In quantum field theory, specifically in the context of Quantum Electrodynamics (QED), the mass of a charged particle does not depend on its velocity. The mass of a particle is considered an intrinsic property that remains constant regardless of its motion.
In QED, the interaction between charged particles and the electromagnetic field is described by the exchange of virtual photons. These virtual photons mediate the electromagnetic force between charged particles. The properties of particles, such as their mass and charge, are treated as fixed quantities in the theory.
However, it is important to note that in relativistic quantum field theories like QED, the energy of a particle is related to its momentum through the relativistic energy-momentum relation:
E^2 = (pc)^2 + (mc^2)^2
where E is the energy, p is the momentum, m is the mass, and c is the speed of light. This relation shows that the energy of a particle depends on its momentum and mass. As a consequence, when a particle with mass moves at high velocities (close to the speed of light), its energy increases significantly due to the relativistic effects.
The increase in energy affects the dynamics of the particle, leading to phenomena such as time dilation and length contraction. However, the mass of the particle itself remains unchanged. The mass is considered an invariant quantity, which means it is the same for all observers regardless of their relative motion.
Therefore, in QED, the mass of a charged particle is not directly dependent on its velocity, but the energy of the particle does increase with velocity due to relativistic effects.