@article{Wu2025, 
author = {Tong Wu and Yong Wang},
title = {The semiclassical limit of the Kastler–Kalau–Walze-type theorem},
year = {2025},
journal = {Electronic Research Archive},
volume = {33},
number = {4},
pages = {2452-2474},
keywords = {the semiclassical limit, the noncommutative residue, the perturbations of the Dirac operator, the Kastler–Kalau–Walze-type theorem},
url = {https://www.sciopen.com/article/10.3934/era.2025109},
doi = {10.3934/era.2025109},
abstract = {In physics, the semiclassical limit principle asserts that as Planck's constant    ℏ  →  0, quantum states reduce to classical configurations. We extend this framework to the noncommutative residue by applying the semiclassical limit to the spectral geometry. By introducing the coefficient    ε, we establish a proof of the Kastler–Kalau–Walze-type theorem for the perturbations of the Dirac operator on four-dimensional compact manifolds with (without) boundary. As    ε  →  0, we demonstrate the emergence of a semiclassical limit, thereby providing the classical formulation of the theorem. This result elucidates the interplay between quantum corrections and classical geometric invariants in the presence of boundary conditions.}
}