Retarded functions, dispersion relations, and Cutkosky rules at zero and finite temperature

Journal Article · Fri Feb 15 04:00:00 EST 1991 · Physical Review, D (Particles Fields); (USA)

DOI:https://doi.org/10.1103/PhysRevD.43.1269· OSTI ID:5697786

Kobes, R ^[1]

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1. Physics Department, University of Winnipeg, Winnipeg, Manitoba, Canada R3B 2E9 (CA)

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. For the general 2-, 3-, and 4-point functions we demonstrate that expressing this sum in the form of the definition of the retarded product leads to identities that can be interpreted as dispersion relations in energies. 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. We contrast this interpretation of the imaginary part of this sum with that of the time-ordered product. We also indicate how dispersionlike relations can be derived for the time-ordered product.

• OSTI ID: 5697786
• Journal Information: Physical Review, D (Particles Fields); (USA), Journal Name: Physical Review, D (Particles Fields); (USA) Vol. 43:4; ISSN PRVDA; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

645400* -- High Energy Physics-- Field Theory
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
DIAGRAMS
DISPERSION RELATIONS
ENERGY
FEYNMAN DIAGRAM
FIELD THEORIES
MATRICES
MATRIX ELEMENTS
PERTURBATION THEORY
QUANTUM CHROMODYNAMICS
QUANTUM FIELD THEORY
S MATRIX
SELF-ENERGY
TEMPERATURE DEPENDENCE