Bound state QED effects from the Schrödinger equation

1992 ◽  
Vol 70 (8) ◽  
pp. 670-682 ◽  
Author(s):  
Tao Zhang ◽  
Lixin Xiao ◽  
Roman Koniuk
Keyword(s):  
Integral Equation ◽  
Scattering Amplitudes ◽  
Principal Quantum Number ◽  
Bound State ◽  
Renormalization Scheme ◽  
Dirac Particles ◽  
Feynman Gauge ◽  
The One ◽  
Qed Effects ◽  
Bound State Qed

We present a new relativistic bound-state formalism for two interacting Fermi–Dirac particles. The kernel of the integral equation for the bound-state system is generated by summing Feynman scattering amplitudes and multiplying by a bound-state amplitude. The method is illustrated through calculations of the hyperfine and fine splittings of positronium up to order α5. Our calculations of the one-loop contributions are carried out in the explicitly covariant Feynman gauge. We also present new results for the hyperfine and fine splittings in positronium to order α5 for arbitrary principal quantum number n, which are easily obtained owing to the virtue of conceptual and calculational simplicity of our formalism. In addition, we present the one-loop renormalization scheme in our formalism.

scholarly journals 1+1 Dimensional Yang-Mills Theories in Light-Cone Gauge

1997 ◽  
Vol 12 (06) ◽  
pp. 1075-1090 ◽  
Author(s):  
A. Bassetto ◽  
G. Nardelli
Keyword(s):  
Integral Equation ◽  
Light Cone ◽  
Wilson Loop ◽  
Bound State ◽  
Light Cone Gauge ◽  
Yang Mills ◽  
Feynman Gauge ◽  
Large N

In 1+1 dimensions two different formulations exist of SU(N) Yang Mills theories in light-cone gauge; only one of them gives results which comply with the ones obtained in Feynman gauge. Moreover the theory, when considered 1+(D-1) dimensions, looks discontinuous in the limit D = 2. All those features are proven in Wilson loop calculations as well as in the study of the [Formula: see text] bound state integral equation in the large N limit.

scholarly journals Bound-state variational wave equation for fermion systems in quantum electrodynamics

2007 ◽  
Vol 85 (8) ◽  
pp. 813-836 ◽  
Author(s):  
A G Terekidi ◽  
J W Darewych ◽  
M Horbatsch
Keyword(s):  
Wave Equation ◽  
Variational Method ◽  
Quantum Electrodynamics ◽  
Principal Quantum Number ◽  
Bound State ◽  
Interaction Kernel ◽  
Loop Contribution ◽  
Arbitrary Mass ◽  
Fermion Systems ◽  
The One

We present a formulation of the Hamiltonian variational method for quantum electrodynamics (QED) that enables the derivation of a relativistic few-fermion wave equation that can account, at least in principle, for interactions to any order of the coupling constant. We derive a relativistic two-fermion wave equation using this approach. The interaction kernel of the equation is shown to be the generalized invariant [Formula: see text] matrix including all orders of Feynman diagrams. The result is obtained rigorously from the underlying quantum field theory (QFT) for an arbitrary mass ratio of the two fermions. Our approach is based on three key points: a reformulation of QED, the variational method, and adiabatic hypothesis. As an application, we calculate the one-loop contribution of radiative corrections to the two-fermion binding energy for singlet states with arbitrary principal quantum number n, and [Formula: see text] = J = 0. Our calculations are carried out in the explicitly covariant Feynman gauge.PACS Nos.: 12.20.–m

scholarly journals Divergent ⇒ complex amplitudes in two dimensional string theory

2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
Ashoke Sen
Keyword(s):  
Scattering Amplitudes ◽  
String Theory ◽  
Matrix Model ◽  
Two Dimensional ◽  
Full Matrix ◽  
Instanton Contribution ◽  
The Matrix ◽  
Theory Result ◽  
The One ◽  
Remarkable Agreement

Abstract In a recent paper, Balthazar, Rodriguez and Yin found remarkable agreement between the one instanton contribution to the scattering amplitudes of two dimensional string theory and those in the matrix model to the first subleading order. The comparison was carried out numerically by analytically continuing the external energies to imaginary values, since for real energies the string theory result diverges. We use insights from string field theory to give finite expressions for the string theory amplitudes for real energies. We also show analytically that the imaginary parts of the string theory amplitudes computed this way reproduce the full matrix model results for general scattering amplitudes involving multiple closed strings.

scholarly journals The Nonlinear Schrödinger Equation for Orthonormal Functions II: Application to Lieb–Thirring Inequalities

2021 ◽  
Author(s):  
Rupert L. Frank ◽  
David Gontier ◽  
Mathieu Lewin
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Bound State ◽  
Nonlinear Schrodinger Equation ◽  
Best Constant ◽  
Nonlinear Schrödinger ◽  
The One ◽  
Bound State Case ◽  
Cubic Nonlinear Schrödinger Equation

