Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

When identical particles cease to be indistinguishable: violation of statistics in quantum spacetime

Nicola Bortolotti, Catalina Curceanu, Antonino Marciano, Kristian Piscicchia

Abstract

Quantum gravity may modify the fundamental symmetries that govern identical particles. In particular, noncommutative spacetime frameworks predict deformations of Bose and Fermi statistics. Here we develop a relativistic quantum field theory based on the most general oscillator algebra compatible with $θ$-deformed Poincaré symmetry. This construction generalizes twisted statistics to a class of quon-like deformations allowing non-involutive particle exchange. We show that the resulting theory is consistent at both the free and interacting levels and derive its implications for atomic systems. Purely twisted statistics predicts Pauli-forbidden atomic transitions at rates incompatible with experiments. By contrast, a class of quon deformations suppresses such processes by powers of the noncommutativity scale, but only if superselection rules between permutation-symmetry sectors are violated. This implies an effective breakdown of particle indistinguishability and provides theoretical motivation for high-precision experimental tests of the Pauli exclusion principle.

When identical particles cease to be indistinguishable: violation of statistics in quantum spacetime

Abstract

Quantum gravity may modify the fundamental symmetries that govern identical particles. In particular, noncommutative spacetime frameworks predict deformations of Bose and Fermi statistics. Here we develop a relativistic quantum field theory based on the most general oscillator algebra compatible with -deformed Poincaré symmetry. This construction generalizes twisted statistics to a class of quon-like deformations allowing non-involutive particle exchange. We show that the resulting theory is consistent at both the free and interacting levels and derive its implications for atomic systems. Purely twisted statistics predicts Pauli-forbidden atomic transitions at rates incompatible with experiments. By contrast, a class of quon deformations suppresses such processes by powers of the noncommutativity scale, but only if superselection rules between permutation-symmetry sectors are violated. This implies an effective breakdown of particle indistinguishability and provides theoretical motivation for high-precision experimental tests of the Pauli exclusion principle.

Paper Structure

This paper contains 15 sections, 178 equations, 5 figures, 1 table.

Table of Contents

  1. Covariance on the Moyal space
  2. Multiparticle state spaces
  3. Quantum field theory
  4. Consistency of the quantization scheme
  5. Correlation functions
  6. Relativistic wave equations for atoms
  7. Evaluation of the rate without SSRs
  8. Unsuppressed scenarios: $\kappa \geq 4$
  9. Maximal suppression: $\kappa=2$
  10. Case $\sigma_\text{nr}=m$
  11. Case $\sigma_\text{nr}=|\boldsymbol p - \boldsymbol q|$
  12. Case $\sigma_\text{nr}=\sqrt{m|\boldsymbol p - \boldsymbol q|}$
  13. Contribution of $H_{if}^a$
  14. Remaining scenarios: $0<\kappa<2$ and $2<\kappa<4$
  15. Directionality in PEP-violating transitions

Figures (5)

  • Figure 1: Six-point Green function with deformed statistics. $\mathcal{Q}_\theta$ and $\mathcal{Q}_\theta'$ are the exchange factors associated to permutations of the initial and final electrons respectively. Red and purple lines denote the electrons and the nucleus, respectively.
  • Figure 2: Structure of the six-point Green function $G_0$ for a helium-like atom in the commutative limit. The kernel $\mathcal{\mathcal{\mathcal{K}}}$ collects all irreducible two-body and three-body interactions. Red and purple lines with blobs denote dressed electron and nucleus propagators, respectively.
  • Figure 3: Pictorial representation of a radiative atomic transition between a PEP-allowed and a PEP-violating state.
  • Figure 4: Structure of the amputated correlation function $\mathcal{I}$ for a helium-like atom. Red and purple lines denote dressed electron and nucleus propagators, respectively. The kernel $\mathcal{\mathcal{\mathcal{K}}}$ collects all irreducible two-body and three-body interactions.
  • Figure 5: Six-point Green function describing the propagation of a helium-like atoms. The blobbed lines are the dressed propagators of the electrons (red) and the nucleus (purple), $\mathcal{I}_\theta$ is the amputated correlation function.