Twistors and Spin 3/2 Potentials in Quantum Gravity

Details Twistors and Spin 3/2 Potentials in Quantum Gravity Twistors and Spin 3/2 Potentials in Quantum Gravity

1995-06-27

arxiv.org/abs/gr-qc/9506058v1

Lect.Notes Pure Appl.Math. 169 (1995) 35-54

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

20 pages, plain-tex, recently appearing in: Twistor Theory, edited by Stephen Huggett (Marcel Dekker, New York, 1994). The aut

Scientific paper

Local boundary conditions involving field strengths and the normal to the boundary, originally studied in anti-de Sitter space-time, have been recently considered in one-loop quantum cosmology. This paper derives the conditions under which spin-lowering and spin-raising operators preserve these local boundary conditions on a 3-sphere for fields of spin 0,1/2,1,3/2 and 2. Moreover, the two-component spinor analysis of the four potentials of the totally symmetric and independent field strengths for spin 3/2 is applied to the case of a 3-sphere boundary. It is shown that such boundary conditions can only be imposed in a flat Euclidean background, for which the gauge freedom in the choice of the potentials remains. Alternative boundary conditions for supergravity involving the spinor-valued 1-forms for gravitinos and the normal to the boundary are also studied.

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