Infrared singularities, vacuum structure and pure phases in local quantum field theory
Morchio, G. ; Strocchi, F.
Annales de l'I.H.P. Physique théorique, Tome 33 (1980), p. 251-282 / Harvested from Numdam
Publié le : 1980-01-01
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     author = {Morchio, G. and Strocchi, F.},
     title = {Infrared singularities, vacuum structure and pure phases in local quantum field theory},
     journal = {Annales de l'I.H.P. Physique th\'eorique},
     volume = {33},
     year = {1980},
     pages = {251-282},
     mrnumber = {601840},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPA_1980__33_3_251_0}
}
Morchio, G.; Strocchi, F. Infrared singularities, vacuum structure and pure phases in local quantum field theory. Annales de l'I.H.P. Physique théorique, Tome 33 (1980) pp. 251-282. http://gdmltest.u-ga.fr/item/AIHPA_1980__33_3_251_0/

[1] J. Schwinger, Quantum Electrodynamics. Dover.

[2] L.D. Landau, Niels Bohr and the Development of Physics. Mc Graw-Hill, New York, 1955. | MR 75092

G. Kallen, Consistency problems in Quantum Electrodynamics. Cern Rep. 57-43 and article in Handuch der Physik.

H. Lehman, K. Symanzik and W. Zimmermann, Nuovo Cimento, t. 1, 1955, p. 1425; t. 2, 1955, p. 425 ; t. 6, 1957, p. 319.

[3] A.S. Wightman, Les Problèmes Mathématiques de la Théorie Quantique des Champs, C. N. R. S., Paris, 1959. Phys. Rev., t. 101, 1956, p. 860.

[4] See S. Weinberg, Rev. Mod. Phys., t. 46, 1974, p. 255.

[5] K. Wilson, Phys. Rev., t. D 10, 1974, p. 2445.

A.M. Polyakov, Phys. Letters, t. 59 B, 1975, p. 82.

A.A. Belavin Et Al., Phys. Letters, t. 59 B, 1975, p. 85.

G. 'T Hooft, Phys. Rev. Letters, t. 37, 1976, p. 8.

R. Jackiw and C. Rebbi, Ibid., t. 37, 1976, p. 172.

C. Callan, R. Dashen and D. Gross, Phys. Letters, t. 63 B, 1976, p. 334.

[6] K. Osterwalder and E. Seiler, Ann. Phys. N. Y., t. 110, 1978, p. 440. D. Bridge, J. Fröhlich and T. Spencer, I. H. E. S., preprints, 1979. | MR 459367

[7] See J. Fröhlich, G. Morchio and F. Strocchi, Ann. Phys. N. Y.

[8] F. Strocchi, Gauss' law in local QFT, Invited talk at the International Symposium on Elementary Particle Physics. Reinhardsbrunn, October 1978.

F. Strocchi, Phys. Rev., t. D 17, 1978. p. 2010. | MR 523177

[9] R. Ferrari, F.E. Picasso and F. Strocchi, Commun. Math. Phys., t. 35, 1974, p.25 ; Nuovo Cimento, t. 39 A, 1977, p. 1. | MR 332032

[10] F. Strocchi, Phys. Letters, t. 62 B, 1976, p. 60; Phys. Rev., t. D 17, 1978, p. 2010.

[11] R.F. Streater and A.S. Wightman, PCT Spin and Statistics and All That. Benjamin, 1964. | MR 161603 | Zbl 0135.44305

[13] R. Haag and D. Kastler, Journ. Math. Phys., t. 5, 1964, p. 848. | Zbl 0139.46003

H. Araki, in Local Quantum Field Theory. Varenna School, 1968, R. Jost, ed.

[14] N.N. Bogolubov and D.W. Shirkov, Introduction to the Theory of Quantized Fields. Interscience, New York, 1959. | MR 110471 | Zbl 0088.21701

H. Epstein and V. Glaser, in Les Houches Lectures, 1970, Statistical Mechanics and Quantum Field Theory. C. De Witt and R. Stora eds., Gordon and Breach, New York, 1971.

K. Hepp, Ibid.

[15] E. Sheibe, unpublished notes Oct. 1960. I am grateful to Prof. H. Reeh for giving me a copy of these notes.

[16] H.-J. Borchers, Algebraic Aspects of Wightman's field theory, in Statistical Mechanics and Field Theory. Haifa Summer School, R. N. Sen and C. Weil eds., New York, 1972. | Zbl 0264.46061

[18] The analysis of S. Doplicher. R. Haag and J. Roberts, Commun. Math. Phys., t. 23. 1971, p. 199: t. 28. 1972, p. 331, is therefore not applicable in this case. | MR 297259

[19] These results were discussed with J. Yngvason, Reports on Math. Physics, t. 12, 1977. p. 57, Proposition 2, and at the Aspen Workshop on Quantum Electrodynamics, Aspen, June 7-27, 1976 (F. Strocchi, Phys. Rev., t. D 17, 1978, p. 2010).

[20] See J. Yngvason, Commun. Math. Phys., t. 34, 1973, p. 315. | Zbl 0269.46031

[22] For mathematical properties of these operators see L. Bracci, G. Morchio and F. Strocchi, Commun. Math. Phys., t. 41, 1975, p. 289.

[24] J. Bognàr, Indefinite Inner Product Spaces. Springer Verlag, 1974. | MR 467261 | Zbl 0286.46028

[25] G. Morchio and F. Strocchi, paper on the Schwinger model, in preparation.

[26] G. Krein, Second Mathematical Summer School, Part I. Naukova Dumka Kiev, 1965, translated in A. M. S. Transl., t. 93, 2, 1970, p. 103, and references therein.

[27] H. Araki, K. Hepp and D. Ruelle, Helv. Phys. Acta, t. 35, 1962, p. 164. | MR 141407 | Zbl 0161.23503

[33] N. Dunford and J.T. Schwartz, Linear Operators, Part I. Interscience, New York, 1958, Chap. VII. | MR 117523 | Zbl 0084.10402

[34] M.A. Naimark, Soviet Mat., t. IV, 1, 1963, p. 543.

[35] J.H. Lowenstein and J.A. Swieca, Ann. Phys. N. Y., t. 68, 1971, p. 172. | MR 307637

S. Coleman, R. Jackiw and L. Susskind, Ann. Phys. N. Y., t. 93, 1975, p. 267.

[36] D. Zwanzinger, Phys. Rev., t. D 17, 1978, p. 457.

[37] A.S. Wightman and L. Garding, Arkiu for Fysik, t. 28, 1964, p. 129, p. 153-156. | Zbl 0138.45401