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1 LM-Orsay - Laboratoire de Mathématiques d-Orsay

Abstract : We construct Hadamard states for the Yang-Mills equation linearized around a smooth, space-compact background solution. We assume the spacetime is globally hyperbolic and its Cauchy surface is compact or equal $ r^d$. We first consider the case when the spacetime is ultra-static, but the background solution depends on time. By methods of pseudodifferential calculus we construct a parametrix for the associated vectorial Klein-Gordon equation. We then obtain Hadamard two-point functions in the gauge theory, acting on Cauchy data. A key role is played by classes of pseudodifferential operators that contain microlocal or spectral type low-energy cutoffs. The general problem is reduced to the ultra-static spacetime case using an extension of the deformation argument of Fulling, Narcowich and Wald. As an aside, we derive a correspondence between Hadamard states and parametrices for the Cauchy problem in ordinary quantum field theory.

Keywords : Hadamard states microlocal spectrum condition pseudo-differential calculus Yang-Mills equation curved spacetimes





Autor: Christian Gérard - Michal Wrochna -

Fuente: https://hal.archives-ouvertes.fr/



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