Local Observables and Renormalization in Dirac–Segal Approach to QFT

Abstract

We explain the Dirac–Segal approach to quantum field theory. We study local observables in this approach and the theory of deformations. We found out that this theory of deformation in the second-order coincides with the renormalization of the same theory, would it be considered in Polyakov approach. We conjecture that it is still true to all orders.

Keywords

Quantum field theory / Segal axioms / Renormalization

References

[1] Feynman R, Hibbs A. Quantum Mechanics and Path Integrals. 1965 New York: McGraw-Hill

[2] Collins J. Renormalization. 1984 Cambridge: Cambridge University Press

[3] Streater, RF., Wightman, AS.: PCT, spin and statistics, and all that. Princeton, Benjamin, New York (1964)

[4] Polyakov A. Gauge Fields and Strings. 1986 Chur: Harwood Academic Publishers

[5] Segal G. The definition of conformal field theory. Differential Geometric Methods in Theoretical Physics. 1988 Dordrecht: Kluwer Academic Publishers. 165-171

[6] Atiyah, M.: New invariants of three and four dimensional manifolds. In: Proceedings of Symposia in Pure Mathematics, 48, AMS, 48,285