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Self-adjoint phase operator. (English. Russian original) Zbl 0463.47025
Theor. Math. Phys. 38, 39-47 (1979); translation from Teor. Mat. Fiz. 38, 58-70 (1979).

47L60 Algebras of unbounded operators; partial algebras of operators
81T05 Axiomatic quantum field theory; operator algebras
81S05 Commutation relations and statistics as related to quantum mechanics (general)
47B25 Linear symmetric and selfadjoint operators (unbounded)
Full Text: DOI
[1] P. Carruthers and M. M. Nieto, Rev. Mod. Phys.,40(2), 411 (1968). · doi:10.1103/RevModPhys.40.411
[2] A. S. Davydov, Quantum Mechanics [in Russian], Fizmatgiz (1973); A. I. Baz’, Ya. B. Zel’dovich, and A. M. Perelomov, Scattering, Reactions, and Decay in Nonrelativistic Quantum Mechanics, Jerusalem (1969).
[3] P. A. M. Dirac, Proc. R. Soc. Ser. A,114, 243 (1927). · JFM 53.0847.01 · doi:10.1098/rspa.1927.0039
[4] V. A. Fock, Investigations in Quantum Field Theory [in Russian] LGU (1957). · Zbl 0078.43105
[5] N. I. Akhiezer and I. M. Glazman, Theory of Linear Operators in Hilbert Space, New York (1961), (1963). · Zbl 0098.30702
[6] P. R. Halmos, Hilbert Space Problem Book, Van Nostrand (1967).
[7] H. C. Volkin, J. Math. Phys.14(12), 1965 (1973). · doi:10.1063/1.1666279
[8] L. Susskind and I. Glogower, Physics,1(1), 49 (1964).
[9] I. C. Garrison and J. Wong, J. Math. Phys.,11(8), 2243 (1970).
[10] V. N. Popov and V. S. Yarunin, Vestn. LGU, No.22, 7 (1973); E. V. Damaskinskii and V. S. Yarunin, Izv. Vyssh. Uchebn. Zaved. Fiz., No. 6, 59 (1978).
[11] J. M. Levy-Leblond, Ann. Phys.,101(1), 319 (1976). · Zbl 0338.47015 · doi:10.1016/0003-4916(76)90283-9
[12] F. Rocca and M. Sirugue, Commun. Math. Phys.,34(2), 111 (1973). · doi:10.1007/BF01646440
[13] J. Provost, F. Rocca, and G. Vallee, Ann. Phys.,94(2), 307 (1975); J. Provost, F. Rocca, G. Vallee, and M. Sirugue, J. Math. Phys.,15(12) 2079 (1974). · doi:10.1016/0003-4916(75)90170-0
[14] G. G. Emch, Algebraic Methods in Statistical Mechanics and Quantum Field Theory, Wiley-Interscience, New York (1972); C. R. Putnam, Commutation Properties of Hilbert Space Operators and Related Topics, Springer, New York (1967).
[15] K. M. Hoffmann, Banach Spaces of Analytic Functions, Prentice-Hall, London (1962).
[16] M. Rosenblum, Pacif. J. Math.,10(3), 987 (1960); Proc. AMS,13(4), 590 (1962); Am. J. Math.,87(3), 709 (1965).
[17] I. E. Segal, Mathematical Problems of Relativistic Physics, AMS, Providence, R. I. (1963); I. E. Segal, K. Dan. Vidensk. Selsk. Mat.-Fys. Medd.,31, 3 (1959).
[18] O. I. Zav’yalov and V. N. Sushko, Teor. Mat. Fiz.,1, 153 (1969); in: Statistical Physics and Quantum Field Theory [in Russian], Fizmatgiz (1973), p. 411.
[19] J. M. Chaiken, Ann. Phys.,42, 22 (1976); Commun. Math. Phys.,8, 164 (1968).
[20] M. A. Naimark, Normed Rings, Groningen (1960).
[21] A. A. Grib, E. V. Damaskinskii, and V. M. Maksimov, Usp. Fiz. Nauk,120, 587 (1970).
[22] K. Napiorhowski and W. Pusz, Rep. Math. Phys.,3, 221 (1972). · doi:10.1016/0034-4877(72)90006-7
[23] H. Araki and E. J. Woods, J. Math. Phys.,4, 637 (1963). · doi:10.1063/1.1704002
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