Yuri N. Berdinsky

Henstock-Kurzweil Path Integrals for Open Quantum Systems: Bosonic and Fermionic Reservoirs — A Machine-Verified Approach

We unify the Henstock-Kurzweil treatment of open quantum systems with bosonic Gaussian reservoirs and fermionic Grassmann reservoirs. Finite cylindrical gauge integrals yield determinant and covariance identities for bosons, while Berezin integration yields Pfaffian identities fo...

Henstock-Kurzweil Path Integrals for Open Quantum Systems: Bosonic and Fermionic Reservoirs — A Machine-Verified Approach

We unify the Henstock-Kurzweil treatment of open quantum systems with bosonic Gaussian reservoirs and fermionic Grassmann reservoirs. Finite cylindrical gauge integrals yield determinant and covariance identities for bosons, while Berezin integration yields Pfaffian identities fo...

Gribov Copies and Gauge Invariance: A Henstock–Kurzweil Continuum Integral on the SU(3) Lattice

The Feynman functional integral of a non-Abelian gauge theory has a Gribov ambiguity: the Landau gauge condition has several solutions on one orbit, the Gribov copies. The gauge-fixed integral is usually defined by restriction to a surface, corrected by the Faddeev–Popov determin...

Construction of Kuelbs–Steadman Spaces and Gauge Closure of the Feynman Functional Integral in Lean 4

This report completes the three missing ingredients of the infinite-dimensional Henstock–Kurzweil (HK) programme, and machine-checks all of them in Lean 4 with Mathlib. First, the Kuelbs–Steadman space KS₂ is constructed concretely as the separable real Hilbert space H carried by...