Infrared singularities, vacuum structure and pure phases in local quantum field theory
Annales de l'institut Henri Poincaré. Section A, Physique Théorique, Volume 33 (1980) no. 3, pp. 251-282.
@article{AIHPA_1980__33_3_251_0,
     author = {Morchio, G. and Strocchi, F.},
     title = {Infrared singularities, vacuum structure and pure phases in local quantum field theory},
     journal = {Annales de l'institut Henri Poincar\'e. Section A, Physique Th\'eorique},
     pages = {251--282},
     publisher = {Gauthier-Villars},
     volume = {33},
     number = {3},
     year = {1980},
     mrnumber = {601840},
     language = {en},
     url = {http://archive.numdam.org/item/AIHPA_1980__33_3_251_0/}
}
TY  - JOUR
AU  - Morchio, G.
AU  - Strocchi, F.
TI  - Infrared singularities, vacuum structure and pure phases in local quantum field theory
JO  - Annales de l'institut Henri Poincaré. Section A, Physique Théorique
PY  - 1980
SP  - 251
EP  - 282
VL  - 33
IS  - 3
PB  - Gauthier-Villars
UR  - http://archive.numdam.org/item/AIHPA_1980__33_3_251_0/
LA  - en
ID  - AIHPA_1980__33_3_251_0
ER  - 
%0 Journal Article
%A Morchio, G.
%A Strocchi, F.
%T Infrared singularities, vacuum structure and pure phases in local quantum field theory
%J Annales de l'institut Henri Poincaré. Section A, Physique Théorique
%D 1980
%P 251-282
%V 33
%N 3
%I Gauthier-Villars
%U http://archive.numdam.org/item/AIHPA_1980__33_3_251_0/
%G en
%F 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'institut Henri Poincaré. Section A, Physique Théorique, Volume 33 (1980) no. 3, pp. 251-282. http://archive.numdam.org/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

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

[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

[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

[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 | Zbl

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

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 | Zbl

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

[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

[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

[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 | Zbl

[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 | Zbl

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

[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

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