The Nontrivial Vacuum Structure of an Extended $t\bar{t}$ BEH (Higgs) Bound State

TL;DR

This paper presents a Lorentz-invariant formalism for top-quark condensation, revealing a complex vacuum structure of the Higgs boson analogous to a BCS condensate, based on an extended wave-function.

Contribution

It introduces an extended internal wave-function in top-quark condensation, leading to a gauge-invariant, Lorentz-invariant vacuum structure of the Higgs boson.

Findings

Develops a manifestly Lorentz-invariant formalism for top-quark condensation.

Reveals a nontrivial vacuum structure of the Higgs boson analogous to a BCS condensate.

Shows the absence of relative time as a gauge invariance in bilocal field theory.

Abstract

In a recent reformulation of top-quark condensation for the Brout-Englert-Higgs boson we introduced an extended internal wave-function, $\phi(r)$. We show how this leads to a manifestly Lorentz invariant formalism, where the absence of ``relative time'' is a gauge invariance of the bilocal field theory. This dictates a novel and nontrivial Lorentz invariant vacuum structure for the BEH boson, the relativistic generalization of a condensed matter state analogous to a BCS condensate.