The concept of mass in the context of quantum field theory, including the effects of the Higgs field, can be subtle. In quantum field theory, particles are described as excitations of underlying fields, and their masses are related to the interactions between these fields. The Higgs field is responsible for the generation of mass for certain particles through a process known as electroweak symmetry breaking.
In quantum mechanics, particles are described by wavefunctions that evolve according to the Schrödinger equation. The wavefunction of a particle includes all possible states the particle can be in, and the probabilities of observing specific states are determined by the wavefunction's amplitude.
The notion of mass in quantum mechanics is related to the concept of energy and is commonly referred to as the "rest mass" or "invariant mass." The rest mass of a particle is an inherent property that remains constant regardless of the particle's state of motion.
However, it is important to distinguish between rest mass and relativistic mass. Relativistic mass is a concept that was used in classical physics and early relativity theory, where the mass of an object was thought to increase with its velocity. In modern physics, relativistic mass is not commonly used or preferred, as it can lead to confusion and is not consistent with the fundamental principles of special relativity.
In the context of quantum mechanics, the mass of a particle is an intrinsic property that does not depend on how the experiment is being done. The wavefunction and associated probabilities are determined by the particle's mass and other relevant physical properties. The experimental conditions may affect the measured values of certain observables, but they do not fundamentally change the mass of the particle itself.
So, in summary, the mass of fundamental particles, including the effects of the Higgs field, is not subject to quantum contextualization that depends on how the experiment is being done. The concept of relativistic mass is not commonly used in modern physics, and the rest mass, or invariant mass, is the intrinsic property associated with a particle's mass in quantum field theory.