5 papers
Why the Bethe Ansatz Works: A Structural Explanation via Interaction Propagation
Joe Gildea
The Bethe Ansatz provides exact solutions for certain interacting quantum many-body systems, yet its success is confined to narrow regimes and breaks down abruptly outside them. De…
Algebraic Phase Theory IV: Morphisms, Equivalences, and Categorical Rigidity
Joe Gildea
We complete the foundational architecture of Algebraic Phase Theory by developing a categorical and -categorical framework for algebraic phases. Building on the structural notio…
Algebraic Phase Theory III: Structural Quantum Codes over Frobenius Rings
Joe Gildea
We develop the quantum component of Algebraic Phase Theory by showing that quantum phase, Weyl noncommutativity, and stabiliser codes arise as unavoidable algebraic consequences of…
Algebraic Phase Theory II: The Frobenius Heisenberg Phase and Boundary Rigidity
Joe Gildea
We develop the representation theory intrinsic to Algebraic Phase Theory (APT) in regimes where defect and canonical filtration admit faithful algebraic realisation. This extends t…
Algebraic Phase Theory I: Radical Phase Geometry and Structural Boundaries
Joe Gildea
We develop Algebraic Phase Theory (APT), an axiomatic framework for extracting intrinsic algebraic structure from phase based analytic data. From minimal admissible phase input we…