Common integrals in quantum field theory: Difference between revisions

Revision as of 16:49, 7 March 2016

Revision as of 07:35, 8 March 2016

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==Bessel functions==

===Integration of the cylindrical propagator with mass===

====First power of a Bessel function====

:<math>\int_0^{\infty} {k\; dk \over k^2 +m^2} J_0 \left( kr \right)=K_0 (mr). </math>

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====Squares of Bessel functions====

The integration of the propagator in cylindrical coordinates is<ref name="Zwillinger_2014"/>

:<math>\int_0^{\infty} {k\; dk \over k^2 +m^2} J_1^2 (kr) =I_1 (mr)K_1 (mr).</math>