Finite calculation of divergent selfenergy diagrams

Abstract

Using dispersive techniques, it is possible to avoid ultraviolet divergences in the calculation of Feynman diagrams, making subsequent regularization of divergent diagrams unnecessary. We give a simple introduction to the most important features of such dispersive techniques in the framework of the so-called finite causal perturbation theory. The method is also applied to the 'divergent' general massive two-loop sunrise selfenergy diagram, where it leads directly to an analytic expression for the imaginary part of the diagram in accordance with the literature, whereas the real part can be obtained by a single integral dispersion relation. It is pointed out that dispersive methods have been known for decades and have been applied to several nontrivial Feynman diagram calculations.

arXiv comment15 pages, Latex, one figure, added references

References in corpus (23)

• Microlocal Analysis and Interacting Quantum Field Theories: Renormalization on Physical Backgrounds
• Two-loop two-point functions with masses: asymptotic expansions and Taylor series, in any dimension
• Analytical and numerical methods for massive two-loop self-energy diagrams
• Analytic two-loop results for selfenergy- and vertex-type diagrams with one non-zero mass
• One-loop leading logarithms in electroweak radiative corrections: II. Factorization of collinear singularities
• A local (perturbative) construction of observables in gauge theories: the example of QED
• An Approach Toward the Numerical Evaluation of Multi-Loop Feynman Diagrams
• Feynman Diagrams to Three Loops in Three Dimensional Field Theory
• Threshold and pseudothreshold values of the sunset diagram
• Threshold expansion of the sunset diagram
• The sunset diagram in SU(3) chiral perturbation theory
• Non-abelian gauge theories as a consequence of perturbative quantum gauge invariance
• Perturbative gauge invariance: electroweak theory II
• Threshold expansion of Feynman diagrams within a configuration space technique
• Causal Perturbation Theory and Differential Renormalization
• The Pseudothreshold Expansion of the 2-loop Sunrise Selfmass Master Amplitudes
• Improved Epstein-Glaser Renormalization II. Lorentz invariant framework
• Cohomological analysis of gauged-fixed gauge theories
• Multidimensional Phase Space and Sunset Diagrams
• Two-Loop Diagrams in Causal Perturbation Theory
• The Threshold Expansion of the 2-loop Sunrise Selfmass Master Amplitudes
• Scalar Matter Coupled to Quantum Gravity in the Causal Approach: Finite One-Loop Calculations and Perturbative Gauge Invariance
• Wess-Zumino Model in the Causal Approach

Cited by in corpus (7)

• Explicitly symmetrical treatment of three-body phase space
• Regularization in quantum field theory from the causal point of view
• Resummation of mass terms in perturbative massless quantum field theory
• Dispersive calculation of the massless multi-loop sunrise diagram
• Spontaneous emission and atomic line shift in causal perturbation theory
• Causal construction of the massless vertex diagram
• Reply to comment on ``A simple explanation of the non-appearance of physical gluons and quarks"