This work extends the theory of quantum records from free continuum field theory to an interacting gauge theory using the exactly solvable massless Schwinger model. The study asks whether the continuum record law survives when the relevant correlation length is not imposed by a bare mass but generated dynamically through the chiral anomaly. Using the open-boundary staggered lattice Schwinger model at fixed physical volume, external charge configurations are introduced through Gauss-law strings and records are quantified by the fidelity distinguishability of reduced edge states relative to the vacuum. Four main results are obtained. First, the gauge-theory record shows systematic convergence under lattice refinement. Although the available lattice sizes do not yet establish a high-precision continuum value, successive differences decrease and independent discretization schemes approach one another. Second, the record obeys an exponential lock law. Its distance dependence is extremely close to E ∼ exp(−2MD), where M = g/√π is the anomaly-generated Schwinger boson mass. Independent lattice sizes and source separations reproduce the predicted decay rate to within a few percent. Third, the record functional detects bosonization. The same physical record is calculated in the bosonized description as a Gaussian record of a free massive scalar field. The fermionic-to-bosonic record ratio decreases monotonically toward an order-one value under refinement, providing a direct information-theoretic bridge between the two descriptions. Fourth, a net-charge configuration produces a stable constraint record under refinement when its Gauss-law flux necessarily crosses the observer's region. The results show that the continuum record framework survives its first interacting gauge-theory test and that the exponential information-locking scale is controlled by a dynamically generated physical mass. The present study is restricted to the 1+1-dimensional massless Schwinger model, finite lattice sizes, integer external charges, and open boundaries. Higher-dimensional gauge theories and the full continuum extrapolation remain open.
This work extends the theory of quantum records from free continuum field theory to an interacting gauge theory using the exactly solvable massless Schwinger model. The study asks whether the continuum record law survives when the relevant correlation length is not imposed by a bare mass but generated dynamically through the chiral anomaly. Using the open-boundary staggered lattice Schwinger model at fixed physical volume, external charge configurations are introduced through Gauss-law strings and records are quantified by the fidelity distinguishability of reduced edge states relative to the vacuum. Four main results are obtained. First, the gauge-theory record shows systematic convergence under lattice refinement. Although the available lattice sizes do not yet establish a high-precision continuum value, successive differences decrease and independent discretization schemes approach one another. Second, the record obeys an exponential lock law. Its distance dependence is extremely close to E ∼ exp(−2MD), where M = g/√π is the anomaly-generated Schwinger boson mass. Independent lattice sizes and source separations reproduce the predicted decay rate to within a few percent. Third, the record functional detects bosonization. The same physical record is calculated in the bosonized description as a Gaussian record of a free massive scalar field. The fermionic-to-bosonic record ratio decreases monotonically toward an order-one value under refinement, providing a direct information-theoretic bridge between the two descriptions. Fourth, a net-charge configuration produces a stable constraint record under refinement when its Gauss-law flux necessarily crosses the observer's region. The results show that the continuum record framework survives its first interacting gauge-theory test and that the exponential information-locking scale is controlled by a dynamically generated physical mass. The present study is restricted to the 1+1-dimensional massless Schwinger model, finite lattice sizes, integer external charges, and open boundaries. Higher-dimensional gauge theories and the full continuum extrapolation remain open.
This work tests whether the theory of quantum records survives the transition from finite lattice models to continuum quantum field theory. Using a free scalar field in 1+1 dimensions with two histories differing by a localized classical source, the record accessible to a spatial region is expressed exactly through the fidelity of equal-covariance Gaussian states. Four principal results are established. First, the continuum record functional is verified against direct truncated-Fock-space Uhlmann fidelity calculations with agreement at approximately 10^−10. Second, the lattice record converges monotonically toward the exact continuum mode-sum result under refinement from 256 to 2048 lattice sites, demonstrating that the framework is not a lattice artifact. Third, a continuum lock law is found: record evidence measured a distance L from a localized source decays as exp(−2mL), with the fitted decay rate agreeing with 2m to high precision. This identifies the finite-volume suppression observed in earlier discrete models as the lattice manifestation of a continuum correlation-length law. Fourth, the distinction between constraint records and arrangement records survives the continuum limit. As the screening length diverges, the ratio between net-charge and zero-charge rearrangement records grows approximately as 1/m², causing the constraint-class record to dominate without bound. An exploratory study of disjoint regions also finds uniformly subadditive record evidence, consistent with redundant access to a common source through continuum vacuum correlations. The results establish the first continuum realization of the record framework in an exactly controlled quantum field theory. The present analysis is restricted to a free scalar field in 1+1 dimensions and coherent mean-shift histories; interacting fields, gauge theories, massless limits, higher dimensions, and gravity remain open.
This note removes the open-boundary constraint from the lattice Schwinger model and studies the periodic theory with its physical Wilson-line zero mode. The goal is to determine which features of the previous lattice results belong to the gauge theory itself and which were caused by the boundary. Using exact diagonalization of the periodic lattice model with fermions and flux degrees of freedom, the study reveals four main results. The transition is restored: the mass-gap collapse and the critical response reappear, with the mass-direction evidence developing an interior peak near the transition region. The θ-lock is recovered at zero fermion mass, with the sector energy sensitivity strongly reduced compared with the open-boundary case, while the mass-induced unlock follows the expected perturbative behavior and becomes critically enhanced near the transition. The transition-amplifier law also returns: sector evidence grows monotonically with the mass deformation, showing that the open-boundary inversion was a boundary artifact caused by pinning both sectors to a single vacuum. The central result is a record-migration law. In the massless theory, the θ-record is stored mainly in matter correlations and can be accessed through charged endpoints of spatial cuts. In the massive broken phase, the record moves into the topological flux sector: the competing vacua differ by a Wilson-loop flux, making the information invisible to purely matter-based local observers. This establishes how the location of quantum information changes across phases of an interacting gauge theory: symmetry breaking does not only create records, it determines who can access them. The results are obtained within the finite periodic lattice framework, with bounded system sizes, rotor truncation checks, and no continuum extrapolation.
This work synthesizes the gauge-theory branch of the quantum-record program and derives a quantitative relation between record irreversibility and Fisher information. The paper first corrects an interpretation from an earlier study of theta records. At a finite angular separation, the fraction of the record that could not be removed by local unitaries was approximately one half in both the massless and massive Schwinger models. The present tangent-space analysis shows that this apparent mass independence was a finite-angle coincidence. In the small-parameter-separation limit, the local-unitary floor is instead governed by a Fisher-information law: E = d²F_Q/8, E_spec = d²F_cl/8, and therefore E_spec/E = F_cl/F_Q, where F_Q is the quantum Fisher information and F_cl is its population, or diagonal, contribution in the eigenbasis of the reduced state. The relation is verified numerically to four decimal places at two mass values, two expansion centers, and two step sizes. The resulting floor fractions are approximately 0.639 in the massless theory and 0.495 in the massive theory. Operationally, the result states that the fraction of a parameter record that no local unitary can erase is precisely the fraction of its Fisher information encoded in eigenvalue populations rather than eigenvector rotations. The paper also consolidates eleven companion studies into a single gauge-record classification. Twenty-nine previously frozen numerical results spanning continuum field theory, interacting gauge theory, boundary conditions, theta physics, symmetry breaking, criticality, and non-Abelian center charge are audited against the general record principle. All twenty-nine are found to be mutually consistent. The resulting classification separates protected carriers—including Gauss flux, zero modes, energy, emergent conserved structures, and center charge—from erasable information classes such as arrangements, reference-frame orientation, and finite-size screening remnants. A final SU(3) diagnostic further localizes a previously observed quark–antiquark residual asymmetry. The effect appears only in the screened regime and only for one string convention, strongly indicating that it originates in the geometry of the screening cloud on the string side, although an analytic derivation remains open. The Fisher relation is demonstrated numerically in the present system rather than proven as a general operator theorem. Establishing that general theorem is the natural next theoretical step.
We introduce the \emph{flavoured lattice Schwinger model}, a (1+1)-dimensional U(1) lattice gauge theory in which the fermion doubling problem is resolved by staggering a Z2 flavour degree of freedom rather than staggering chirality. Unlike the standard approaches, this construction preserves an exact axial U(1) symmetry at finite lattice spacing. We derive the continuum limit, showing that the model reduces to the \emph{two-flavour} massless Schwinger model, with flavours α∈{0,1} sharing one dynamical U(1) gauge field. The central result is a well-defined, regularised, gauge-invariant lattice axial charge QGA whose continuum non-conservation ⟨dQGA/dt⟩=−(2g/π)∫dx⟨E(x)⟩ arises as a direct dynamical consequence of minimal gauge coupling. A particle-hole transformation on the χ flavour exposes a hidden UL(2)×UR(2) chiral symmetry; non-Abelian bosonisation then identifies the model with a massive abelian Schwinger sector tensored with the level-1SU(2) Wess--Zumino--Witten model. Finally, we show that embedding the flavoured fermions in a ribbon-shaped (2+1)D Bernevig--Hughes--Zhang topological insulator and gauging the bulk in a constant background field factorises the boundary theory into \emph{two decoupled} single-flavour Schwinger models, one on each edge, identifying the lattice factor of 2 as one quantum of Schwinger anomaly per edge.
This work extends the continuum theory of quantum records from 1+1 dimensions to 2+1 and 3+1 dimensions, where long-range fields, asymptotic charges, and gravitational information become physically relevant. Using Gaussian free fields in finite Dirichlet boxes, the study computes the exact fidelity-based record retained by spatial regions for localized charge and dipole histories. Five principal results are obtained. First, the exponential lock law survives dimensional extension: record evidence at distance L decays approximately as exp(−2mL) in both 2+1 and 3+1 dimensions. Second, the long-range charge record behaves qualitatively differently with dimension. As the mass is reduced toward the Coulomb regime, the 3+1-dimensional charge record approaches a finite value, while the corresponding 1+1-dimensional record diverges. The 2+1-dimensional behavior lies between these cases. Third, the study finds that finite Dirichlet boundaries are not passive. They behave as grounded walls carrying image charge and therefore retain part of the physical record. Boundary ownership is present in every tested dimension but is weakest in 3+1 dimensions. When the correlation length becomes short enough that the walls are Yukawa-screened, the boundary dependence nearly disappears. Fourth, charge records increasingly dominate dipole or rearrangement records with distance. Finite boundaries and finite mass both reduce this multipole distinguishability, providing two distinct mechanisms for record erasure. Fifth, lattice refinement shows clean convergence toward the continuum result. The results provide a controlled higher-dimensional realization of the record framework and show that finite long-range charge memory naturally emerges in 3+1 dimensions. They also reveal a concrete mechanism by which information not retained locally in the bulk can be carried by the boundary. The present model uses free fields, coherent histories, and grounded Dirichlet boundaries. It does not compute dynamical gravity; insulating boundaries, interacting theories, asymptotic limits, and gravity remain open problems.
Quantum Darwinism explains classical objectivity through the redundant proliferation of records in an environment. This note studies that mechanism inside a gauge theory, where Gauss's law constrains which records can exist and where they can be stored. Using exact lattice Schwinger model calculations with both open and periodic boundaries, including the Wilson-line rotor, this work shows that record redundancy is determined by the relation between information and gauge constraints. Three fundamental record classes are identified. First, unscreenable charges produce perfectly redundant records: every accessible downstream region can read the same information because the constraint itself distributes the record without requiring copying dynamics. Second, screened charges produce bilocal records, with information divided between the screening cloud and the boundary-delivered image while intermediate regions remain blind. Third, symmetry-breaking order produces graded redundant records, while topological flux records represent the opposite extreme: globally distinguishable but invisible to local matter fragments. The study also reveals a constraint-induced discordant split. In the flux sector, mutual information can remain large while readable evidence is almost absent, showing that a gauge theory can contain correlations that no local fragment can convert into classical information. The central conclusion is that classical objectivity in gauge theories is not determined only by environmental interaction. It is controlled by the structure of the constraints: Gauss's law decides which records can be broadcast, localized, or hidden. All results are obtained through exact diagonalization with independent verification checks and documented numerical convergence tests.