Oswaldo Vazquez | Searcharxiv

arXiv2023

A survey of the electroweak configuration space and the W boson mass

Following the recent work of V. Moncrief, A. Marini, R. Maitra and P. Mondal on the geometry of field theoretic configuration spaces, this account examines how the regularized Ricci curvature of the $SU(2)_L \times U(1)_Y$ Yang-Mills orbit space may provide an intrinsic mass to the W boson which contributes to the value obtained from the renormalized Higgs mechanism. Though the discussion is heuristic, one hopes that this infinite-dimensional technology, which does not postulate extensions to the Standard Model, could explain the mass anomaly reported by the CDF II collaboration.

hep-th↗

arXiv2023

Continuation Criterion For Solutions To The Einstein Equations

We prove a continuation condition in the context of 3+1 dimensional vacuum Einstein gravity in Constant Mean extrinsic Curvature (CMC) gauge. More precisely, we obtain quantitative criteria under which the physical spacetime can be extended in the future indefinitely as a solution to the Cauchy problem of the Einstein equations given regular initial data. In particular, we show that a gauge-invariant $H^{2}$ Sobolev norm of the spacetime Riemann curvature remains bounded in the future time direction provided the so-called deformation tensor of the unit timelike vector field normal to the chosen CMC hypersurfaces verifies a spacetime $L^\infty$ bound. To this end, we implement a novel technique to obtain this refined estimate by using Friedlander's parametrix for tensor wave equations on curved spacetime and Moncrief's subsequent improvement. We conclude by providing a physical explanation of our result as well as its relation to the issues of determinism and weak cosmic censorship.

gr-qc↗