Variational methods in relativistic quantum mechanics

M Esteban, M Lewin, E Séré - Bulletin of the American Mathematical …, 2008 - ams.org
This review is devoted to the study of stationary solutions of linear and nonlinear equations
from relativistic quantum mechanics, involving the Dirac operator. The solutions are found as …

Theory and applications of the sine-Gordon equation

A Barone, F Esposito, CJ Magee, AC Scott - La Rivista del Nuovo Cimento …, 1971 - Springer
In 1939 I~ RENKEL and KONTOROVA studied the propagation of a (, slip~> in an infinite
chain of elastically bound atoms lying over a fixed lower chain of similar atoms [1]. To …

An infinite sequence of localized semiclassical states for nonlinear Maxwell–Dirac system

J Zhang, Y Zhang - The Journal of Geometric Analysis, 2024 - Springer
In this paper, we study the following nonlinear Maxwell–Dirac system α·(i ħ∇+ q (x) A (x)) ua
β u+ V (x) uq (x) ϕ (x) u=| u| p-2 u,-Δ ϕ= q (x)| u| 2,-Δ A k= q (x)(α ku)· u, k= 1, 2, 3, for x∈ R 3 …

Maximum mass of relativistic self-gravitating Bose-Einstein condensates with repulsive or attractive self-interaction

PH Chavanis - Physical Review D, 2023 - APS
We derive an approximate analytical expression of the maximum mass of relativistic self-
gravitating Bose-Einstein condensates with repulsive or attractive| φ| 4 self-interaction. This …

Stationary states of nonlinear Dirac equations with general potentials

Y Ding, J Wei - Reviews in Mathematical Physics, 2008 - World Scientific
STATIONARY STATES OF NONLINEAR DIRAC EQUATIONS WITH GENERAL POTENTIALS
Page 1 Reviews in Mathematical Physics Vol. 20, No. 8 (2008) 1007–1032 c World Scientific …

Excited Dirac stars with higher azimuthal harmonic index

LX Huang, SX Sun, R Zhang, C Liang… - Journal of Cosmology …, 2024 - iopscience.iop.org
In this paper, we investigate the properties of the first excited state Dirac stars (DSs) with
higher azimuthal harmonic index (specifically, the azimuthal harmonic indexes m D= 3/2 …

Asymptotically flat, spherical, self-interacting scalar, Dirac and Proca stars

CAR Herdeiro, E Radu - Symmetry, 2020 - mdpi.com
We present a comparative analysis of the self-gravitating solitons that arise in the Einstein–
Klein–Gordon, Einstein–Dirac, and Einstein–Proca models, for the particular case of static …

[PDF][PDF] Existence of localized solutions for a classical nonlinear Dirac field

T Cazenave, L Våzquez - 1986 - projecteuclid.org
_?> H ) > G - Page 1 Communications in Commun. Math. Phys. 105, 35-47 (1986) ^^PhJoieS
© Springer-Verlag 1986 Existence of Localized Solutions for a Classical Nonlinear Dirac …

Multi-state Dirac stars

C Liang, JR Ren, SX Sun, YQ Wang - The European Physical Journal C, 2024 - Springer
In this paper, we construct the multi-state Dirac stars (MSDSs) consisting of two pairs of
Dirac fields. The two pairs of Dirac fields are in the ground state and the first excited state …

Numerical methods for nonlinear Dirac equation

J Xu, S Shao, H Tang - Journal of Computational Physics, 2013 - Elsevier
This paper presents a review of the current state-of-the-art of numerical methods for
nonlinear Dirac (NLD) equation. Several methods are extendedly proposed for the (1+ 1) …