arXiv subjects

Tongyu Zhang

Publications and source records attributed to Tongyu Zhang.

3 recordsLinked to original sources

arXiv2026

Scalar Finite-Proper-Time Field Theory as Spectral Operator Calculus

We formulate a finite-proper-time construction for Euclidean scalar $\lambda\phi^4$ theory in which a retained endpoint $s_0$ is assigned to complete internal histories rather than independently to individual Schwinger segments. The theory is defined through paired open and closed spectral functions and their Fr\'echet/Duhamel hierarchy. Functional differentiation inserts operators along an existing proper-time history and partitions its total length, while interaction vertices sew separately complete histories. We introduce a corresponding complete-history diagrammatic calculus and derive the resulting one- and two-loop structures. We distinguish the retained endpoint from an auxiliary regulator or renormalisation-group scale and test whether its effects survive ordinary parameter matching and admissible field redefinitions. For the one-loop four-point function, fixing the renormalised mass, field normalisation, and quartic coupling leaves a finite momentum-dependent remainder. We establish a perturbative non-redundancy description of the retained endpoint against finite renormalisable-parameter redefinitions and local $S$-matrix-preserving field redefinitions at this order. The low-energy theory can be represented as an effective field theory, but its higher-derivative coefficients are not independent. This provides a concrete distinction between a retained finite proper-time scale and an arbitrary cutoff prescription.

hep-th↗

arXiv2025

Electromagnetic Modes in Spherical Cavities: Complete Theory of Angular Spectra, Dispersion Relations, and Self-Adjoint Extensions

We present a complete theory of electromagnetic modes in spherical cavities, resolving fundamental questions about the nature of angular quantization. The standard result that angular indices $(\ell,m)$ must be integers is shown to be a consequence of domain constraints -- regularity at both poles and single-valuedness in the azimuthal coordinate -- rather than a requirement imposed by Maxwell's equations themselves. We prove that, for the sectoral case $ν=m$, the function $\sin^{m}θ$ exactly solves the angular eigenvalue equation for any real $m>0$, giving rise to a continuous dispersion curve. We demonstrate why non-sectoral modes (tesseral and zonal) appear only at isolated integer points on the full sphere, and show how boundary modifications such as cones and wedges convert these isolated points into continuous families of modes. Complete field solutions, wave impedances, and energy integrability conditions are derived. At the limiting point $(ν, m) = (0, 0)$, the electromagnetic field vanishes identically while the underlying Debye potential remains non-trivial -- a distinction with implications for mode counting that connects to longstanding questions in gauge theory and cavity quantization. Full-wave simulations validate the theoretical predictions with sub-percent accuracy. These results raise the possibility of structural analogues in wave equations on curved spacetimes, where conical deficits or horizon excisions similarly modify the angular domain.

math-ph↗

arXiv2024

Discontinuities in the Evolution of Properties of Kerr Black Holes in the Extremal Limit

Ever since its discovery by Roy Kerr in 1963, the geometry around rotating, electrostatically-neutral black holes, otherwise known as Kerr black holes, has significantly contributed to theoretical developments in the fields of general relativity, thermodynamics and beyond. Extremal Kerr black holes, in which the spin parameter of the rotating black hole is at a maximum without breaching certain postulates, has especially been of interest to the research community due to its sensitivity to higher order corrections to Einstein's theory of relativity. In this paper, we review some unresolved open questions regarding the discontinuity of certain properties of the Kerr black hole as it approaches the extreme limit. These include the form of the innermost stable circular orbit (ISCO), the nature of vanishing entropy, and the disappearance of the trapped surface as a Kerr black hole approaches extremality. We conclude that current theories are likely not suitable for studies of extremal black holes, and we posit that further development in theory may likely require a quantum approach to gravity. G=c=1 and Einstein summation convention are assumed throughout this paper.

gr-qc↗