Yang–Mills action as an eigenvalue problem in the theory of elasticity and some measure theoretical interpretation of ‘tHooft’s instanton

Theory of elasticity is a highly mathematical, rigorously derived and experimentally verified classical field. It is the basis of all applied mechanical and engineering material sciences. The present note gives an unconventional analogy between theory of elasticity and quantum field theory. We present and solve the Yang–Mills instanton problem as a buckling Eigenvalue problem of an axially loaded strut and interpret the loading parameter as the instanton action. Subsequently, we give the instanton action a geometrical interpretation as the volume of the SO(3) special orthogonal group: vol SO(3) = 8p2.