Discrete-spacetime formulation of quantum field theory on a finite lattice. Founded by Wilson (1974) as a non-perturbative regulator that preserves gauge invariance exactly. Central tools: Wilson gauge action, Wilson / staggered /…
lattice-field-theory
Wilson gauge action: S = β Σ_□ [1 − (1/N) Re Tr U_□]
Wilson's 1974 lattice gauge action: gauge fields U_μ(x) ∈ SU(N) live on links of a hypercubic lattice; the action sums over all plaquettes…
Nielsen-Ninomiya no-go: naive lattice fermions double into 2^d species
Nielsen-Ninomiya (1981) no-go theorem: no local, Hermitian, translation-invariant lattice fermion action on a cubic lattice can…
Staggered (Kogut-Susskind) fermions: 4 tastes, preserves U(1)×U(1) chiral
Staggered / Kogut-Susskind fermions (1975) distribute 16 naive doublers across 16 lattice sites via a site-dependent phase η_μ(x) =…
Hybrid Monte Carlo: molecular dynamics trajectory + Metropolis accept/reject
Duane-Kennedy-Pendleton-Roweth (1987) hybrid Monte Carlo (HMC): augment the link variables with fictitious conjugate momenta π, evolve the…
Strong-coupling plaquette expansion: ⟨U_□⟩ = β/(2N²) + O(β²) for SU(N)
Strong-coupling (β → 0, i.e. g₀ → ∞) character expansion of the plaquette expectation in pure SU(N) lattice gauge theory. Expanding…
Wilson-loop area law ↔ quark confinement: ⟨W_C⟩ ∼ exp(−σ·Area)
Wilson's 1974 order-parameter criterion for confinement: the expectation value of a large rectangular Wilson loop of dimensions R×T in pure…
Asymptotic-freedom continuum limit: a(β) = a₀ · exp[−β/(2b₀ N)] for N-colour
Renormalisation-group relation between lattice spacing a and bare coupling β = 2N/g₀² in asymptotically free Yang-Mills. At two-loop…