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arXiv · 2109.04728

H\"older Continuity of the Integrated Causal Lagrangian in Minkowski Space

Marco Oppio
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Abstract

It is proven that the kernel of the fermionic projector of regularized Dirac sea vacua in Minkowski Space is $L^4$-integrable. The proof is carried out in the specific setting of a continuous exponentially-decaying cutoff in momentum space. As a direct consequence, the corresponding causal Lagrangian is shown to be $L^1$-integrable. Some topological features of the integrated causal Lagrangian are analyzed. In particular, local H\"older-like estimates are proved for continuous regular variations of spacetime, of which a few examples are discussed. Particular emphasis is placed on first-order perturbations of Dirac sea vacua induced by external electromagnetic fields.

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Marco Oppio. 2021-09-10. H\"older Continuity of the Integrated Causal Lagrangian in Minkowski Space. https://arxiv.org/abs/2109.04728

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