Yang–Mills & the Mass Gap
YANG–MILLS & THE MASS GAP
Understand the gap.
Explore the frontier.
A guided path from your first gauge theory course to one of the deepest open problems in physics and mathematics.
Begin with two semesters of QFT. Build the mathematics along the way.
A positive threshold above the vacuum. That is what must be proved.
A CLEAR PLACE TO BEGIN
Big questions.
A manageable first step.
You know the language of fields and gauge symmetry. Start with the physical question, then discover exactly what remains to be proved.
Find your route →What is the mass gap problem?
Understand the target, the physical picture, and why the word “existence” matters.
Read a spectrum from a correlator
See how Euclidean time reveals the energies of physical states.
FOLLOW THE IDEAS
At the research frontier
What has been established, in which setting, and what comes next. Every result keeps its assumptions in view.
Volume-uniform lattice area law at strong coupling
Theorem 1.6 gives rectangular Wilson-loop area-law bounds in the stated small-beta lattice regime with constants independent of lattice volume.
Gauge covariance selects the stochastic mass counterterm
The source establishes uniqueness of the gauge-covariant Yang–Mills mass renormalization for local stochastic three-dimensional Yang–Mills–Higgs dynamics.
Elimination beyond a loop cutoff supplies indirect relations
The framework generates direct loop equations and relations obtained by eliminating longer intermediate loops, with SU(2) applications in two, three and four lattice dimensions.
SEE THE WHOLE PROBLEM
See how each result
connects to the whole.
A result can control short distances, establish an area law on a lattice, or reveal a mechanism in a compactified theory. The proof map shows how each connects to the full question.
Explore the proof map ↗An editorial map of obligations, not a progress score or a prescribed proof.
BUILD YOUR UNDERSTANDING
Explore the subject
The physics of the mass gap
States, scales, spectra, and the meaning of confinement.
Defining quantum Yang–Mills
From a formal path integral to a physical quantum theory.
Lattice theory & continuum limits
What a regulator gives us. What removing it demands.
Mathematical bridges
The analysis and probability you need, when you need them.
Controlled models & mechanisms
Learn from theories we can solve and regimes we can control.
Research approaches
Follow the ideas, compare the results, find the next obstacle.
LEARN BY CHANGING SOMETHING
Make the ideas tangible.
Explore how a correlator reveals a spectrum, what changes as the lattice spacing shrinks, how positivity reconstructs states, and when the box creates an apparent gap.
Enter the laboratories ↗