Physical interpretation of oscillatory contributions to particle production

Ascertain the physical interpretation of particle production associated with the oscillatory terms in the non-relativistic spectrum for the finite box (r=1), determining whether these terms correspond to soft particles that carry negligible energy or to a cancellation between positive- and negative-energy contributions, and reconcile their role in particle number with their absence in the total energy.

Background

In the non-relativistic regime, the authors derive a spectrum that includes oscillatory terms (O.T.’s). The total radiated energy can be obtained from the leading Planck term alone, whereas the finite particle count requires inclusion of the oscillations.

They discuss two possible physical scenarios for the oscillations—soft particles without energy, or canceling positive/negative energy contributions—and note prior results where particle numbers do not reveal negative energy flux, concluding that the correct physical interpretation remains unresolved.