Attempt to Learn “Particle from Field”, “Mass Creation” and “Force from Interaction”

The three questions bother me a lot in QM and QFT. By DrPhysicsA, I could claim that I got the gist of them.

The concept of quantized particle properties, as introduced by Prank and Einstein, alongside the wave characteristics of light, logically culminates in the application of wave equations to describe particles under quantization constraints. This shift in perspective towards a field-based understanding represents a significant advancement, offering a more coherent explanation for complex light phenomena.

Math is an indispensable tool for physicists to discover law of universe!

solve to get alpha and beta matrix, and now we can rewrite the Dirac equation as

the 4d full version is

this is the route that’s going to lead to Higgs term and Higgs bosom.

Second, How Mass Arises? Mass in particle physics does not come from “stuff” like classical matter but from interactions with the Higgs field and the binding energy of quantum forces.

The Higgs field is an invisible quantum field that permeates all of space. Particles acquire mass by interacting with it, via the Brout-Englert-Higgs mechanism (BEH mechanism, Nobel Prize 2013). The key ideas are: Massless particles (e.g., photons) do not interact with the Higgs field and remain massless.Massive particles (e.g., electrons, quarks, W/Z bosons) “drag” against the Higgs field, slowing them down—this resistance is what we perceive as mass. The Higgs boson (discovered in 2012 at CERN) is an excitation of the Higgs field—like a splash in water.

that being said, you need to know 99% of your mass isn’t from Higgs interactions but from quantum binding energy inside protons and neutrons!’

The major item is the third one: how force is manifested by force carrier/particles, especially how EM forces arise when charged particles (e.g., electrons) exchange virtual photons.

Feynman diagrams visualized this:

e⁻ —-γ—- e⁻ (Two electrons repel by exchanging a photon)

The math shows that forces are not fundamental but emerge from particle exchanges.
The same framework extends to all forces (even gravity, with gravitons in hypothetical QFT gravity)

Derivation of the QED Interaction Term

The interaction term in Quantum Electrodynamics (QED) describes how electrons (and other charged particles) couple to photons, leading to electromagnetic forces. Here’s a step-by-step derivation: