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 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 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 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.
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 note extends the record-classification framework into a two-dimensional lattice gauge theory by studying pure Z2 gauge theory on finite tori. Using exact diagonalization in winding sectors, the work tests how quantum information is stored, distributed, and destroyed across different gauge phases. The classification survives and becomes sharper. The constraint record becomes a topological redundancy: any enclosing loop can recover the enclosed charge parity exactly at every coupling and in every phase, as a direct consequence of Gauss's law. String records appear only where confinement localizes flux into physical strings. The toric-code sector qubit forms a matter-blind record class, preserved in the topological phase but destroyed by confinement. Across the phase diagram, different records migrate or disappear, but the constraint record remains invariant. The study also identifies an important boundary case: antipodally placed charges do not produce a missing record, but an undefined local record because degenerate winding routes prevent a unique assignment. The results show that quantum records in gauge theories are determined by the underlying constraint structure and topology. Some information becomes redundantly accessible through global constraints, some becomes localized through confinement, and some survives only as nonlocal topological information. All results are obtained through exact finite-lattice calculations with documented verification checks and reproducibility data.
This work tests the channel-erasure clause of the theory of quantum records in an interacting gauge theory. Using theta-dependent reduced states of the periodic Schwinger model, the study asks how much information can survive not merely local unitary transformations, but an entire physically defined class of noisy quantum channels. The channel class consists of operations whose Kraus operators are block-diagonal in coarse-grained eigenspaces of the observer region's energy operator. These channels preserve the corresponding energy-bin probability distribution exactly. Fidelity monotonicity then produces a rigorous lower bound on the record that no channel in the class can erase. The resulting channel-class test reveals a strong separation between two kinds of theta records. For the massive, energy-carried record, coarse-grained energy preservation guarantees that approximately 33.5% of the original record survives. For the massless, rotation-borne record, the corresponding guaranteed floor is only approximately 0.86%. The nearly 39-fold separation is reproduced at a second lattice size, while a second theta separation retains a substantial massive-record floor. More than 800 randomly generated channels satisfy the predicted protection bound with zero violations. The distinction is not controlled by the mean energy shift: the massless theory actually exhibits the larger first-moment energy difference. Protection instead depends on the distinguishability of the full preserved coarse-grained energy distributions. The study also demonstrates explicitly that protection is class-relative. Energy-preserving channels cannot cross the carrier-dependent fidelity floor, whereas an unrestricted replace-with-average channel erases both records to machine precision. Together with companion results on local-unitary reversibility, this establishes a hierarchy of record erasure: local unitaries encounter a spectral floor, energy-preserving channels can pass that floor but remain constrained by the preserved carrier distribution, and unrestricted channels can erase the record completely. The protection distinction depends on energy resolution: refinement of the spectral bins makes the chiral rotation increasingly visible in energy populations. The channel-class dichotomy established here is therefore explicitly a coarse-grained physical statement rather than an absolute energy-sector distinction. The analysis is restricted to finite-lattice compact QED at the tested coupling and subsystem sizes. Optimization over the full channel class and an analytic derivation of the resolution dependence remain open.