Gauge-Invariant Field Theory of Signal-Worker Interactions

In the paper's words

The transition of Quantum Architectonics from a materials-centric discipline to a fundamental ontology of information-matter interaction necessitates a rigorous field-theoretic description. This study bridges that gap by promoting the Signal-Worker ontology to a continuous Gauge-Invariant Quantum Field Theory, where “Workers” are treated as fermionic matter fields and “Signals” as non-Abelian gauge bosons. We construct a SU(2) invariant Lagrangian that recovers the discrete H_SW model as a stable infrared fixed point, demonstrating that the lattice architecture of current models is a fundamental emergent reality rather than a mere approximation.

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

Numbers it reports

1. the Gauge-Invariant Action The dynamics of the coupled Signal-Worker system are governed by an action functional $S = \int d^4x \mathcal{L}$ that must remain invariant under local gauge transformations.

   from 2.2 Construction of

2. Furthermore, it assigns an energy cost to the forbidden process: cloning is not just “impossible” in the abstract; it is dynamically suppressed by the infinite action of the gauge field (Oppenheim & Reznik, 2009).

   from 4.6 Comparison with

How it is done

1. We construct a $SU(2)$ invariant Lagrangian that recovers the discrete $H_{SW}$ model as a stable infrared fixed point, demonstrating that the lattice architecture of current models is a fundamental emergent reality rather than a mere approximation.

   from Deriving

2. Yet, as we approach the fundamental limits of information processing, this metric assumes a more prohibitive character.

   from 1.2 The LCI Paradox:

3. However, this discrete approach fails when we attempt to describe topological protection, which is inherently a global property of the state manifold.

   from 1.3 Limitations of

4. In standard QFT, gauge symmetries dictate the form of interactions and enforce conservation laws through Noether’s theorem.

   from 1.4 The Promise of

What would falsify it

1. Our numerical scaling analysis predicts that the robustness of the LCI scales exponentially with the system size $N$ (number of workers).

   from 4.5 Scaling Laws in

Where the claim stops

1. In these scenarios, the finite-dimensional Hilbert space of the workers is sufficient to capture the relevant physics, and the “Signal” can be adequately approximated as a static potential or a hopping parameter.

   from 1.3 Limitations of

2. However, this discrete approach fails when we attempt to describe topological protection, which is inherently a global property of the state manifold.

   from 1.3 Limitations of

3. Without a continuum description, we cannot rigorously define the winding numbers or Chern classes that characterize these protected phases.

   from 1.3 Limitations of

Where to read

1. Deriving240 words · 1 min
2. 1.0 Introduction1,570 words · 7 min
3. 2.0 Methodology: The2,024 words · 9 min
4. 3.0 Results: Gauge1,727 words · 8 min
5. 4.0 Discussion:1,407 words · 6 min
6. Changelog9 words · 1 min
7. Appendices528 words · 2 min