Quantum decay process of metastable vacuum states in SU(2) Yang-Mills theory: A probability theoretical point of view

The problem of vacuum-tunneling phenomena such as the quantum decay process of metastable vacuum states in SU(2) Yang-Mills theory is investigated from a probability theoretical point of view. This is done by adopting the stochastic quantization procedure to quantize the Yang-Mills field in the $A_0=0\mathrm{}$ gauge. The mechanism of vacuum tunneling can be illustrated within the realm of the stochastic quantization. It is shown that the quantized vacuum field configuration, which manifests the decay process of metastable vacuum states, is a Euclidean-Markov field of Gaussian type. The validity of the Euclidean path-integral description of vacuum-tunneling phenomena is also shown from the probability theoretical point of view. Passing to the semiclassical limit, the concept of an instanton is justified as a classical Euclidean Yang-Mills field which manifests the most probable tunneling path.