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E. J. Thompson

Publications and source records attributed to E. J. Thompson.

15 recordsLinked to original sources
arXiv2026

On the Four-Loop Higgs--Gluon Form Factor in Nonlocal Quantum Field Theory

In particle physics the virtual N$^3$LO contribution to gluon-fusion Higgs production in the Standard Model requires four-loop multi-scale QCD amplitudes that in dimensional regularization are dominated by singular integral reduction and difficult master-integral evaluations. In this note we show that a nonlocal UV completion makes each fixed-order four-loop Feynman diagram fully convergent in four dimensions while keeping the analytic structure needed for Lehmann-Symanzik-Zimmermann (LSZ) reduction formula. For gluon-fusion $gg\!\to\!H$ we derive a closed form Schwinger-parameter representation where all loop-momentum integrals are performed analytically and thus leaving finite parameter integrals viable for direct numerical evaluation without needing the usual UV subtractions. This method heps to isolate the collider-hard contribution as a convergent four-loop form factor. The strong coupling then is defined by a finite normalization condition in the entire-function regularization scheme and it is related to the $\overline{\mathrm{MS}}$ coupling by finite matching where after this matching, the regulator-dependent corrections decouple in the local limit $E_M\!\to\!\infty$.

hep-ph↗
arXiv2026

Can a Local Quantum-Mechanical Description of Physical Reality Be Considered Complete?

In a complete quantum theory, one would construct it based on what we can observe in a system and operationally define in our universe. This philosophy goes back to some of the original ideals of quantum theory defined by W. Heisenberg, N. Bohr, and others as part of the Copenhagen school of thought. We argue in this letter that that if one wishes to construct a complete quantum field theory, that it is most natural to construct it based on a nonlocal theory of observable principles. If this interpretation is valid, then the one-particle nonrelativistic limit that recovers quantum mechanics would as well be dynamically nonlocal. In this interpretation we derive the nonlocal Schr\"odinger equation. We will as well demonstrate that the canonical position--momentum commutator and the Heisenberg uncertainty principle emerge from translation covariance.

quant-ph↗
arXiv2026

A First Bound on the Moffat Energy and Thorium-229 Clock as a Probe of the Nonlocal Time-Energy Structure and a Proposed Experiment for the use of Nuclear Entanglement and Squeezed States to Test Nonlocal Quantum Field Theory

In this paper we derive the nonlocal Time-Energy uncertainty principle and then apply the published $^{229}$Th nuclear clock data as a first probe of the nonlocality scale \(E_M\). By using the direct clock-energy channel, we find conservative lower bounds on \(E_M\) at the tens of MeV scale, with optimistic present-data estimates reaching the hundred MeV scale. Including the known nuclear sensitivity enhancement of the $^{229}$Th transition gives us stronger model dependent bounds in the GeV range, while nuclear-scale reference-energy scenarios can reach the TeV range. The conclusion we draw from this is that nuclear clocks already provide an experimental route from nonlocal time--energy uncertainty to measurable laboratory bounds on non-Planckian nonlocality. We explore the idea of using a squeezed-state experiment with the $^{229}\mathrm{Th}$ nuclear clock to test the time--energy structure of nonlocal quantum field theory. The idea is reasonably obtainable within the near future of nuclear clock experiments. One would prepare an ensemble of thorium nuclei in a coherent superposition of the nuclear ground state and the low-lying isomeric clock state, entangle the participating nuclei through a collective interaction, and generate a family of spin-squeezed states with a tunable squeezing parameter $r$. Then a phase-controlled analysis pulse will rotate the selected collective nuclear quadrature into a measurable ground-isomer population difference. Near a strongly polarized collective state the normalized operators $J_y/\sqrt{S}$ and $J_z/\sqrt{S}$ obey the same approximate canonical algebra as the phase and amplitude quadratures of a squeezed optical mode. We use this experiment to either probe or bound the nonlocal energy scale $E_M$.

quant-ph↗
arXiv2026

De Sitter Cores from Nonlocal Quantum Field Theories

Nonlocal quantum field theories achieve perturbative ultraviolet finiteness by inserting gauge- and diffeomorphism-covariant entire-function regulators into all kinetic terms. These operators can be viewed as nonlocal smearing maps acting on sources in the Einstein equations. In this paper I show that, when the same entire-function regulator responsible for UV-finite loops is applied to the energy-momentum tensor of a point mass, the resulting static, spherically symmetric solution develops a regular de~Sitter core in place of a curvature singularity.

physics.gen-ph↗
arXiv2026

An inquiry into the Absence of Fermion Doubling and why the Nielsen-Ninomiya Theorem Does Not Apply to Nonlocal Quantum Field Theory

