Discrete symmetries of Feynman integral families correspond to permutations of Feynman parameters and induce group actions on twisted cohomology whose characters are Euler characteristics of fixed-point sets, yielding a formula for master integral counts in symmetric banana diagrams up to four loops
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A machine-checked Lean 4 formalization of Stokes' theorem on smooth singular cubes with true Fréchet pullback, chain-level extensions, and comparison to prior HOL Light work.
A new complete gauge fixing at initial data via Hodge decomposition on complete Riemannian manifolds enables existence proofs for Hadamard states in the quantization of Maxwell theory on globally hyperbolic Lorentzian manifolds.
Diagrams of Eilenberg-MacLane spaces of any height are formal over Q, implying spectral sequence collapse at page 2 for any diagram over any small category.
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Discrete symmetries of Feynman integrals
Discrete symmetries of Feynman integral families correspond to permutations of Feynman parameters and induce group actions on twisted cohomology whose characters are Euler characteristics of fixed-point sets, yielding a formula for master integral counts in symmetric banana diagrams up to four loops
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Stokes' Theorem for Smooth Singular Cubes in Lean 4: True Pullback, Bridges to mathlib4, and Chain-Level d^2=0
A machine-checked Lean 4 formalization of Stokes' theorem on smooth singular cubes with true Fréchet pullback, chain-level extensions, and comparison to prior HOL Light work.
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On the Quantisation of Linear Gauge Theories on Lorentzian Manifolds: Maxwell's Theory via Complete Gauge Fixing
A new complete gauge fixing at initial data via Hodge decomposition on complete Riemannian manifolds enables existence proofs for Hadamard states in the quantization of Maxwell theory on globally hyperbolic Lorentzian manifolds.
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On formality of diagrams of Eilenberg-MacLane spaces
Diagrams of Eilenberg-MacLane spaces of any height are formal over Q, implying spectral sequence collapse at page 2 for any diagram over any small category.
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