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

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. Quantum-field theories involve important relations following from the symmetry properties of a theory. Search for symmetries and constraints imposed by them on the physical characteristics of the system are of particular importance in QCD, which is a theory with confinement, where "observables" are composite states-hadrons. Low-energy theorems or Ward identities (scale and chiral) are of fundamental importance for a deeper insight into the nonperturbative properties of the QCD vacuum. Low-energy theorems of QCD were obtained in the early 1980s [32]. Low-energy theorems of QCD, which follow from the general symmetry properties and are independent of the details of the confinement mechanism, make it possible to obtain information sometimes otherwise inaccessible. In addition, they can be

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