzer, H. J., 1973, Brandeis Univ. preprint
- Schwarz, J. H., 1971, Phys. Lett. 37B, 315
- Schwarz, J. H., 1972, Nucl. Phys. B46, 61
- Schwarz, J. H., 1973, Physics Reports, 8C, No. 4
- Schwarz, J. H., 1974, Nucl. Phys. B68, 221
- Schwarz, J. H., and C. C. Wu, 1973, Phys. Letters 47B, 453
- Schwarz, J. H., and C. C. Wu, 1974, Nucl. Phys. B73, 77
- Sciuto, S., 1969, Nuovo Cimento Letters 2, 411
- Shapiro, J. A., 1969, Phys. Rev. 179, 1345
- Shapiro, J. A., 1970, Phys. Letters 338, 361
- Shapiro, J. A., 1971, Phys. Rev. D4, 1249
- Susskind, L., 1970, Nuovo Cimento 69, 457
- 't Hooft, G., 1973, CERN preprint TH 1786
- 't Hooft, G., and M. Veltman, 1973, Diagrammar CERN 73-9
- Thorn, C. B., 1971, Phys. Rev. D4, 1112
- Veneziano, G., 1968, Nuovo Cimento 57A, 190
- Veneziano, 1969, Phys. Letters 30B, 351
- Veneziano, G., 1974, Phys. Reports 9C, No. 1
- Virasoro, M. A., 1969, Phys. Rev. 177, 2309
- Virasoro, M. A., 1970, Phys. Rev. D1, 2933
- Virasoro, M. A., 1971, Phys. Rev. D3, 2384
- Zumino, B., 1973, CERN preprint TH 1779
- Zweig, G., 1964, CERN preprint TH 402 (unpublished)