×

zbMATH — the first resource for mathematics

The \(C^ *\)-algebras of a free Boson field. (English) Zbl 0137.45601

Keywords:
quantum theory
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Haag, R.: Colloque international sur les problémes mathématiques de la théorie quantique des champs. Lille (1959). Pub. CNRS Paris.
[2] – Proceedings of the Midwest Conference of Theoretical Physics Minneapolis (1961).
[3] —- Ann. Physik11, 29 (1963).
[4] —- Proceedings of the Conference in Function Spaces and Physical Applications. M.I.T. Cambridge Mass. (1964).
[5] Araki, H.: Einführung in die axiomatische Quantenfeldtheorie. E.T.H. Lectures notes, Zürich 1961/62.
[6] Haag, R., andD. Kastler: J. Math. Phys.5, 848 (1964). · Zbl 0139.46003
[7] Kastler, D.: Proceedings of the 1964 M.I.T. Conference quoted above.
[8] Haag, R., andB. Schroer: J. Math. Phys.3, 248 (1962). · Zbl 0125.21903
[9] Araki, H.: J. Math. Phys.5, 1 (1964). · Zbl 0151.44401
[10] Takeda, Z.: Tôhoku Math. Journ.7, 67 (1955). · Zbl 0065.34903
[11] von Neumann, J.: Math. Ann.104, 570 (1931). · Zbl 0001.24703
[12] Hove, L. van: Mém. Acad. Roy. Belg., No 1618 (1951).
[13] Cook, J. M.: Trans. Am. Math. Soc.74 (1953).
[14] Friedrichs, K. O.: Mathematical Aspects of the Quantum Theory of Fields. New York: Interscience Pub. 1953. · Zbl 0052.44504
[15] Gårding, L., andA. S. Wightman: Proc. Nat. Acad. Sci. U.S.A.40, 617 (1954). · Zbl 0057.09603
[16] Haag, R.: Mat. Fys. Medd. Danske Vid. Selsk.29, No 12 (1955).
[17] – Lectures in Theoretical Physics, Vol. III, Boulder (1960). · Zbl 0103.39802
[18] Segal, I. M.: Mathematical Problems of Relativistic Physics. Am. Math. Soc., Providence R.I. (1963) and therein quoted literature ranging from 1956 to 1963.
[19] Coester, F., andR. Haag: Phys. Rev.117, 1137 (1960). · Zbl 0093.21605
[20] Araki, H.: Princeton Thesis (1960).
[21] —- J. Math. Phys.1, 492 (1960);4, 1343 (1963);5, 1 (1964). · Zbl 0099.22906
[22] Lew, J. S.: Princeton Thesis (1960).
[23] Fukutome, H.: Progr. Theor. Phys.23, 989 (1960). · Zbl 0093.21403
[24] Gelfand, I. M., andN. J. Vilenkin: Generalized Functions, in Russian, Vol. 4, Chap. IV. We are indebted to Dr.A. Guichardet for communication of these results.
[25] Bargmann, V.: Comm. Pure. Appl. Math.14, 187 (1961). · Zbl 0107.09102
[26] Wigner, E.: Phys. Rev.40, 749 (1932). · Zbl 0004.38201
[27] Moyal, J. E.: Proc. Cambridge Phil. Soc.45, 99 (1949).
[28] Shale, D.: Trans. Am. Math. Soc.103, 149 (1962).
[29] Klauder, J. R.: J. Math. Phys.4, 1055 (1963);4, 1058 (1963);5, 177 (1964). · Zbl 0127.18701
[30] McKenna, J., andJ. R. Klauder: J. Math. Phys.5, 878 (1964). (The references [29] and [30] came to the author’s attention after completion of the present work.) · Zbl 0137.23902
[31] Weyl, H.: Z. Physik46, 1 (1927).
[32] Neumark, M. A.: Normierte Ringe. Berlin: VEB Deutscher Verlag der Wissenschaften 1959. · Zbl 0089.10101
[33] Rickart, C. E.: General Theory of Banach Algebras. New York: Van Nostrand 1960. Appendix § 3. · Zbl 0095.09702
[34] Hewitt, E., andK. A. Ross: Abstract Harmonic Analysis. Berlin-Göttingen-Heidelberg: Springer 1963. · Zbl 0115.10603
[35] Dixmier, J.: LesC*-algèbres et leurs représentations. Paris: Gauthier-Villars 1964.
[36] Mackey, G. W.: Acta Math.99, 265 (1958). · Zbl 0082.11301
[37] Segal, I. E.: Bull. Am. Math. Soc.53, 73 (1947). · Zbl 0031.36001
[38] Kadison, R. V.: Proc. Nat. Acad. Sci. USA,43, 273 (1937), see also Ref. [33], Theorem (4.9.10), p. 253. · Zbl 0078.11502
[39] Rosenberg, A.: Am. J. Math.75, 523 (1953). · Zbl 0053.25903
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.