In this paper we will examine if nonlocal quantum field theory will suffer from the fermion doubling pathology. We find that for a nonlocal Dirac theory, that no additional fermion species are introduced. This is provided that the form factor is nonvanishing at every point. The proof follows from the invertibility of the entire-function operator, which implies that the nonlocal Dirac operator has exactly the same kernel and finite-momentum zero set as the original local Dirac operator. We will distinguish this result from the standard Nielsen-Ninomiya theorem, which applies local lattice fermions on a compact Brillouin zone. We provide a general criterion for fermion doubling, a test for genuine and false doubling, and then a test procedure for mathematical and physical fermion doubling. We then will go on to distinguish this result from finite derivative truncations, which can introduce spurious polynomial zeros. We then conclude that fermion doubling is absent in the full continuum nonlocal theory.

hep-th↗
arXiv2026

On the Meaning of Localization in Non-Local Quantum Field Theory and On the Limits of a Space-Time Description and the Physical Meaning of Phase Space in a Nonlocal Continuum

First: In this paper we explore and derive an uncertainty principle for an ultraviolet complete nonlocal quantum field theory where under our hypothesises of an induced equal time detector response kernel, we then prove that the observed localization width obeys an exact variance addition law. Then when we combine this with the ordinary Heisenberg inequality and we obtain a nonlocal uncertainty relation. The bound reduces to the usual local relation in the infrared or local limit when $E_M \to \infty$, while in the ultraviolet it implies a minimal localization length of order $L_M$. We go on to explain what this means for locality, microcausality, the interpretation of spacetime points, and the ultraviolet structure of quantum field theory. In this formulation we note and prove that spacetime will remain a Lorentz covariant continuum at the level of the manifold description but pointlike localization ceases to be a physically realizable observable notion below the nonlocality scale. Second: In a previous paper we derived an uncertainty relation for nonlocal fields by showing that the physical localization width in nonlocal quantum field theory is broadened by the response kernel generated from the entire-function regulator. In this follow up we will reinterpret that result as just the position-sector limit of a more symmetric statement as we did not take into account the inherent nonlocality of momentum. We find under normalized, centered response kernels for both position and momentum, we prove the variance laws and derive the corresponding nonlocal phase-space uncertainty relation. The result still preserves the conclusions of the original paper all while strengthening the interpretation as nonlocal quantum field theory implies not merely a minimal measurable length, but a finite phase-space cell. We also explore experimental routes to test the theory.

physics.gen-ph↗
arXiv2026

On the Standard Model Mass Spectrum and Interactions In the Holomorphic Unified Field Theory

We present a unified, ultraviolet-finite framework for the full Standard Model particle mass spectrum based on the Holomorphic Unified Field Theory augmented by nonlocal entire-function regulators. Starting from a single holomorphic action on the complexified spacetime manifold \( M^4_{\mathbb{C}} \), with a Hermitian metric unifying gravity, gauge, and matter sectors, we embed exponential regulator insertions to render all loop integrals finite without breaking gauge or diffeomorphism invariance. After spontaneous breaking of the electroweak and grand unified symmetries, analytic expressions for the charged lepton, quark, and neutrino mass matrices are derived in terms of holomorphic Yukawa textures and regulator form factors. A minimal Froggatt-Nielsen flavon sector fixes all \( \mathcal{O}(1) \) coefficients in terms of two continuous inputs. Regulator-suppressed one- and two-loop renormalization group evolution then yields predictions for all fermion masses, CKM and PMNS mixing angles, \( W \) and \( Z \) boson masses, and the Higgs boson mass and self-couplings. Finally, under a mild set of geometric and topological assumptions we show that gauge coupling unification, three chiral families, hypercharge quantization, and the shape of the Higgs potential are genuine predictions of the holomorphic nonlocal framework.

hep-ph↗
arXiv2026

On the Invariant and Geometric Structure of the Holomorphic Unified Field Theory

We present the invariant structure of a Holomorphic Unified Field Theory in which gravity and gauge interactions arise from a single geometric framework. The theory is formulated using a product principal bundle, with one connection, and curvature equipped with a Hermitian field on a complexification of spacetime. From a single $\mathrm{Diff}(M)\times G$-invariant action, variation yields the Einstein and Yang-Mills equations together with their paired Bianchi identities. A compatibility condition is implemented either definitionally or through an auxiliary penalty functional. It enforces that the antisymmetric part of our Hermitian field is the gauge field's exact curvature on the real slice.

physics.gen-ph↗
arXiv2026

$\mathbb Z_2$-Stable Dark Matter via Broken $\text{SU}(5)$ Gauge Bosons

I construct and analyze a dark matter sector that is neutral under the unbroken Standard Model gauge group and couples only to the broken $\text{SU}(5)$ gauge directions, the leptoquark vectors $X,Y$. An exact $\mathbb Z_2$ renders the dark matter stable. I give a gauge-covariant definition of projectors onto the unbroken Standard Model and broken ($X,Y$) subspaces, demonstrate that the covariant derivative of dark matter selects only $X,Y$, and integrate out $X,Y$ at tree level to obtain the leading effective operators. I also derive the loop-induced $χ^2\,G^a_{μν}G^{aμν}$ coupling to gluons, prove color neutrality, and show consistency with cold dark matter phenomenology. Cosmological production proceeds via UV freeze-in or even more suppressed channels in.

