Approximate Lorentz invariance of the vacuum: a physical solution of the `hierarchy problem' ?

Abstract

In the `condensed phase&#39; of effective quantum field theories one expects deviations from exact Lorentz invariance at ultralow momenta | k| < delta where the shell &#39;delta&#39; should only vanish in the strict local limit of the theory when the ultraviolet cutoff &#39;Lambda&#39; tends to infinity. I explore this idea for the Higgs condensate suggesting that, in this case, the resulting relation connecting &#39;delta&#39;, &#39;Lambda&#39; and the Fermi scale might provide a simple physical solution of the `hierarchy problem&#39;. In this picture, the Planck scale is not a purely ultraviolet quantity but embodies in its numerical value the peculiar infrared-ultraviolet connection that is realized in the scalar condensate.