## Bulletin of the American Mathematical Society

### Notes towards the construction of nonlinear relativistic quantum fields. II: The basic nonlinear functions in general space-times

Irving Segal

#### Article information

Source
Bull. Amer. Math. Soc., Volume 75, Number 6 (1969), 1383-1389.

Dates
First available in Project Euclid: 4 July 2007

https://projecteuclid.org/euclid.bams/1183530935

Mathematical Reviews number (MathSciNet)
MR0251991

Zentralblatt MATH identifier
0196.28005

Subjects
Primary: 2846 8147
Secondary: 3495 4665

#### Citation

Segal, Irving. Notes towards the construction of nonlinear relativistic quantum fields. II: The basic nonlinear functions in general space-times. Bull. Amer. Math. Soc. 75 (1969), no. 6, 1383--1389. https://projecteuclid.org/euclid.bams/1183530935

#### References

• 1. I. Segal, Notes toward the construction of non-linear 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.
• 2. I. Segal, Nonlinear functions of weak processes. I, J. Functional Analysis 4 (1969), 404-456.
• 3. I. Segal, Foundations of the theory of dynamical systems of infinitely many degrees of freedom. I, Mat.-Fys. Medd. Danske Vid. Selsk. 31 (1959), no. 12, 39 pp. MR 22 #3477. II, Canad J. Math. 13 (1961), 1-18. MR 23 #B1877. III, Illinois J. Math. 6 (1962), 500-523. MR 26 #1075.
• 4. I. Segal, Local nonlinear functions of quantum fields, Proc. Conf. in Honor of M. H. Stone (Chicago, 1968) (to appear).
• 5. I. Segal, Nonlinear functions of weak processes. II, J. Functional Analysis (to appear).
• 6. I. Segal, Local non-commutative analysis, Proc. Sympos. in Honor of S. Bochner (Princeton, 1968) (to appear).
• 7. G. C. Wick, The evaluation of the collision matrix, Phys. Rev. (2) 80 (1950), 268-272. MR 12, 380.
• 8. I. Segal, Interprétation et solution d'équations non linéaires quantifiées, C. R. Acad. Sci. Paris 259 (1964), 301-303. MR 29 #4453.
• 9. L. Gårding and A. S. Wightman, Fields as operator-valued distributions in relativistic quantum field theory, Ark. Fys. 28 (1964), 129.
• 10. I. Segal, Hypermaximality of certain operators on Lie groups, Proc. Amer. Math. Soc. 3 (1952), 13-15. MR 14, 448.

• Part III: Irving Segal. Notes towards the construction of nonlinear relativistic quantum fields. III: Properties of the $C^*$-dynamics for a certain class of interactions. Bull. Amer. Math. Soc., Volume 75, Number 6 (1969), 1390--1395.