hep-ph↗
arXiv2026

On the Complexified Spacetime Manifold Mapping of AdS to dS

In a complex manifold, one can bridge anti-de Sitter and de Sitter spacetimes via analytic continuation, preserving geometric invariants and regularity, avoiding singularities during the AdS-dS transition. It unifies gravitational and gauge interactions under a complexified symmetry group, maintaining bulk unitarity for both AdS and dS. Boundary unitarity is upheld in AdS but not in dS due to the spacelike conformal boundary. The theory uses holographic principles like the MacDowell-Mansouri and Quantum Extremal Surface prescriptions to align entanglement and black hole entropy with AdS/CFT and general relativity. HUFT provides insights into AdS and dS holography, the cosmological constant, and quantum gravity unitarity and entanglement.

gr-qc↗
arXiv2025

On Gauge-Invariant Entire-Function Regulators and UV Finiteness in NonLocal Quantum Field Theory

In this paper we clarify the status of gauge invariant entire function regulators in NonLocal Quantum Field Theory, in this the regulator is implemented as an entire function of the covariant Laplace--Beltrami operator. Working in the background-field formalism and expanding around flat, trivial backgrounds, we show that plane waves diagonalize the d'Alembertian so that the entire function reduces to a multiplicative form factor in Minkowski momentum space. After Wick rotation to the Euclidean axis, this produces exponential ultraviolet damping in loop integrals without introducing additional poles or branch cuts. Our analysis provides a gauge covariant justification for the use of entire function regulators in nonlocal quantum field theory.

hep-th↗
arXiv2025

Finite Nonlocal Holomorphic Unified Quantum Field Theory

In this paper the non-local finite quantum-gravity framework is incorporated into the Complex non-Riemannian Holomorphic Unified Field Theory formulated on a complexified four-dimensional manifold. By introducing entire-function regulators $F(\Box) = \exp\!\bigl(\Box / M_*^2\bigr)$ into the holomorphic Einstein-Hilbert action, we achieve perturbative UV finiteness at all loop orders, while preserving BRST invariance and holomorphic gauge symmetry. We derive the modified gauge-gravity coupling sector, perform a one-loop effective-action computation in a contour-regularized metric background, and demonstrate the absence of new counterterms and problematic complex-pole structures. Extending the construction to nontrivial curved backgrounds, we verify infrared recovery of General Relativity and full holomorphic gauge invariance. Finally, we explore phenomenological consequences, including corrected graviton and gauge-boson scattering amplitudes in self-dual backgrounds, finite Hawking spectra for regularized Schwarzschild and Kerr geometries, and proposed tests of the equivalence principle. This work lays the foundation for a self-consistent, unitary four-dimensional quantum-gravity and Holomorphic Unified Field Theory framework.

physics.gen-ph↗
arXiv2025

On Recent measurements of Toponium Threshold Enhancement in Entire-Function-Regulated Nonlocal Quantum Field Theory

Based on recent (not so recent now) data from the LHC we want to present a reinterpretation of the the recently reported threshold enhancement in top-antitop production at the LHC, we do this in an entire-function-regulated nonlocal quantum field theory. The main result show that the observed threshold excess can be made to fit by a data-driven nonlocal scale $\Lambda_{\mathrm{ker}}$ and small RG effects, while keeping global QCD tests intact. We quantify and then contrast the properties of the heavyquark systems such as charmonium and bottomonium, highlighting the unique role of the top quark's decay width in shaping the phenomenology of toponium. We find that toponium becomes a powerful tool for both infrared boundstate dynamics and ultraviolet completion effects opening new avenues for precision tests of QCD.

physics.gen-ph↗
arXiv2025

Dynamical Dark Energy at Late Time $Λ$CDM

We investigate the dynamical properties of dark energy through a detailed analysis of its equation of state parameter $w(z)$ as a function of redshift. We derive a general expression for $w(z)$ from the Friedmann-Lemaître-Robertson-Walker (FLRW) equations, establishing a direct relationship between the dark energy equation of state and the observable Hubble parameter $H(z)$ and its derivative. Using the relation $w(z) = -1 + \frac{2(1+z)}{3H(z)} \frac{dH}{dz}$, we develop an approximation method valid for $z \lesssim 1$ that accounts for the changing balance between matter and dark energy contributions to cosmic expansion. We compare our theoretical framework with recent observational data from the Dark Energy Spectroscopic Instrument (DESI) DR2, analysing how well the commonly used Chevallier-Polarski-Linder (CPL) parametrization $w(z) = -1 + w_a \frac{z}{1+z}$ captures the evolution of dark energy. Our results indicate that the dark energy equation of state exhibits a monotonic evolution with redshift, transitioning from deceleration to acceleration around $z \approx 0.7$. Notably, our predicted $w_{\mathrm{DE}}$ remains greater than $-1$ across all redshifts, avoiding phantom energy scenarios that would violate the null energy condition. This work demonstrates how precise measurements of the cosmic expansion history can constrain the nature of dark energy and provides a framework for testing dynamical dark energy models against current and future cosmological observations.

astro-ph.CO↗