Let me make the story straightforward here: All events of our universe ignoring dark matter, gravity and expansion of space; at small length scale ultimately reduces to interactions of countable finite/infinite number of fermions (particles with half-integer spin, also termed as matter particles due to the Pauli exclusion principle) via the exchange of gauge bosons (particles with integer spin). The type of gauge boson classifies the strength and type of the interaction. If gauge boson is photon(\(\gamma\)), the interaction is termed as electromagnetic; if it is \(W^{\pm}\) or \(Z^{0}\) then the interaction is weak, for it to be gluons; the interaction is a strong force.
Not all particles can participate in all four forces.
- Particles with colour and electric charges (quarks) participate in all forces
- Particles with only electric charge(charged leptons, i.e. \(e^{\pm},\mu^{\pm},\tau^{\pm},\) and charged gauge bosons \( W^{\pm}\)) participate in electromagnetic and weak forces
- All particles (neutral or charged) participate in the weak interaction.
- Particles with only colour charge (gluons) participate in only strong interaction.
The strength of interaction varies as strong \(\gg\) Electromagnetic \(\gg\) weak \(\gg\) gravitational.
There are 12 matter particles:
- 6 leptons: \(\{e^{-},\mu_e,\nu^{-},\nu_\mu,\tau^{-},\nu_\tau\}\),
- and six quarks \(\{u,d,c,s,t,b\}\) with three colour charges
- and 12 force carrier particles \(\{8 g, w^{\pm},z^0,\gamma\}\), together with Higgs particle (provides masses to all fundamental particles except neutrinos), constitutes building blocks of standard model of particle physics.
The theory describing strong force is Quantum Chromodynamics (QCD). QCD is written in framework of quantum field theory (like QED and GWS (Glashow-Weinberg-Salam theory)). We generally describe interacting quantum field theory as some perturbation to free quantum theory of fields. It turns out that the QCD theory has input parameters or bare coupling constants (quark masses and inverse gauge coupling \(\beta=2N_c/g^2\)). The coupling constant of QCD (\(g_{QCD}=g\)) is not constant and depends on scale (length scale or energy scale). On the basis of scale, we classify two realms of QCD: non-perturbative region (\(g>1\) for \(E\leq 197.7MeV\) or \(r \geq 1fm\)) and perturbative region (\(g<1\) for \(E \geq 197.7MeV\) or \(r \leq 1fm\)). QCD is successful in explaining the perturbative phenomena but cannot explain the non-perturbative phenomena like quark confinement or colour confinement, properties of bound states of quarks (masses of hadrons, decay rates), the full spectrum of hadronic states, and phase transition in QCD.
The non-perturbative range is filled with existence of hadrons (baryons or heavy composite particles ex. protons, neutrons, and mesons or light composite particles ex. pions (\(\pi^{\pm},\pi^{0}\)), kaons (\(K^{\pm},k^{0}\)), ..) which can be explained via quark confinement, which in turn is responsible for existence of atoms, molecules and life itself.
So far, we have yet to be able to mathematically prove that only non-Abelian theory like QCD is confining in low energy limit in 3 space and one-time dimension, and it remains one of the millennium prize problems.
To describe and predict the non-perturbative regime, we discretize space and time on a lattice with boundary conditions (periodic in space, anti-periodic in time for quarks and periodic in time for gauge fields), where quark fields live on sites of the lattice and gluon fields lives on links connecting them (also termed as gauge links). We call this the lattice formalism of QCD or better termed lattice-QCD. In short, the goal of Lattice-QCD is to prove that the QCD is the correct theory of strong interactions in both the perturbative and non-perturbative regions.