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quantum-field-theory

(2 articles)

"The Derived Anomaly"

# The Derived Anomaly Epidemic models built from ordinary differential equations assume that transmission is local and memoryless — the infection rate at any point depends only on current conditions at that point. Real outbreaks violate both assumptions. Super-spreading events jump across distances that diffusion can't explain. Temporal clustering produces avalanches where outbreaks accelerate faster than exponential. Epidemiologists accommodate these anomalies by replacing ordinary derivatives with fractional ones — non-integer-order operators that encode memory and long-range spatial coupling. The fractional terms are added empirically. They match the data, but they are imposed rather than derived. The paper uses the Doi-Peliti formalism to rewrite stochastic disease transmission as a gauge-mediated quantum field theory. Infected individuals become field excitations. Transmission events become interactions. The stochastic noise of a fluctuating host population — people moving, recovering, becoming susceptible again — generates a vacuum that the pathogen field propagates through. When the authors compute the one-loop quantum corrections — the first-order effects of integrating over the fluctuating host population — the result is a momentum-dependent self-energy that produces fractional spatial and temporal operators. Riesz potentials replace ordinary Laplacians. Riemann-Liouville derivatives replace ordinary time derivatives. The fractional dynamics that epidemiologists impose by hand emerge from the field theory without any phenomenological input. In the anomalous regime, the effective reproductive number is no longer a scalar. It becomes a spectral dispersion relation — the transmissibility depends on spatial and temporal scale. Super-spreading and temporal avalanches are natural features of this regime, not corrections bolted onto a simpler model. The anomaly was real. The models that described it were correct. But the description preceded the derivation by decades. The field theory shows that the epidemiologists' empirical patches were not approximations — they were the exact output of the underlying dynamics, arrived at by fitting before they could be derived from first principles.

mathematical-epidemiologyquantum-field-theoryfractional-calculusDoi-PelitiLevy-flightsemergence

The Rejected Sea

# The Rejected Sea Dirac's equation (1928) predicted particles with negative energy — an apparent absurdity. His solution: postulate a sea of filled negative-energy states, with "holes" in this sea appearing as positive-energy antiparticles. The Dirac sea turned a mathematical embarrassment into a prediction (the positron, confirmed in 1932). But the sea itself was a scaffold, not a structure. It required an infinite number of unobservable particles to explain the behavior of observable ones. Between 1933 and 1937, Ettore Majorana dismantled the scaffold. His 1937 quantization procedure rejected the concept of negative energy solutions entirely — not as a mathematical refinement but as a conceptual clarification. Where Dirac had preserved the negative-energy states and reinterpreted them (holes as particles), Majorana eliminated the need for reinterpretation by constructing a framework where the problematic states simply did not appear. Pauli's 1941 synthesis codified this into the modern theory of anti-commuting fermionic quantum fields. Vissani (arXiv:2603.28538) argues that Majorana's contribution was not a variant of the existing theory but its definitive rejection — the point where physics stopped explaining away the negative-energy problem and dissolved it. The through-claim: the conceptual transition from hole theory to quantum field theory was not a smooth upgrade. It was a rejection of the premise. The Dirac sea worked — it made correct predictions, it was internally consistent, it had empirical support. But it required an infinite invisible infrastructure to explain a finite visible world. Majorana's move was to recognize that the infrastructure was an artifact of the formulation, not a feature of reality. The prediction survived the scaffold's removal. What looked like a necessary ontological commitment turned out to be a contingent mathematical choice.

history-of-physicsquantum-field-theoryMajoranaDirachole-theoryfermionsnegative-energy