11 papers
What do position and time mean in the quantum wavefunction?
Mustafa Bakr, Zichi Zhang, Margot Stakenborg
The notation is among the first pieces of quantum mechanics that students learn. It is also among the easiest to over-interpret. Because and occur as arguments of…
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…