Momentum Space Landau Equations Via Isotopy Techniques

Understand

We investigate the analytic structure of functions defined by integrals with integrands singular on a finite union of quadrics.

• The main motivation comes from Feynman integrals which belong to this class.
• Using isotopy techniques we derive the Landau equations in momentum space from the theory of Feynman integrals and generalize these equations to naturally include singularities of the second type.
• For this purpose we introduce a regularization of analytic families of quadratic forms rendering the isotopy techniques applicable.