Yuri N. Berdinsky

Infinite-Dimensional Localization of the Yang-Mills Functional Integral on the Gribov Region: Complex Kuelbs-Steadman Premeasures and a Gauge Bypass of the Singer Barrier

This is the ninth paper of a programme constructing the Feynman functional integral without a Wick rotation, based on the non-absolutely convergent Henstock–Kurzweil (HK) integral and on Kuelbs–Steadman spaces. The subject here is the non-abelian continuum: the configuration spac...

The First Gribov Region, BRS Symmetry and Slavnov-Taylor Identities in the Truncated Henstock-Kurzweil Yang-Mills Theory

This is the seventh paper of the programme devoted to the construction of the Feynman functional integral without Wick rotation, based on the non-absolutely convergent Henstock–Kurzweil (HK) integral and on Kuelbs–Steadman spaces. In the truncated Yang–Mills theory on TL3×Sβ1TL3×...

Normalized CutOut in the Non-Abelian Continuum Henstock–Kurzweil Integral: The Cartan Class of Configurations and zeta-Regularization of the Faddeev–Popov Determinant

This is the tenth paper of a programme constructing the Feynman functional integral without a Wick rotation, based on the non-absolutely convergent Henstock–Kurzweil (HK) integral and on Kuelbs–Steadman spaces. Its predecessor formalized the finite-mode non-abelian continuum and...

The Yang–Mills Functional Integral on Finitely Many Fourier Modes on the Torus T⁴ as a Henstock–Kurzweil Path Integral: Gauge Fixing, the Ghost Sector, and Gribov Copies

This is the fifth paper of the programme constructing the Henstock–Kurzweil (HK) functional integral without Wick rotation, and the first in which the bosonic sector, the ghost sector and the oscillating premeasure are combined in a single formula. The price of this combination i...

The Yang–Mills Functional Integral at Finite Temperature as a Henstock–Kurzweil Path Integral: Matsubara Mode Decomposition and Gribov Copies

This is the sixth paper of the programme in which the Feynman functional integral is constructed without a Wick rotation, by means of the non-absolute Henstock–Kurzweil (HK) gauge integral. Here the Yang–Mills functional integral is built at finite temperature, on the product T³_...

The Yang–Mills Functional Integral at Finite Temperature as a Henstock–Kurzweil Path Integral: Matsubara Mode Decomposition and Gribov Copies

This is the sixth paper of the programme in which the Feynman functional integral is constructed without a Wick rotation, by means of the non-absolute Henstock–Kurzweil (HK) gauge integral. Here the Yang–Mills functional integral is built at finite temperature, on the product T³_...

Algebraic Completeness of Feynman Premeasures: The Henstock–Kurzweil Path Integral and Operator Wick Calculus in Lean 4

This work brings the gauge closure of the Feynman functional integral for the free field, without Wick rotation, into machine-verified form. First, the restriction to box divisions of cylinders is removed: a direction bound is proved, showing that every nonempty cylindrical cell...

The Faddeev–Popov Determinant and the Henstock–Kurzweil Path Integral: Berezin Representation, Spectral Limit, and Gribov Copies

This is the fourth paper of the programme constructing the Feynman path integral as a Henstock–Kurzweil (HK) integral without a Wick rotation, and the first one dealing with the gauge (ghost) sector of a non-abelian theory. The Faddeev–Popov determinant is constructed as an algeb...

Self-Referential Universe: Ontology of the Unified Field, the Role of the Subject, and the Mathematical Nature of Qualia

The monograph proposes a unified ontological framework in which fundamental physics, metaphysics, and the cognitive sciences are treated as three interconnected descriptions of a single self-referential structure of reality. The phenomenon of subjective experience has traditional...

Self-Referential Universe: Ontology of the Unified Field, the Role of the Subject, and the Mathematical Nature of Qualia

The monograph proposes a unified ontological framework in which fundamental physics, metaphysics, and the cognitive sciences are treated as three interconnected descriptions of a single self-referential structure of reality. The phenomenon of subjective experience has traditional...