A river switched in a split second does not immediately forget the intervention. The fast currents have already settled into the new channel, but slow ripples are still spreading across the water, encoding the entire history of the turn. The truncation of a Majorana fermion in the new work works much the same way: the particle is not cut in space, but its wave packet is forced to change its propagation channel by rotating it in time.
The authors' key move is to describe this rotation not through a specific mechanism but through a simple rule: the output wave is obtained from the input by multiplying by a time-dependent rotation matrix. As long as the rotation is smooth, everything looks innocent. But if the initial and final orientations of the channels do not match, pair creation comes into play, and its trace in the vacuum turns out to be surprisingly stubborn. At arbitrarily small frequencies, the contribution of this trace grows as a logarithm, meaning it refuses to decay.
This logarithm is not an abstract quirk of formulas. It means that the vacuum before the switch and the vacuum after the switch no longer overlap: the field state remembers that the channels were once different. Physicists know this behavior as the orthogonality catastrophe, and here it appears in its pure form, without any additional interactions.
However, there is another side to this coin. If the switch is tuned so that pairs are not created at all, the gate behaves as an ideal causal filter. Outside the switching region, exact local identities hold, and the retained sector of the field becomes equivalent to a single-particle state, while the discarded sector becomes the vacuum. In other words, a local observer sees exactly the particle they should see, with no traces of global memory.
This separation between the global infrared response and the local causal structure is the main result of the work. Previously, it was unclear how to rigorously describe the truncation of a Majorana packet without resorting to literal cutting, and how to separate slow memory waves from fast local dynamics. Now there is a benchmark against which microscopic models of Majorana boundaries in topological superconductors can be compared. And the river, having returned to a calm flow, still carries in its slow ripples the trace of that instantaneous turn it once experienced.
In the formula for the infrared divergence, the coefficient in front of the logarithm equals (1 − cos ϑ_−)/π², and for a 90-degree rotation of the channels (ϑ_− = π/2) it becomes 1/π², a beautiful number arising purely from the geometric mismatch of the initial and final orientations.
The idea of a 'truncated particle' echoes a motif from science fiction where a hero passes through a portal and leaves part of their wave function in another world, but here instead of mysticism there is rigorous mathematics: globally the field remembers the operation through soft modes, while locally an observer can only see the retained fragment.