Exploring High Multiplicity Amplitudes in Quantum Mechanics

Understand

Calculations of $1\to N$ amplitudes in scalar field theories at very high multiplicities exhibit an extremely rapid growth with the number $N$ of final state particles.

• This either indicates an end of perturbative behaviour, or possibly even a breakdown of the theory itself.
• It has recently been proposed that in the Standard Model this could even lead to a solution of the hierarchy problem in the form of a "Higgsplosion".
• To shed light on this question we consider the quantum mechanical analogue of the scattering amplitude for $N$ particle production in $\phi^4$ scalar quantum field theory, which corresponds to transitions $\langle N \lvert \hat{x} \rvert 0 \rangle$ in the anharmonic oscillator with quartic coupling $\lambda$.