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Notes towards the construction of nonlinear relativistic quantum fields. III: Properties of the $C^*$-dynamics for a certain class of interactions


Author: Irving Segal
Journal: Bull. Amer. Math. Soc. 75 (1969), 1390-1395
MSC (1959): Primary 4748, 8146; Secondary 2846, 8135
DOI: https://doi.org/10.1090/S0002-9904-1969-12429-8
Part II: Bull. Amer. Math. Soc., Volume 75, Number 6 (1969), 1383--1389
MathSciNet review: 0251992
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  • 1. I. Segal, Notes toward the construction of nonlinear relativistic quantum fields.
    I: The Hamiltonian in two space-time dimensions as the generator of a C*-automorphism group, Proc. Nat. Acad. Sci. U.S.A. 57 (1967), 1178-1183, MR 35 #5195. II: The basic nonlinear functions in general space-times, Bull. Amer. Math. Soc. 75 (1969), 1383-1389. MR 214344

  • 2. I. Segal, Tensor algebras over Hilbert spaces. I, Trans. Amer. Math. Soc. 81 (1956), 106-134. MR 17, 880. MR 76317
  • 3. Einar Hille, A class of reciprocal functions, Ann. of Math. (2) 27 (1926), no. 4, 427–464. MR 1502747, https://doi.org/10.2307/1967695
  • 4. E. Nelson, A quartic interaction in two dimensions, Proc. Conf. Math. Theory Elementary Particles (Dedham, Mass., 1965) M.I.T. Press, Cambridge, Mass., 1966, pp. 69-73. MR 35 #1309. MR 210416
  • 5. I. Segal, Mathematical characterization of the physical vacuum for a linear Bose Einstein field (Foundations of the dynamics of infinite systems. III) Illinois J. Math. 6 (1962), 500-523. MR 26 #1075. MR 143519
  • 6. T. Andô, Positive linear operators in semi-ordered linear spaces, J. Fac. Sci. Hokkaido Univ. Ser. I 13 (1957), 214-228. MR 19, 1067. MR 92127
  • 7. I. Segal, Nonlinear functions of weak processes. I, J. Functional Analysis 4 (1969), 404-456. MR 249061

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DOI: https://doi.org/10.1090/S0002-9904-1969-12429-8

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