Change of Metric for Modified Wave Functions

In this appendix, we describe the change of metric that occurs when a 4-spinor wave function is modified by operations on the small component. The unmodified spinor is expressed as 

The metric operator Q is the operator that appears in the orthogonality condition, 

Without modifications to the wave function, the metric is simply the unit matrix, 

For a number of approaches, we want to modify the small component such that t where 

But in order to maintain the normalization for this new spinor, we have to change the metric, which we can derive by substituting for the small component in the normalization expression. 

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