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The Pauli exclusion principle from the optical theorem

Peter Matak

TL;DR

The work investigates how the Pauli exclusion principle manifests in perturbative scattering through the optical theorem by analyzing a toy model with two Majorana fermions $\chi_1,\chi_2$ and a light scalar mediator $\phi$. By examining forward-scattering diagrams and the corresponding imaginary parts, the authors show that apparent same-state fermion contributions arise from the interference of two disconnected amplitudes with a relative fermionic minus sign. This interference yields cancellations that restore Pauli statistics, ensuring the optical theorem remains valid. The results illuminate the subtle interplay between unitarity and quantum statistics and extend to bosonic cases with opposite sign, highlighting a general mechanism by which quantum-statistical effects are encoded in forward-scattering amplitudes.

Abstract

We analyze a specific class of forward-scattering diagrams with imaginary kinematics, which, via the optical theorem, describe processes involving two identical fermions occupying the same state. What initially seems to be a contradiction turns out to be a key element in how the Pauli exclusion principle manifests itself in scattering theory. The discussion is entirely basic and could easily fit into any quantum field theory textbook. To the best of our knowledge, however, this point has not been addressed in the literature, and we aim to fill this gap.

The Pauli exclusion principle from the optical theorem

TL;DR

The work investigates how the Pauli exclusion principle manifests in perturbative scattering through the optical theorem by analyzing a toy model with two Majorana fermions and a light scalar mediator . By examining forward-scattering diagrams and the corresponding imaginary parts, the authors show that apparent same-state fermion contributions arise from the interference of two disconnected amplitudes with a relative fermionic minus sign. This interference yields cancellations that restore Pauli statistics, ensuring the optical theorem remains valid. The results illuminate the subtle interplay between unitarity and quantum statistics and extend to bosonic cases with opposite sign, highlighting a general mechanism by which quantum-statistical effects are encoded in forward-scattering amplitudes.

Abstract

We analyze a specific class of forward-scattering diagrams with imaginary kinematics, which, via the optical theorem, describe processes involving two identical fermions occupying the same state. What initially seems to be a contradiction turns out to be a key element in how the Pauli exclusion principle manifests itself in scattering theory. The discussion is entirely basic and could easily fit into any quantum field theory textbook. To the best of our knowledge, however, this point has not been addressed in the literature, and we aim to fill this gap.

Paper Structure

This paper contains 4 sections, 12 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Two fermions occupying the same quantum state?
  3. Interference of two disconnected diagrams
  4. Summary

Figures (1)

  • Figure 1: The lowest-order connected forward-scattering diagram for the $\chi_1\chi_2$ initial state within the model defined in Eq. \ref{['eq3']} ( a). Diagrams b and c correspond to Eqs. \ref{['eq9']} and \ref{['eq12']} intgrated over the full phase-space, respectively.