Abstract
The decay rate of a false vacuum is studied in gauge theory, paying particular attention to its gauge invariance. Although the decay rate should not depend on the gauge parameter ξ according to the Nielsen identity, the gauge invariance of the result of a perturbative calculation has not been clearly shown. We give a prescription to perform a one-loop calculation of the decay rate, with which a manifestly gauge-invariant expression of the decay rate is obtained. We also discuss the renormalization necessary to make the result finite, and show that the decay rate is independent of the gauge parameter even after the renormalization.
Highlights
B is the bounce action, the Euclidean classical action of the bounce configuration
In [6], a gauge fixing function which reduces to the Rξ gauge around the false vacuum has been adopted. (We call such a gauge as an Rξ-like gauge.) the procedure proposed in [6] cannot be applied if gauge symmetry is preserved in the false vacuum
We study the decay of the false vacuum in 4-dimensional (4D) gauge theory, paying particular attention to the gauge invariance of the decay rate
Summary
We consider a model with U(1) gauge symmetry; application of our argument to the case with non-abelian gauge groups is straightforward. When v = 0, we should take account of all the bounce configurations labeled by Θ(0) for the calculation of the decay rate of the false vacuum It is highly non-trivial because the fluctuation operators around the bounce depend on Θ(0), and because we have to understand the measure for the integration over Θ(0). Such complications can be avoided with a gauge fixing function which does not contain the scalar field [10]. On the contrary, when v = 0, all the classical solutions parameterized by θ contribute to the false-vacuum decay because all the bounce parameterized by θ has the same asymptotic value at r → ∞, and contributes to the vacuum decay
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