10 papers
Scalar Finite-Proper-Time Field Theory as Spectral Operator Calculus
Mustafa Bakr, Tongyu Zhang
We formulate a finite-proper-time construction for Euclidean scalar theory in which a retained endpoint is assigned to complete internal histories rather than independ…
Minimum Virtual Proper Time and Finite Mass--Charge Matching in QED
Mustafa Bakr
We formulate a finite-proper-time version of QED defined by a gauge-covariant generating functional in which every complete internal virtual history carries a physical lower endpoi…
The Zero-Frequency Limit of Spherical Cavity Modes: On the Formal Endpoint at v=1
Mustafa Bakr, Smain Amari
The transverse magnetic (TM) modes of a spherical cavity satisfy a dispersion relation connecting the angular eigenvalue to the resonant frequency through zeros of the spheric…
Group-Theoretical Origin of the Sectoral-Tesseral-Zonal Trichotomy in Spherical Harmonics
Mustafa Bakr, Smain Amari
The spherical harmonics fall into three families -- sectoral (), tesseral (), and zonal () -- which exhibit fundamentally different be…
Electromagnetic Modes in Spherical Cavities: Complete Theory of Angular Spectra, Dispersion Relations, and Self-Adjoint Extensions
Mustafa Bakr, Tongyu Zhang, Smain Amari
We present a complete theory of electromagnetic modes in spherical cavities, resolving fundamental questions about the nature of angular quantization. The standard result that angu…
Quantum Mechanics in a Spherical Wedge: Complete Solution and Implications for Angular Momentum Theory
Mustafa Bakr, Smain Amari
We solve the stationary Schrödinger equation for a particle confined to a 3D spherical wedge -- the region …