×

zbMATH — the first resource for mathematics

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).

MSC:
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)
PDF BibTeX XML Cite
Full Text: DOI
References:
[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
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.