physics, mathematical physics, philosophy of physics
theory (physics), model (physics)
experiment, measurement, computable physics
Axiomatizations
Tools
Structural phenomena
Types of quantum field thories
standard model of particle physics
force field (physics) gauge bosons
photon - electromagnetic field (abelian Yang-Mills field)
scalar bosons
matter field fermions (spinors)
hadron (bound states of the above quarks)
minimally extended supersymmetric standard model
superpartner gauge field fermions
Exotica
The Yang–Mills field is the gauge field of Yang-Mills theory.
It is modeled by a cocycle $\hat F \in \mathbf{H}(X, \mathbf{B}U(n)_{conn})$ in differential nonabelian cohomology. Here $\mathbf{B} U(n)_{conn}$ is the moduli stack of $U(n)$-principal connections, the stackification of the groupoid of Lie-algebra valued forms, regarded as a groupoid internal to smooth spaces.
This is usually represented by a vector bundle with connection.
As a nonabelian Čech cocycle the Yang-Mills field on a space $X$ is represented by
a cover $\{U_i \to X\}$
a collection of $Lie(U(n))$-valued 1-forms $(A_i \in \Omega^1(U_i, Lie(U(n))))$;
a collection of $U(n)$-valued smooth functions $(g_{i j} \in C^\infty(U_{i j}, U(n)))$;
such that on double overlaps
and such that on triple overlaps
For $U(n) = U(1)$ this is the electromagnetic field.
For $U(n) = SU(2) \times U(1)$ this is the “electroweak field”;
For $U(n) = SU(3)$ this is the strong nuclear force field.