Analytic Properties of Triangle Feynman Diagrams in Quantum Field Theory

We discuss dispersion representations for the triangle diagram <inline-formula> <math display="inline"> <semantics> <mrow> <mi>F</mi> <mo>(</mo> <msup> <mi>q</mi> <mn>2</mn> </msup> <mo>,</mo> <msubsup> <mi>p</mi> <mn>1</mn> <mn>2</mn> </msubsup> <mo>,</mo> <msubsup> <mi>p</mi> <mn>2</mn> <mn>2</mn> </msubsup> <mo>)</mo> </mrow> </semantics> </math> </inline-formula>, the single dispersion representation in <inline-formula> <math display="inline"> <semantics> <msup> <mi>q</mi> <mn>2</mn> </msup> </semantics> </math> </inline-formula> and the double dispersion representation in <inline-formula> <math display="inline"> <semantics> <msubsup> <mi>p</mi> <mn>1</mn> <mn>2</mn> </msubsup> </semantics> </math> </inline-formula> and <inline-formula> <math display="inline"> <semantics> <msubsup> <mi>p</mi> <mn>2</mn> <mn>2</mn> </msubsup> </semantics> </math> </inline-formula>, with special emphasis on the appearance of the anomalous singularities and the anomalous cuts in these representations.

Abstract licence: CC BY

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