Abstract
A criterion is derived for the existence of a selfadjoint and semibounded momentum operator in a non-Fock representation of the free photon field given by a coherent state. The representation of the translation group is constructed and it is shown that the rotation group, hence the homogeneous Lorentz group, cannot be unitarily implemented in the so-called infrared sectors.
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References
Jauch, J. M., Rohrlich, F.: Helv. Phys. Acta27, 613 (1954).
Glauber, R.: Phys. Rev.130, 2529 (1963);131, 2766 (1963).
Klauder, J. R., Sudarshan, E. C. G.: Fundamenatls of quantum optics. New York: Benjamin 1968.
Chung, V.: Phys. Rev.140, B 1110, (1965).
Greco, M., Rossi, G.: Nuovo Cimento50 A, 168 (1967).
Storrow, J. K.: Nuovo Cimento54 A, 15 (1968).
Kibble, T. W. B.: Phys. Rev.173, 1527;174, 1882;175, 1624 (1968).
Glauber, R. J.: Phys. Rev.84, 395 (1951).
Kibble, T. W. B.: J. Math. Phys.9, 315 (1968).
Bloch, F., Nordsieck, A.: Phys. Rev.52, 54 (1937).
Pauli, W., Fierz, M.: Nuovo Cimento15, 167 (1938).
Blanchard, Ph.: Commun. Math. Phys.15, 156 (1969).
Klauder, J. K., McKenna, J., Woods, E. J.: J. Math. Phys.7, 882 (1966).
—— J. Math. Phys.11, 609 (1970).
Streater, R. F.: Lectures at the Varenna Summer School 1968.
Roberts, J. E., Roepstorff, G.: Commun. Math. Phys.11, 321 (1969).
Segal, I. E.: Mat. Fys. Medd. Danske Vid. Selsk.31, no. 12 (1959).
—— Canad. J. Math.13, 1 (1961).
Shale, D.: Trans. Am. Math. Soc.103, 149 (1962).
Kastler, D.: Commun. Math. Phys.1, 14 (1965) and therein quoted literature.
Manuceau, J.: Ann. Inst. Henri Poincaré8, 117 (1968).
—— Ann. Inst. Henri Poincaré8, 139 (1968).
Araki, H.: Publ. RIMS5, 361 (1970).
Bargmann, V.: Ann. Math.59, 1 (1954), Sec. 6a.
Gel'fand, I. M., Vilenkin, N. Ya.: Generalized functions, Vol. 4, Chap. II, Sec. 4. New York-London: Academic Press 1964.
Halmos, P. R.: Measure theory. Princeton: Van Nostrand 1950.
Schwartz, L.: Méthodes mathematiques pour les sciences physique. Paris: Hermann 1961.
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Roepstorff, G. Coherent photon states and spectral condition. Commun.Math. Phys. 19, 301–314 (1970). https://doi.org/10.1007/BF01646637
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DOI: https://doi.org/10.1007/BF01646637