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Spinor two-point functions in maximally symmetric spaces

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Allen,  Bruce
Observational Relativity and Cosmology, AEI-Hannover, MPI for Gravitational Physics, Max Planck Society;

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CommMathPhys106-201.pdf
(Publisher version), 589KB

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Citation

Allen, B., & Lütken, C. A. (1986). Spinor two-point functions in maximally symmetric spaces. Communications in Mathematical Physics, 106(2), 201-210. doi:10.1007/BF01454972.


Cite as: http://hdl.handle.net/11858/00-001M-0000-0013-5DD6-4
Abstract
The two-point function for spinors on maximally symmetric four-dimensional spaces is obtained in terms of intrinsic geometric objects. In the massless case, Weyl spinors in anti de Sitter space can not satisfy boundary conditions appropriate to the supersymmetric models. This is because these boundary conditions break chiral symmetry, which is proven by showing that the ldquoorder parameterrdquo $$\left\langle {\bar \psi \psi } \right\rangle $$ for a massless Dirac spinor is nonzero. We also give a coordinate-independent formula for the bispinor $$S(x)\bar S(x')$$ introduced by Breitenlohner and Freedman [1], and establish the precise connection between our results and those of Burges, Davis, Freedman and Gibbons [2].