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Single-scale Feynman diagrams yield integrals that are periods, namely projective integrals of rational functions of Schwinger parameters. Algebraic geometry may therefore inform us of the types of number to which these integrals evaluate.…
Quantum Antidot (AD) structures have remarkable properties in the integer quantum Hall regime, exhibiting Coulomb-blockade charging and the Kondo effect despite their open geometry. In some regimes a simple single-particle (SP) model…
We explore the space of consistent three-particle couplings in $\mathbb Z_2$-symmetric two-dimensional QFTs using two first-principles approaches. Our first approach relies solely on unitarity, analyticity and crossing symmetry of the…
The Lasserre's reconstruction algorithm is extended to the D-polytopes with the construction of their shape space. Thus, the areas of d-skeletons $(1\leq d\leq D)$ can be expressed as functions of the areas and normal bi-vectors of the…
The geometry of four-qubit entanglement is investigated. We replace some of the polynomial invariants for four-qubits introduced recently by new ones of direct geometrical meaning. It is shown that these invariants describe four points, six…
We unify problems about the equivariant geometry of symmetric quiver representation varieties, in the finite type setting, with the corresponding problems for symmetric varieties $GL(n)/K$ where $K$ is an orthogonal or symplectic group. In…
A shape invariant nonseparable and nondiagonalizable three-dimensional model with quadratic complex interaction was introduced by Bardavelidze, Cannata, Ioffe, and Nishnianidze. However, the complete hidden symmetry algebra and the…
Recently it was shown by Castro, Maloney and Strominger (CMS) that 4D Kerr black holes have a "hidden" conformal symmetry. Using some old results of Cvetic and Larsen, I show that this result is very likely to hold also for the most general…
In this paper, we describe the generation of the CPT-even, aether-like terms via the new CPT-even magnetic-like coupling. We carry out a study the loop corrections generated by this coupling. Previous investigations has been initiated on…
We review completely monotone (CM) and Stieltjes functions, which are classes of functions obeying an infinite hierarchy of positivity constraints. While these are classical concepts in analysis, such properties have recently been shown to…
4-dimensional $A_{4}$ polytopes and their dual polytopes have been constructed as the orbits of the Coxeter-Weyl group $W(A_{4})$ where the group elements and the vertices of the polytopes are represented by quaternions. Projection of an…
Quaternionic representations of Coxeter (reflection) groups of ranks 3 and 4, as well as those of E_8, have been used extensively in the literature. The present paper analyses such Coxeter groups in the Clifford Geometric Algebra framework,…
By exploring possible physical sense of notions, structures, and logic in a class of noncommutative geometries, we try to unify the four fundamental interactions within an axiomatic quantum picture. We identify the objects and algebraic…
We investigate one-loop four-point scattering of non-abelian gauge bosons in heterotic string theory and identify new connections with the corresponding open-string amplitude. In the low-energy expansion of the heterotic-string amplitude,…
Effective field theories (EFTs) provide a powerful framework to parametrise unknown aspects of possible ultraviolet (UV) physics. For scalar fields in de Sitter space, however, new emergent phenomena can arise when the cut-off scale of the…
We consider a superintegrable Hamiltonian system in a two-dimensional space with a scalar potential that allows one quadratic and one cubic integral of motion. We construct the most general associative cubic algebra and we present specific…
We take a major step towards computing $D$-dimensional one-loop amplitudes in general gauge theories, compatible with the principles of unitarity and the color-kinematics duality. For $n$-point amplitudes with either supersymmetry…
In recent years, the intersection of algebra, geometry, and combinatorics with particle physics and cosmology has led to significant advances. Central to this progress is the twofold formulation of the study of particle interactions and…
Singletons are those unitary irreducible modules of the Poincare or (anti) de Sitter group that can be lifted to unitary modules of the conformal group. Higher-spin algebras are the corresponding realizations of the universal enveloping…
We present a new geometric interpretation of equivariant cohomology in which one replaces a smooth, complex $G$-variety $X$ by its associated arc space $J_{\infty} X$, with its induced $G$-action. This not only allows us to obtain geometric…