Mathematical Physics

    

Alpha Integration: Universal Path Integrals with Gauge Invariance

Authors: YoonKi Kim

We introduce Alpha Integration, a novel path integral framework that applies to wide range of function including locally integrable functions, distributions, and fields—across arbitrary spaces and n dimensions (n ∈N), while preserving gauge invariance without approximations. This method extend to Rn(n ∈N), smooth manifolds, infinite-dimensional spaces, and complex paths, enabling rigorous integration of all f ∈Du2032 with formal mathematical proofs. This framework is further generalized to infinite-dimensional spaces, complex paths, and arbitrary manifolds,with its consistency validated through extensive testing across diverse functions, fields, and spaces. Alpha Integration thus offers a robust and efficient alternative to traditional path integral techniques, serving as a versatile tool for mathematical and physical analysis.

Comments: 23 Pages. Contact email: yk.reserch@gmail.com

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Submission history

[v1] 2025-03-13 21:05:08 (removed)
[v2] 2025-03-18 20:46:03

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