We develop a general framework for generating estimators of a given quantity which are unbiased to a given order in the difference between the true value of the underlying quantity and the fiducial position in theory space around which we expand the
likelihood. We apply this formalism to rederive the optimal quadratic estimator and show how the replacement of the second derivative matrix with the Fisher matrix is a generic way of creating an unbiased estimator (assuming choice of the fiducial model is independent of data). Next apply the approach to estimation of shear lensing, closely following the work of Bernstein and Armstrong (2014). Our first order estimator reduces to their estimator in the limit of zero shear, but it also naturally allows for the case of non-constant shear and the easy calculation of correlation functions or power spectra using standard methods. Both our first-order estimator and Bernstein and Armstrongs estimator exhibit a bias which is quadratic in true shear. Our third-order estimator is, at least in the realm of the toy problem of Bernstein and Armstrong, unbiased to 0.1% in relative shear errors $Delta g/|g|$ for shears up to $|g|=0.2$.
Photon quantization is implemented in the standard model extension (SME) using the Gupta-Bleuler method and BRST concepts. The quantization prescription applies to both the birefringent and non-birefringent CPT-even couplings. A curious incompatibili
ty is found between the presence of the Lorentz-violating terms and the existence of a nontrivial conjugate momentum $Pi^0$ yielding problems with covariant quantization procedure. Introduction of a mass regulator term can avoid the vanishing of $Pi^0$ and allows for the implementation of a covariant quantization procedure. Field-theoretic calculations involving the SME photons can then be performed using the mass regulator, similar to the conventional procedure used in electrodynamics for infrared-divergence regulation.
