Explanipedia

Analytic Scalar Field Theory Open

Thomas Curtright · 2025

We discuss scalar field theories with potentials V(ϕ)=\k{appa}(ϕ^2)^{ν} for generic ν. We conjecture that these models evade various no-go theorems for scalar fields in four spacetime dimensions.

Bernoulli and Euler Partitions Open

Thomas Curtright · 2025

Exact rational partitions are presented for Bernoulli and Euler numbers as novel sums involving Faulhaber and Salié coefficients.

Bernoulli Partitions Open

Thomas Curtright · 2025

Scale invariant scattering suggests that all Bernoulli numbers B_{2n} can be naturally partitioned, i.e., written as particular finite sums of same-signed, monotonic, rational numbers. Some properties of these rational numbers are discusse…

Scale Invariant Scattering and Bernoulli Numbers Open

Thomas Curtright · 2024

Non-relativistic quantum mechanical scattering from an inverse square potential in two spatial dimensions leads to a novel representation of the Bernoulli numbers.

Scattering Shadows Open

Thomas Curtright, G. S. Verma · 2024

We discuss the regions forbidden to classical scattering trajectories by repulsive potentials. We give explicit results for the asymptotic form of these regions, far from the scattering center, in terms of the scattering angle function.

Scale Invariant Scattering in 2D Open

Thomas Curtright, Christophe Vignat · 2024

For a non-relativistic scale invariant system in two spatial dimensions, the quantum scattering amplitude f (θ) is given as a dispersion relation, with a simple closed form for Im f (θ) as well as the integrated cross-section σ ∝ Im f (θ =…

Newtonian Gravity on an N-Sphere Open

Thomas Curtright, Hassan Alshal · 2024

We consider some elementary features of Newtonian gravity, or electrostatics, as defined on an N -sphere.In particular, we present and discuss "the shell theorem" for this system.

Geometric Cloaks and Resonances Open

Thomas Curtright, Suresh C. Subedi · 2024

Selected spatial geometries can either enhance or suppress scattering amplitudes, to produce either extremely sharp resonances or approximate invisibility for a specified angular momentum.A simple model is presented in detail for an impene…

Lie Groups and Propagators Exemplified Open

Thomas Curtright, Zikun Cao, A. Peca, Debasish Sarker, B. D. Shrestha · 2024

Concise methods are used to compute the propagator for a nonrelativistic particle subject to a potential with x 2 and 1/x 2 terms.

Mean sinc sums and scale invariant scattering Open

Thomas Curtright · 2024

Scattering from a scale invariant potential in two spatial dimensions leads to a class of novel identities involving the sinc function.

Scale Invariant Scattering and Bernoulli Numbers Open

Thomas Curtright · 2023

Non-relativistic quantum mechanical scattering from an inverse square potential in two spatial dimensions leads to a novel representation of the Bernoulli numbers.

Mean Sinc Sums and Scale Invariant Scattering Open

Thomas Curtright · 2022

Scattering from a scale invariant potential in two spatial dimensions leads to a class of novel identities involving the sinc function.

Lie Groups and Propagators Exemplified Open

Thomas Curtright, Z. Cao, A. Peca, Debasish Sarker, B. D. Shrestha · 2021

Concise methods are used to compute the propagator for a non-relativistic particle subject to a potential with x^2 and 1/x^2 terms.

Dual fields of massive/massless gravitons in IR/UV completions Open

Ashkbiz Danehkar, Hassan Alshal, Thomas Curtright · 2021

In the holographic picture, the Brout-Englert-Higgs (BEH) mechanism in [Formula: see text]-dimensional Yang–Mills theories is conjectured to provide a Higgs-like mechanism for gravity in [Formula: see text] dimensions, resulting in massive…

Potentials versus Geometry Open

Thomas Curtright, Suresh C. Subedi · 2021

We discuss some equivalence relations between the non-relativistic quantum mechanics for particles subjected to potentials and for particles moving freely on background geometries. In particular, we illustrate how selected geometries can b…

On Enceladian Fields Open

T.S. Van Kortryk, Thomas Curtright, Hassan Alshal · 2020

We fantasize about an alternative history for theories of electromagnetism and gravitation.

Massive dual spinless fields revisited Open

Thomas Curtright · 2019

Massive dual spin 2 revisited Open

Thomas Curtright, Hassan Alshal · 2019

We reconsider a massive dual spin 2 field theory in four spacetime\ndimensions. We obtain the Lagrangian that describes the lowest order coupling\nof the field to the four-dimensional curl of its own energy-momentum tensor. We\nthen find s…

Massive dual gravity in N spacetime dimensions Open

Hassan Alshal, Thomas Curtright · 2019

A bstract We describe a field theory for “massive dual gravity” in N spacetime dimensions. We obtain a Lagrangian that gives the lowest order coupling of the field to the N -dimensional curl of its own energy-momentum tensor. We then brief…

Massive Dual Fields Revisited Open

Thomas Curtright · 2019

Massive Dual Spin 2 Open

Thomas Curtright, Hassan Alshal · 2019

We reconsider a massive dual spin 2 field theory in four spacetime dimensions. We obtain the Lagrangian that describes the lowest order coupling of the field to the four-dimensional curl of its own energy-momentum tensor. We then find some…

Grounded hyperspheres as squashed wormholes Open

Hassan Alshal, Thomas Curtright · 2019

We compute exterior Green functions for equipotential, grounded hyperspheres in N-dimensional electrostatics by squashing Riemannian wormholes, where an image charge is placed in the branch of the wormhole opposite the branch containing th…

Fundamental Supermultiplet in Twelve Dimensions Open

Thomas Curtright · 2018

We discuss a set of local fields which provide the on-shell massless states expected for the fundamental linear representation of supersymmetry in twelve dimensions. We recover the states of the anticipated N = 16, S = 4, massless supermul…

The conducting ring viewed as a wormhole Open

Thomas Curtright, Hassan Alshal, Pramod Baral, Sunxiang Huang, Jiazhen Liu , et al. · 2018

We compute the exterior Green function for a grounded equi-potential circular ring in two-dimensional electrostatics by treating the system geometrically as a "squashed wormhole" with an image charge located in a novel but obvious position…

Image Charges Re-Imagined Open

Hassan Alshal, Thomas Curtright, Suresh C. Subedi · 2018

We discuss the grounded, equipotential ellipse in two-dimensional electrostatics to illustrate different ways of extending the domain of the potential and placing image charges such that homogeneous boundary conditions are satisfied. In pa…

Color characters for white hot string bits Open

Thomas Curtright, Sourav Raha, Charles B. Thorn · 2017

The state space of a generic string bit model is spanned by $N\times N$ matrix creation operators acting on a vacuum state. Such creation operators transform in the adjoint representation of the color group $U(N)$ (or $SU(N)$ if the matric…

Spin multiplicities Open

Thomas Curtright, T.S. Van Kortryk, Cosmas Zachos · 2016

Charged line segments and ellipsoidal equipotentials Open

Thomas Curtright, N M Aden, X Chen, M J Haddad, Sabit Karayev , et al. · 2016

This is a survey of the electrostatic potentials produced by charged\nstraight-line segments, in various numbers of spatial dimensions, with\ncomparisons between uniformly charged segments and those having non-uniform\nlinear charge distri…

Elementary Results for the Fundamental Representation of SU(3) Open

Thomas Curtright, Cosmas Zachos · 2015

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