Year: 2025
Type: article
Abstract: This work establishes the first derivation of geometry-dependent Kirchhoff’s laws via conformal symmetry, enabling new types of self-sustaining circuits unattainable in classical lumped-element theory. Building on Bessel-Hagen’s extension of Noether’s theorem to Maxwell’s equations, we develop a conformal circuit formalism that fundamentally extends traditional circuit theory through two key innovations: (1) Geometry-dependent weighting factors (wi∝ai−1) in Kirchhoff’s laws derived from scaling symmetry; (2) A dilaton-like field (δ) mediating energy exchange between circuits and conformal backgrounds. Unlike prior symmetry applications in electromagnetism, our approach directly maps the 15-parameter conformal group to component-level circuit transformations, predicting experimentally verifiable phenomena: (i) 10.2% deviations from classical current division in RF splitters; (ii) 4.2% resonant frequency shifts with 2.67× Q-factor enhancement; (iii) Power-law scaling (Jz∝a−2) in cylindrical conductors. This theoretical framework proposes how conformal symmetry could enable novel circuit behaviors, including potential self-sustaining oscillations, subject to experimental validation.
Source: Applied Sciences
DOI: 10.3390/app15179333
Author: Mario J. Pinheiro
Institutions: University of Lisbon, Instituto Superior Técnico
Language: English
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $2,896
OpenAlex ID: W4413619803