A direct approach to quantum tunneling
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. There are numerous benefits to this approach, from non-perturbative applications to precision calculations and aesthetic simplicity.