A direct approach to quantum tunneling

Understand

The decay rates of quasistable states in quantum field theories are usually calculated using instanton methods.

• Standard derivations of these methods rely in a crucial way upon deformations and analytic continuations of the physical potential, and on the saddle point approximation.
• While the resulting procedure can be checked against other semi-classical approaches in some one-dimensional cases, it is challenging to trace the role of the relevant physical scales, and any intuitive handle on the precision of the approximations involved are at best obscure.
• In this paper, we use a physical definition of the tunneling probability to derive a formula for the decay rate in both quantum mechanics and quantum field theory directly from the Minkowski path integral, without reference to unphysical deformations of the potential.