Majorana Zitterbewegung Current Correlator: Vanishing ZBW Signal as a Z2 Topological Invariant

In the paper's words

Computes the Majorana ZBW current correlator in free-field theory. Shows that the reality condition enforces a vanishing expectation value, establishing a Z_2 topological distinction between Dirac and Majorana fermions accessible via ZBW measurement.

The abstract, verbatim, and its opening sentence is the claim. Every line below is quoted from the text.

Numbers it reports

1. In the companion paper (P1), we constructed the Bruhat-Tits tree of ZBW-coupled eigenstates and found: Dirac: Full ZBW transition graph with $O(n^2)$ edges Majorana: 57% fewer edges (P1 §4b) [CODE-EXECUTED] The vanishing of the ZBW current correlator explains this edge reduction: with no ZBW current fluctuations, the Majorana transition graph has fewer allowed transitions.

   from 4.3 Connection to Bruhat-Tits Tree

2. Combined with P1 (https://papers.qnfo.org/papers), which showed that the Bruhat-Tits tree of ZBW-coupled eigenstates has different topology for Dirac and Majorana (57% edge reduction), this paper provides the field-theoretic foundation for the ZBW-Majorana-TQC chain: P1: ZBW is a p-adic observable (ultrametric readout) P2 (this work): The ZBW current correlator is a $\mathbb{Z}_2$ diagnostic Future P3: Bruhat-Tits readout protocol for Majorana systems Future P4: Bridge to p-Adic Anyons and adelic QEC The experimental measurement of $\mathcal{O}_{\text{ZBW}}$ in candidate Majorana systems would provide direct evidence for or against the p-adic ZBW hypothesis.

   from 7. Conclusions

3. In the companion paper "Zitterbewegung as a p-Adic Observable" (P1, https://papers.qnfo.org/papers), we demonstrated that the single-particle ZBW velocity amplitude is identical for Dirac and Majorana fermions (ratio $A_{\text{Maj}}/A_{\text{Dir}} = 1.0$ across all momenta) [CODE-EXECUTED] .

   from 1. Introduction

4. At $p=0$, they are identical (ratio = 1.0000).

   from 2.4 Numerical Results [CODE-EXECUTED]

How it is done

1. We compute the Zitterbewegung contribution to the current-current correlator $\langle j^\mu(x) j^\nu(0) \rangle$ for both Dirac and Majorana fermions in (2+1) dimensions.

   from Abstract

2. The ZBW current correlator can be probed via: Electron energy loss spectroscopy (EELS) — measures $\text{Im}[\langle j^\mu j^\nu \rangle]$ at momentum transfer $\mathbf{q} \sim 1/\lambda_C$ Resonant inelastic X-ray scattering (RIXS) — accesses the Compton-scale current fluctuations Tunnel junction noise spectroscopy — measures current noise at frequencies $\omega \sim 2E/\hbar$

   from 5.1 Measuring $\mathcal{O}_{\text{ZBW}}$

3. This experiment is the highest-priority test of the ZBW-Majorana hypothesis.

   from 5.3 Priority

4. Combined with P1 (https://papers.qnfo.org/papers), which showed that the Bruhat-Tits tree of ZBW-coupled eigenstates has different topology for Dirac and Majorana (57% edge reduction), this paper provides the field-theoretic foundation for the ZBW-Majorana-TQC chain: P1: ZBW is a p-adic observable (ultrametric readout) P2 (this work): The ZBW current correlator is a $\mathbb{Z}_2$ diagnostic Future P3: Bruhat-Tits readout protocol for Majorana systems Future P4: Bridge to p-Adic Anyons and adelic QEC The experimental measurement of $\mathcal{O}_{\text{ZBW}}$ in candidate Majorana systems would provide direct evidence for or against the p-adic ZBW hypothesis.

   from 7. Conclusions

What would falsify it

1. The prediction is falsifiable: If $\mathcal{O}_{\text{ZBW}} = 0$ in a candidate Majorana system (nanowire, topological superconductor) → Majorana nature confirmed If $\mathcal{O}_{\text{ZBW}} \neq 0$ in the same system → either the system is not in the Majorana phase, or the prediction is wrong

   from 5.2 Falsifiability

2. In the companion paper "Zitterbewegung as a p-Adic Observable" (P1, https://papers.qnfo.org/papers), we demonstrated that the single-particle ZBW velocity amplitude is identical for Dirac and Majorana fermions (ratio $A_{\text{Maj}}/A_{\text{Dir}} = 1.0$ across all momenta) [CODE-EXECUTED] .

   from 1. Introduction

3. The current operator $j^\mu = \bar{\psi}\gamma^\mu\psi$ is the natural object to study because: It is gauge-invariant and physically observable It couples to electromagnetic probes (photon exchange) Its correlator $\langle j^\mu(x) j^\nu(0)\rangle$ encodes both static (vacuum polarization) and dynamic (ZBW) information The ZBW contribution to this correlator is a $\mathbb{Z}_2$ topological invariant

   from 1. Introduction

Where the claim stops

The paper's text states no limitation or caveat in its own sentences.

Where to read

1. Abstract160 words · 1 min
2. 1. Introduction140 words · 1 min
3. 2. Dirac Current Correlator267 words · 1 min
4. 3. Majorana Current Correlator344 words · 1 min
5. 4. The $\mathbb{Z}_2$ Topological Invariant200 words · 1 min
6. 5. Experimental Implications134 words · 1 min
7. 6. Discussion208 words · 1 min
8. 7. Conclusions134 words · 1 min