Low-energy relation for the trace of the energy-momentum tensor in QCD and the gluon condensate in a magnetic field

TL;DR

This paper derives a low-energy relation for the trace of the energy-momentum tensor in QCD within a magnetic field, revealing how the gluon condensate varies with magnetic field strength, combining nonperturbative analysis with field dependence.

Contribution

It introduces a novel low-energy equation for the trace of the energy-momentum tensor in a magnetic field and establishes the equality of derivatives of quark and gluon contributions, providing new insights into QCD vacuum structure.

Findings

Derived the low-energy relation for the trace of the energy-momentum tensor in a magnetic field.

Showed the equality of derivatives of quark and gluon contributions with respect to magnetic field.

Determined the dependence of the gluon condensate on magnetic field strength for both strong and weak fields.

Abstract

A treatment is given of the nonperturbative QCD vacuum in a magnetic field. The low-energy equation for the trace of the energy-momentum tensor in a magnetic field is derived. It is shown that the derivatives with respect to a magnetic field of the quark and gluon contributions to the trace of the energy-momentum tensor are equal. The dependence of the gluon condensate on the magnetic field strength is derived both for strong and weak fields.