Exploring Quantization Conditions: Relating Finite-Volume Data to Infinite-Volume Observables

We explore the formalisms, originally developed by Martin Luscher and others, that relate finite-volume spectra to infinite-volume scattering and transition amplitudes. This is particularly relevant for numerical Lattice Field Theory calculations. Such calculations necessitate a Wick rotation to imaginary time and it is numerically infeasible to analytically continue the resulting Euclidean correlators back to real-time, and thus we cannot directly calculate the desired observables. This is particularly relevant for multi-hadron scattering and decay amplitudes. By contrast, energy levels and time-independent matrix elements of the finite-volume system carry no information about the space-time signature and can be used to constrain these observables.