Related papers: The Intrinsic and Extrinsic Hierarchy Problems
We argue that the hierarchy problem of the standard model of particle physics can be solved by adding a state-dependent term to the Higgs sector. We present an example of a scalar field with a Higgs-like potential with an additional term…
It has long been noticed that high dimension data exhibits strange patterns. This has been variously interpreted as either a "blessing" or a "curse", causing uncomfortable inconsistencies in the literature. We propose that these patterns…
We argue that the familiar gauge hierarchy between the fundamental Planck scale M_{Pl} and the electroweak scale M_{W}, can be naturally explained in higher dimensional theories with relatively large radii (R_c > 1/M_{Pl}) extra dimensions.…
Heisenberg's uncertainty principle states that it is not possible to compute both the position and momentum of an electron with absolute certainty. However, this computational limitation, which is central to quantum mechanics, has no…
In this paper we consider the electromagnetic scattering problem by an obstacle characterised by a Generalized Impedance Boundary Condition in the harmonic regime. These boundary conditions are well known to provide accurate models for thin…
A strictly truncated (weak-coupling) perturbation theory is applied to the attractive Holstein and Hubbard models in infinite dimensions. These results are qualified by comparison with essentially exact Monte Carlo results. The second order…
In this note we present a simple Lax description of the hierarchy of the intermediate long wave equation (ILW hierarchy). Although the linear inverse scattering problem for the ILW equation itself was well known, here we give an explicit…
Having in mind that physical systems have different levels of structure we develop the concept of external, internal and total improper Lorentz transformation (space inversion and time reversal). A particle obtained from the ordinary one by…
Electromagnetic Inverse Scattering Problems (EISP) have gained wide applications in computational imaging. By solving EISP, the internal relative permittivity of the scatterer can be non-invasively determined based on the scattered…
In this paper, we represent a resolution for the hierarchy problem where the inverse size of the extra dimension and the fundamental Planck scale would all be of the order of the TeV scale by proposing a fiber fabric of spacetime. The…
The Holographic Naturalness (HN) is a new paradigm towards an explanation of the Cosmological Constant (CC) and the Higgs Hierarchy (HH) in the Universe. Motivated by the Holographic Principle, and inspired by the (A)dS/CFT correspondence,…
Puzzles often give birth to the great discoveries, the false discoveries sometimes stimulate the exiting ideas in theoretical physics. The historical examples of both are described in Introduction and in section ``Cosmological Puzzles''.…
Systems of ordinary differential equations (or dynamical forms in Lagrangian mechanics), induced by embeddings of smooth fibered manifolds over one-dimensional basis, are considered in the class of variational equations. For a given…
We start with a Riemann-Hilbert Problems (RHP) with canonical normalization whose sewing functions depends on several additional variables. Using Zakharov-Shabat theorem we are able to construct a family of ordinary differential operators…
To investigate the effect of problem presentation on LLMs' ability to solve optimization problems, we introduce the dataset of Everyday Hard Optimization Problems (EHOP), a collection of NP-hard problems expressed in natural language. EHOP…
If we interpret the Bekenstein-Hawking entropy of the Hubble horizon as thermodynamic entropy, then the entanglement entropy of the superhorizon modes of curvature perturbation entangled with the subhorizon modes will exceed the…
Based on Quantum Gravity arguments, it has been suggested that all kinetic terms of light particles below the UV cut-off could arise in the IR via quantum (loop) corrections. These loop corrections involve infinite towers of states becoming…
We present an algorithm to decide the intruder deduction problem (IDP) for a class of locally stable theories enriched with normal forms. Our result relies on a new and efficient algorithm to solve a restricted case of higher-order…
We study the asymptotic behavior of Riemann-Hilbert problems (RHP) arising in the AKNS hierarchy of integrable equations. Our analysis is based on the $\dbar$-steepest descent method. We consider RHPs arising from the inverse scattering…
In any theory it is unnatural if the observed parameters lie very close to special values that determine the existence of complex structures necessary for observers. A naturalness probability, P, is introduced to numerically evaluate the…