Full-sky formulae for weak lensing power spectra from total angular
  momentum method
  We systematically derive full-sky formulae for the weak lensing power spectra
generated by scalar, vector and tensor perturbations from the total angular
momentum (TAM) method. Based on both the geodesic and geodesic deviation
equations, we first give the gauge-invariant expressions for the deflection
angle and Jacobi map as observables of the CMB lensing and cosmic shear
experiments. We then apply the TAM method, originally developed in the
theoretical studies of CMB, to a systematic derivation of the angular power
spectra. The TAM representation, which characterizes the total angular
dependence of the spatial modes projected along a line-of-sight, can carry all
the information of the lensing modes generated by scalar, vector, and tensor
metric perturbations. This greatly simplifies the calculation, and we present a
complete set of the full-sky formulae for angular power spectra in both the
E-/B-mode cosmic shear and gradient-/curl-mode lensing potential of deflection
angle. Based on the formulae, we give illustrative examples of non-vanishing
B-mode cosmic shear and curl-mode of deflection angle in the presence of the
vector and tensor perturbations, and explicitly compute the power spectra.
