This article has been updated Abstract Superstring field theory expresses the perturbative S-matrix of superstring theory as a sum of Feynman diagrams each of which is manifestly free from ultraviolet divergences. The interaction vertices fall off exponentially for large space-like external momenta making the ultraviolet finiteness property manifest, but blow up exponentially for large time-like external momenta making it impossible to take the integration contours for loop energies to lie along the real axis. This forces us to carry out the integrals over the loop energies by choosing appropriate contours in the complex plane whose ends go to infinity along the imaginary axis but which take complicated form in the interior navigating around the various poles of the propagators. We consider the general class of quantum field theories with this property and prove Cutkosky rules for the amplitudes to all orders in perturbation theory. Besides having applications to string field theory, these results also give an alternative derivation of Cutkosky rules in ordinary quantum field theories.
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Digore We contrast this interpretation of the imaginary part of this sum with that of the time-ordered product. The tules anniversary edition of the Review of Particle Physics urles, published in Physical Review Dprovides a comprehensive review of the field of particle physics and of related areas in cosmology.
The factors of i come into play depending on whether we are using the normal or complex conjugated version of the Feynman rules. Particle Data Group Phys. We also indicate how dispersionlike relations can be derived for the time-ordered product.
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Could you post your calculation as an answer? By deriving a set of Cutkosky rules, we show that the weights involved in these relations arise in finding the imaginary part of this sum, and thus have an interpretation in terms of reaction rates.
QuantumDot Do you mean using the formula for the residue of a higher-order pole? Given a cut diagram, there is a convention that we label the vertices of the diagram black or white, black vertices follow standard Feynman rules and are accompanied by a factor of i and white ones the complex conjugated version so come with a -i.
Topics include Higgs bosons, supersymmetry, big bang nucleosynthesis, probability, statistics, and accelerators and detectors. Sep 6, 6. I just now finished calculating a simplified version of the two loop integral above and found that nothing strange is going on in the imaginary part. Sign up using Facebook. Aug 24, 3. Home Questions Tags Users Unanswered. Related Posts
Abstract Some properties at zero and finite temperature in the real-time formalism of a sum of graphs, previously shown in some examples to be equivalent to the retarded product, are discussed. Cutkosky rules for a two-loop diagram Ask Question. Given a cut diagram, there is a convention that we label the vertices of the diagram black or white, black vertices follow standard Feynman rules and are accompanied by a factor of i and white ones the complex conjugated version so come with a -i. Could you post your calculation as an answer? Aug 27, 4. Aug 24, 1. We also indicate how dispersionlike relations can be derived for the time-ordered product.
Cutkosky rules for superstring field theory