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Add phase integrals #59

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Phase integrals are required to compute cross-sections in background fields. Integrals are defined in @szabo137's thesis eqs. (2.51)-(2.53).

Envisaged usage is as follows

  • Define a setup S which consists of a pulse envelope (shape and width/duration)
  • Define the method M used to compute the integrals (analytic, numeric)
    then computing the integrals depends on the chosen direction (of polarization/observation) pol, the background intensity a0, the photon number parameter l, and the kinematic factors alpha
phase_integral_setup =PhaseIntegral(S, M)
compute_B1x(phase_integral_setup, pol, a0, l, alpha_1x, alpha_1y, alpha_2) # other directions and integrals are named accordingly

The parameters pol, a0, ... are defined somewhere else, i.e. previously in the cross-section computation and outside QEDfields.jl.

@steindev steindev added help wanted Extra attention is needed 06 - Feature-request Missing a feature or functionality labels Jan 29, 2025
@SimeonEhrig
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@steindev Can you please rebase. Otherwise the CI does not work.

@steindev steindev force-pushed the topic-2024-10_phase-integrals branch from b06a255 to 6d95340 Compare January 30, 2025 09:07
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