Mass in Quantum Physics
In classical mechanics, the inert mass of a particle appears in the Euler–Lagrange equation as a parameter m,
After quantization, replacing the position vector x with a wave function, the parameter m appears in the kinetic energy operator,
In the ostensibly covariant (relativistically invariant) Dirac equation, and in natural units, this becomes
Where the "mass" parameter m is now simply a constant associated with the quantum described by the wave function ψ.
In the Standard Model of particle physics as developed in the 1960s, there is the proposal that this term arises from the coupling of the field ψ to an additional field Φ, the so-called Higgs field. In the case of fermions, the Higgs mechanism results in the replacement of the term mψ in the Lagrangian with . This shifts the explanandum of the value for the mass of each elementary particle to the value of the unknown couplings Gψ. The discovery of a massive Higgs boson would be regarded as a strong confirmation of this theory. But there is indirect evidence for the reality of the Electroweak symmetry breaking as described by the Higgs mechanism, and the non-existence of the Higgs boson would indicate a "Higgsless" description of this mechanism.
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