Quantized Electromagnetic Field Tensor

The EM field tensor is a stress-energy tensor.

From Wikipedia:

The stress–energy tensor, sometimes called the stress–energy–momentum tensor or the energy–momentum tensor, is a tensor physical quantity that describes the density and flux of energy and momentum in spacetime, generalizing the stress tensor of Newtonian physics. It is an attribute of matter, radiation, and non-gravitational force fields. This density and flux of energy and momentum are the sources of the gravitational field in the Einstein field equations of general relativity, just as mass density is the source of such a field in Newtonian gravity.

It is used in relativistic physics, but it can be quantized by a Lagrangian formulation.

Doubt clearance

• The electron field, also known as the electron-positron field, is a matter field, whose quanta are the electron and positron.

• The electric field, also known as the electromagnetic field, is a force field, whose quanta are the photons.

• All particles are excitations of their own particle-antiparticle field.

• Charged particles such as quarks, electrons, muons and taus, and their antiparticles interact via the electromagnetic field.
• For example, electrons and positrons are affected by the electromagnetic field, but neutrinos aren't.
• Quarks are disturbances in the quark field, and they interact via the gluon field.