In the cases of one particle system and pure SU(2) Yang-Mills system, the instanton solution and its contribution to the vacuum structure is considered.
Using Euclidean instanton method which is non-perturbative and applicable in the semiclassical limit, vacuum-to-vacuum amplitude of one particle system in one dimensional space is calculated. In particular, double well potential and periodic potential are studied by this method and dilute gas approximation. Here, zero modes which exist in invariant theory are treated by collective coordinates method. It is shown that instanton dominates vacuum tunneling through a potential barrier. Homotopy theory which can be applied to the study of the global properties of gauge group is discussed.
A regular, spherically symmetric instanton solution of the pure SU(2) Yang-Mills theory is studied. It is shown that the effect of instanton is $0 (e^{-8x^2/g^2}$).
By canonical quantization formalism in $A_4=0$ temporal gauge, vacuum tunneling and θ-vacua which are true vacua of the theory are considered.
θ-vacua are the ground states of independent, and in general, inequivalent worlds.
