Epstein-Glaser renormalization and differential renormalization

We derive, based only on simple principles of renormalization in coordinate space, closed renormalized amplitudes and renormalization group constants at one- and two-loop orders for scalar field theories in general backgrounds. This is achieved through a renormalization procedure we develop exploiting the central idea behind differential renormalization, which needs as the only inputs the propagator and the appropriate Laplacian for the backgrounds in question. We work out this coordinate space renormalization in some detail, and subsequently back it up with specific calculations for scalar theories both on curved backgrounds, manifestly preserving diffeomorphism invariance, and at finite temperature.

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Path integrals, differential renormalization-group, and stochastic systems near criticality

International Journal of Engineering Science ◽

10.1016/0020-7225(92)90150-f ◽

1992 ◽

Vol 30 (10) ◽

pp. 1401-1405 ◽

Cited By ~ 5

Author(s):

Tom Cchag

Keyword(s):

Renormalization Group ◽

Stochastic Systems ◽

Path Integrals ◽

Differential Renormalization

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DIFFICULTIES OF AN INFRARED EXTENSION OF DIFFERENTIAL RENORMALIZATION

International Journal of Modern Physics A ◽

10.1142/s0217751x94000492 ◽

1994 ◽

Vol 09 (07) ◽

pp. 1067-1096 ◽

Cited By ~ 4

Author(s):

L. V. AVDEEV ◽

D. I. KAZAKOV ◽

I. N. KONDRASHUK

Keyword(s):

Perturbation Theory ◽

Fourier Transformation ◽

Two Dimensions ◽

Test Scheme ◽

Two Dimensional ◽

Differential Identities ◽

Feynman Integrals ◽

Differential Renormalization ◽

Self Consistent ◽

Infrared Singularities

We investigate the possibility of generalizing the differential renormalization of D. Z. Freedman, K. Johnson and J. I. Latorre in an invariant fashion to theories with infrared divergencies via an infrared [Formula: see text] operation. Two-dimensional σ models and the four-dimensional ɸ4-theory diagrams with exceptional momenta are used as examples, while dimensional renormalization serves as a test scheme for comparison. We write the basic differential identities of the method simultaneously in co-ordinate and momentum space, introducing two scales which remove ultraviolet and infrared singularities. A consistent set of Fourier-transformation formulae is derived. However, the values for tadpole-type Feynman integrals in higher orders of perturbation theory prove to be ambiguous, depending on the order of evaluation of the subgraphs. In two dimensions, even earlier than this ambiguity manifests itself, renormalization-group calculations based on the infrared extension of differential renormalization lead to incorrect results. We conclude that the procedure of extended differential renormalization does not perform the infrared [Formula: see text] operation in a self-consistent way.

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