Spacetime Dependent Lagrangians and the Vacuum Expectation Value of the Higgs field

TL;DR

This paper employs spacetime dependent Lagrangian formalism to derive a classical Yang-Mills solution, estimating the Higgs vacuum expectation value and exploring boundary non-commutativity relevant for D-brane actions.

Contribution

It introduces a novel application of spacetime dependent Lagrangians to determine the Higgs vacuum expectation value and incorporates boundary non-commutativity for D-brane construction.

Findings

Derived a classical solution for Yang-Mills theory using spacetime dependent Lagrangians.

Estimated the Higgs vacuum expectation value as proportional to the inverse of the coupling.

Showed the solution can include non-commuting boundary coordinates relevant for D-branes.

Abstract

The spacetime dependent lagrangian formalism of references [1-2] is used to obtain a classical solution of Yang-Mills theory. This is then used to obtain an estimate of the vacuum expectation value of the Higgs field, viz. $\phi_{a}=A/e$, where $A$ is a constant and $e$ is the Yang-Mills coupling (related to the usual electric charge). The solution can also accommodate non-commuting coordinates on the boundary of the theory which may be used to construct D-brane actions. PACS:11.15.-q ; 11.27+d ; 11.10.Ef