The Non-relativistic Scattering Problem for a Superposition of δ-potentials

The Dirac electron is considered as a particle-like solution consistent with its own Kerr–Newman (KN) gravitational field. In our previous works we considered the regularized by López KN solution as a bag-like soliton model formed from the Higgs field in a supersymmetric vacuum state. This bag takes the shape of a thin superconducting disk coupled with circular string placed along its perimeter. Using the unique features of the Kerr–Schild coordinate system, which linearizes Dirac equation in KN space, we obtain the solution of the Dirac equations consistent with the KN gravitational and electromagnetic field, and show that the corresponding solution takes the form of a massless relativistic string. Obvious parallelism with Heisenberg and Schrödinger pictures of quantum theory explains remarkable features of the electron in its interaction with gravity and in the relativistic scattering processes.

Download Full-text

Spin effects in the effective field theory approach to Post-Minkowskian conservative dynamics

Journal of High Energy Physics ◽

10.1007/jhep06(2021)012 ◽

2021 ◽

Vol 2021 (6) ◽

Author(s):

Zhengwen Liu ◽

Rafael A. Porto ◽

Zixin Yang

Keyword(s):

Field Theory ◽

Effective Field Theory ◽

Scattering Problem ◽

Finite Size ◽

Effective Field ◽

Compact Objects ◽

Scattering Data ◽

Theory Approach ◽

Spin Effects ◽

Radial Action

Abstract Building upon the worldline effective field theory (EFT) formalism for spinning bodies developed for the Post-Newtonian regime, we generalize the EFT approach to Post-Minkowskian (PM) dynamics to include rotational degrees of freedom in a manifestly covariant framework. We introduce a systematic procedure to compute the total change in momentum and spin in the gravitational scattering of compact objects. For the special case of spins aligned with the orbital angular momentum, we show how to construct the radial action for elliptic-like orbits using the Boundary-to-Bound correspondence. As a paradigmatic example, we solve the scattering problem to next-to-leading PM order with linear and bilinear spin effects and arbitrary initial conditions, incorporating for the first time finite-size corrections. We obtain the aligned-spin radial action from the resulting scattering data, and derive the periastron advance and binding energy for circular orbits. We also provide the (square of the) center-of-mass momentum to $$ \mathcal{O}\left({G}^2\right) $$ O G 2 , which may be used to reconstruct a Hamiltonian. Our results are in perfect agreement with the existent literature, while at the same time extend the knowledge of the PM dynamics of compact binaries at quadratic order in spins.

Download Full-text

Imaging of bi-anisotropic periodic structures from electromagnetic near-field data

Journal of Inverse and Ill-Posed Problems ◽

10.1515/jiip-2020-0114 ◽

2020 ◽

Vol 0 (0) ◽

Author(s):

Dinh-Liem Nguyen ◽

Trung Truong

Keyword(s):

Inverse Scattering ◽

Maxwell Equations ◽

Field Data ◽

Periodic Structures ◽

Near Field ◽

Scattering Problem ◽

Three Dimensional ◽

Inverse Scattering Problem ◽

Factorization Method ◽

Unique Determination

AbstractThis paper is concerned with the inverse scattering problem for the three-dimensional Maxwell equations in bi-anisotropic periodic structures. The inverse scattering problem aims to determine the shape of bi-anisotropic periodic scatterers from electromagnetic near-field data at a fixed frequency. The factorization method is studied as an analytical and numerical tool for solving the inverse problem. We provide a rigorous justification of the factorization method which results in the unique determination and a fast imaging algorithm for the periodic scatterer. Numerical examples for imaging three-dimensional periodic structures are presented to examine the efficiency of the method.

Download Full-text