  We construct a field-based Bayesian Hierarchical Model for cosmic shear that
includes, for the first time, the important astrophysical systematics of
intrinsic alignments and baryon feedback, in addition to a gravity model. We
add to the BORG-WL framework the tidal alignment and tidal torquing model
(TATT) for intrinsic alignments and compare them with the non-linear alignment
(NLA) model. With synthetic data, we have shown that adding intrinsic
alignments and sampling the TATT parameters does not reduce the constraining
power of the method and the field-based approach lifts the weak lensing
degeneracy. We add baryon effects at the field level using the enthalpy
gradient descent (EGD) model. This model displaces the dark matter particles
without knowing whether they belong to a halo and allows for self-calibration
of the model parameters, which are inferred from the data. We have also
illustrated the effects of model misspecification for the baryons. The
resulting model now contains the most important physical effects and is
suitable for application to data.
