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Spin-3/2 Potentials

Part of the Fundamental Theories of Physics book series (FTPH, volume 69)

Abstract

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 chapter derives the conditions under which spin-lowering and spin-raising operators preserve these local boundary conditions on a three-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 three-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.

The second part of this chapter studies the two-spinor form of the Rarita-Schwinger potentials subject to local boundary conditions compatible with BRST invariance and local supersymmetry. The Rarita-Schwinger field equations are studied in an arbitrary four-real-dimensional Riemannian background with boundary. Gauge transformations on the potentials are shown to be compatible with the field equations providing a set of second-order partial differential equations hold. An equivalent, first-order form of the compatibility conditions is also obtained. The boundary conditions do not restrict severely the choice of background four-geometries, as it happens in the case of Dirac’s potentials with reflective boundary conditions on field strengths. The recent construction by Penrose of secondary potentials which supplement the Rarita-Schwinger potentials is then extended from Ricci-flat space-times to arbitrary curved backgrounds. Remarkably, the traces of such secondary potentials are linearly related to the independent spinor fields appearing in the Rarita-Schwinger equations. The resulting set of equations for these secondary potentials is hence ontained.

Keywords

Gauge Transformation Twistor Space Spinor Field Preservation Condition Gauge Freedom 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Kluwer Academic Publishers 2002

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