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In Newmann-Penrose formalism, a Null rotation with ##l## fixed is

$$l^a−>l^a\\

n^a−>n^a+\bar{c}m^a+c\bar{m}^a+c\bar{c}l^a\\

m^a−>m^a+cl^a\\

\bar{m}^a−>\bar{m}^a+\bar{c}l^a$$

Using this transformation, how to prove?

$$π−>π+2\bar{c}ϵ+\bar{c}^2κ+D\bar{c}$$

Ref: 2-Spinors by P.O'Donell, p.no, 65

$$l^a−>l^a\\

n^a−>n^a+\bar{c}m^a+c\bar{m}^a+c\bar{c}l^a\\

m^a−>m^a+cl^a\\

\bar{m}^a−>\bar{m}^a+\bar{c}l^a$$

Using this transformation, how to prove?

$$π−>π+2\bar{c}ϵ+\bar{c}^2κ+D\bar{c}$$

Ref: 2-Spinors by P.O'Donell, p.no, 65

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