GHP formalism

The GHP formalism notices that given a spin-frame ${\displaystyle (o^{A},\iota ^{A})}$ with ${\displaystyle o_{A}\iota ^{A}=1,}$ the complex rescaling ${\displaystyle (o^{A},\iota ^{A})\rightarrow (\lambda o^{A},\lambda ^{-1}\iota ^{A})}$ does not change normalization. The magnitude of this transformation is a boost, and the phase tells one how much to rotate. A quantity of weight ${\displaystyle (p,q)}$ is one that transforms like ${\displaystyle \eta \rightarrow \lambda ^{p}{\bar {\lambda }}^{q}\eta .}$ One then defines derivative operators which take tensors under these transformations to tensors. This simplifies many NP equations, and allows one to define scalars on 2-surfaces in a natural way.

• General relativity
• NP formalism

• Geroch, Robert, Held, A. and Penrose, Roger (1973). "A space-time calculus based on pairs of null directions". Journal of Mathematical Physics. 14 (7): 874–881. Bibcode:1973JMP....14..874G. doi:10.1063/1.1666410.{{cite journal}}: CS1 maint: multiple names: authors list (link)

• Penrose, Roger; Rindler, Wolfgang (1987). Spinors and Space-Time: Volume 1, Two-Spinor Calculus and Relativistic Fields. Cambridge: Cambridge University Press. ISBN 0-521-33707-0.

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