The mass of both the proton and the electron can be calculated within the framework of quantum field theory, specifically through a process known as renormalization. However, there are certain differences in the calculations for the proton and the electron that arise due to their respective properties and the theoretical approach employed.
In the case of the proton, its mass can be determined by considering the strong interactions between quarks. Protons are composed of three quarks (two up quarks and one down quark) held together by the strong nuclear force. The mass of the proton emerges from the collective mass and energy contributions of these constituent quarks, as well as the gluons that mediate the strong force.
On the other hand, the electron is an elementary particle and is not composed of smaller constituents. Its mass arises from its interactions with the Higgs field within the Standard Model of particle physics. The Higgs mechanism is responsible for the generation of particle masses, and it imparts mass to the electron as well as other fundamental particles in the Standard Model.
Calculating the electron's mass within the framework of quantum field theory involves intricate calculations, including contributions from the Higgs field, electroweak interactions, and quantum fluctuations. These calculations are technically challenging and require advanced mathematical techniques such as renormalization. However, despite the complexity, the electron's mass can be accurately predicted and is known experimentally.
In summary, while the mass of both the proton and the electron can be calculated within the framework of quantum field theory, the proton's mass is determined by the interactions between its constituent quarks, while the electron's mass arises from its interactions with the Higgs field and other fundamental processes.