Bound states in quantum electrodynamics

1972 ◽  
Vol 5 (16) ◽  
pp. 1048-1053 ◽  
Author(s):  
T. Roy
Keyword(s):  
Quantum Electrodynamics ◽  
Bound States

scholarly journals Dynamical Symmetries of the H Atom, One of the Most Important Tools of Modern Physics: SO(4) to SO(4,2), Background, Theory, and Use in Calculating Radiative Shifts

Symmetry ◽  
2020 ◽  
Vol 12 (8) ◽  
pp. 1323 ◽  
Author(s):  
G. Jordan Maclay
Keyword(s):  
Hydrogen Atom ◽  
Quantum Electrodynamics ◽  
Particle Physics ◽  
Bound States ◽  
Integrated Treatment ◽  
Invariance Group ◽  
Elementary Particle Physics ◽  
Background Theory ◽  
Modern Physics ◽  
History Of

Understanding the hydrogen atom has been at the heart of modern physics. Exploring the symmetry of the most fundamental two body system has led to advances in atomic physics, quantum mechanics, quantum electrodynamics, and elementary particle physics. In this pedagogic review, we present an integrated treatment of the symmetries of the Schrodinger hydrogen atom, including the classical atom, the SO(4) degeneracy group, the non-invariance group or spectrum generating group SO(4,1), and the expanded group SO(4,2). After giving a brief history of these discoveries, most of which took place from 1935–1975, we focus on the physics of the hydrogen atom, providing a background discussion of the symmetries, providing explicit expressions for all of the manifestly Hermitian generators in terms of position and momenta operators in a Cartesian space, explaining the action of the generators on the basis states, and giving a unified treatment of the bound and continuum states in terms of eigenfunctions that have the same quantum numbers as the ordinary bound states. We present some new results from SO(4,2) group theory that are useful in a practical application, the computation of the first order Lamb shift in the hydrogen atom. By using SO(4,2) methods, we are able to obtain a generating function for the radiative shift for all levels. Students, non-experts, and the new generation of scientists may find the clearer, integrated presentation of the symmetries of the hydrogen atom helpful and illuminating. Experts will find new perspectives, even some surprises.

scholarly journals Weakly bound states of dtμ muonic molecular ion in quantum electrodynamics

2019 ◽  
Vol 1390 ◽  
pp. 012083 ◽  
Author(s):  
A V Eskin ◽  
V I Korobov ◽  
A P Martynenko ◽  
V V Sorokin
Keyword(s):  
Quantum Electrodynamics ◽  
Bound States ◽  
Weakly Bound ◽  
Molecular Ion

scholarly journals QUANTUM ELECTRODYNAMICS OF RELATIVISTIC BOUND STATES WITH CUTOFFS

2004 ◽  
Vol 01 (02) ◽  
pp. 271-314 ◽  
Author(s):  
JEAN-MARIE BARBAROUX ◽  
MOUEZ DIMASSI ◽  
JEAN-CLAUDE GUILLOT
Keyword(s):  
Current Density ◽  
Coulomb Potential ◽  
Ground State ◽  
Quantum Electrodynamics ◽  
Bound States ◽  
Coupling Constants ◽  
Relativistic Electrons ◽  
Small Coupling ◽  
Electrons And Positrons ◽  
Relativistic Bound States

We consider a Hamiltonian with ultraviolet and infrared cutoffs, describing the interaction of relativistic electrons and positrons in the Coulomb potential with photons in Coulomb gauge. The interaction includes both interaction of the current density with transversal photons and the Coulomb interaction of charge density with itself. We prove that the Hamiltonian is self-adjoint and has a ground state for sufficiently small coupling constants.

scholarly journals SINGULARITY-FREE BREIT EQUATION FROM CONSTRAINT TWO-BODY DIRAC EQUATIONS

1996 ◽  
Vol 05 (04) ◽  
pp. 589-615 ◽  
Author(s):  
HORACE W. CRATER ◽  
CHUN WA WONG ◽  
CHEUK-YIN WONG
Keyword(s):  
Quantum Electrodynamics ◽  
Bound States ◽  
Two Body Problem ◽  
Dirac Equations ◽  
Coupled Equations ◽  
Interaction Terms ◽  
Potential Form ◽  
Orthogonality Constraint ◽  
Hyperbolic Form ◽  
Breit Equation

We examine the relation between two approaches to the quantum relativistic two-body problem: (1) the Breit equation, and (2) the two-body Dirac equations derived from constraint dynamics. In applications to quantum electrodynamics, the former equation becomes pathological if certain interaction terms are not treated as perturbations. The difficulty comes from singularities which appear at finite separations r in the reduced set of coupled equations for attractive potentials even when the potentials themselves are not singular there. They are known to give rise to unphysical bound states and resonances. In contrast, the two-body Dirac equations of constraint dynamics do not have these pathologies in many nonperturbative treatments. To understand these marked differences we first express these contraint equations, which have an “external potential” form, similar to coupled one-body Dirac equations, in a hyperbolic form. These coupled equations are then recast into two equivalent equations: (1) a covariant Breit-like equation with potentials that are exponential functions of certain “generator” functions, and (2) a covariant orthogonality constraint on the relative momentum. This reduction enables us to show in a transparent way that finite-r singularities do not appear as long as the exponential structure is not tampered with and the exponential generators of the interaction are themselves nonsingular for finite r. These Dirac or Breit equations, free of the structural singularities which plague the usual Breit equation, can then be used safely under all circumstances, encompassing numerous applications in the fields of particle, nuclear, and atomic physics which involve highly relativistic and strong binding configurations.

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