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H\"older Continuity of the Integrated Causal Lagrangian in Minkowski Space
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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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Cited by 1 Pith paper
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A Geometric Derivation of the Einstein Equations from the Causal Action Principle
Using osculating vacua, the authors derive Einstein's equations from the causal action principle, with the gravitational coupling identified as the square of the regularization length.
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