AbstractIn this paper we disprove part of a conjecture of Lieb and Thirring concerning the best constant in their eponymous inequality. We prove that the best Lieb–Thirring constant when the eigenvalues of a Schrödinger operator $$-\Delta +V(x)$$ - Δ + V ( x ) are raised to the power $$\kappa $$ κ is never given by the one-bound state case when $$\kappa >\max (0,2-d/2)$$ κ > max ( 0 , 2 - d / 2 ) in space dimension $$d\ge 1$$ d ≥ 1 . When in addition $$\kappa \ge 1$$ κ ≥ 1 we prove that this best constant is never attained for a potential having finitely many eigenvalues. The method to obtain the first result is to carefully compute the exponentially small interaction between two Gagliardo–Nirenberg optimisers placed far away. For the second result, we study the dual version of the Lieb–Thirring inequality, in the same spirit as in Part I of this work Gontier et al. (The nonlinear Schrödinger equation for orthonormal functions I. Existence of ground states. Arch. Rat. Mech. Anal, 2021. https://doi.org/10.1007/s00205-021-01634-7). In a different but related direction, we also show that the cubic nonlinear Schrödinger equation admits no orthonormal ground state in 1D, for more than one function.

scholarly journals DK I = 0, $$ D\overline{K} $$ I = 0, 1 scattering and the $$ {D}_{s0}^{\ast } $$(2317) from lattice QCD

2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
Gavin K. C. Cheung ◽  
◽  
Christopher E. Thomas ◽  
David J. Wilson ◽  
Graham Moir ◽  
...  
Keyword(s):  
Elastic Scattering ◽  
Scattering Amplitudes ◽  
Lattice Qcd ◽  
Finite Volume ◽  
Energy Region ◽  
Light Quark ◽  
Bound State ◽  
Vector Resonance ◽  
Quark Masses ◽  
Partial Waves

Abstract Elastic scattering amplitudes for I = 0 DK and I = 0, 1 $$ D\overline{K} $$ D K ¯ are computed in S, P and D partial waves using lattice QCD with light-quark masses corresponding to mπ = 239 MeV and mπ = 391 MeV. The S-waves contain interesting features including a near-threshold JP = 0+ bound state in I = 0 DK, corresponding to the $$ {D}_{s0}^{\ast } $$ D s 0 ∗ (2317), with an effect that is clearly visible above threshold, and suggestions of a 0+ virtual bound state in I = 0 $$ D\overline{K} $$ D K ¯ . The S-wave I = 1 $$ D\overline{K} $$ D K ¯ amplitude is found to be weakly repulsive. The computed finite-volume spectra also contain a deeply-bound D* vector resonance, but negligibly small P -wave DK interactions are observed in the energy region considered; the P and D-wave $$ D\overline{K} $$ D K ¯ amplitudes are also small. There is some evidence of 1+ and 2+ resonances in I = 0 DK at higher energies.

scholarly journals Bound states of a Klein–Gordon particle in the presence of a smooth potential well

2020 ◽  
Vol 35 (23) ◽  
pp. 2050140
Author(s):  
Eduardo López ◽  
Clara Rojas
Keyword(s):  
Bound States ◽  
Gordon Equation ◽  
Bound State ◽  
Potential Well ◽  
One Dimensional ◽  
Smooth Potential ◽  
Klein Gordon ◽  
The One ◽  
Potential Parameters ◽  
Klein Gordon Equation

We solve the one-dimensional time-independent Klein–Gordon equation in the presence of a smooth potential well. The bound state solutions are given in terms of the Whittaker [Formula: see text] function, and the antiparticle bound state is discussed in terms of potential parameters.

EXACT SOLUTIONS OF THE KLEIN–GORDON EQUATION FOR THE ROSEN–MORSE TYPE POTENTIALS VIA NIKIFOROV–UVAROV METHOD

2008 ◽  
Vol 23 (35) ◽  
pp. 3005-3013 ◽  
Author(s):  
A. REZAEI AKBARIEH ◽  
H. MOTAVALI
Keyword(s):  
Exact Solutions ◽  
Gordon Equation ◽  
Bound State ◽  
S Wave ◽  
Vector Potentials ◽  
Klein Gordon ◽  
The One ◽  
Uvarov Method ◽  
Equal Scalar ◽  
Klein Gordon Equation

The exact solutions of the one-dimensional Klein–Gordon equation for the Rosen–Morse type potential with equal scalar and vector potentials are presented. First, we briefly review Nikiforov–Uvarov mathematical method. Using this method, wave functions and corresponding exact energy equation are obtained for the s-wave bound state. It has been shown that the results for Rosen–Morse type potentials reduce to the standard Rosen–Morse well and Eckart potentials in the special case. The PT-symmetry for these potentials is also considered.

Transition energy measurements in hydrogenlike and heliumlike ions strongly supporting bound-state QED calculations

2014 ◽  
Vol 90 (3) ◽  
Author(s):  
K. Kubiček ◽  
P. H. Mokler ◽  
V. Mäckel ◽  
J. Ullrich ◽  
J. R. Crespo López-Urrutia
Keyword(s):  
Transition Energy ◽  
Bound State ◽  
Bound State Qed

Illuminating the proton radius conundrum: the μHe+ Lamb shiftThis paper was presented at the International Conference on Precision Physics of Simple Atomic Systems, held at École de Physique, les Houches, France, 30 May – 4 June, 2010.

2011 ◽  
Vol 89 (1) ◽  
pp. 47-57 ◽  
Author(s):  
A. Antognini ◽  
F. Biraben ◽  
J. M.R. Cardoso ◽  
D. S. Covita ◽  
A. Dax ◽  
...  
Keyword(s):  
Nuclear Polarization ◽  
Bound State ◽  
Atomic Systems ◽  
Charge Radii ◽  
Polarization Contribution ◽  
Proton Radius ◽  
Nuclear Rms Charge Radii ◽  
Proton Radius Puzzle ◽  
Bound State Qed

We plan to measure several 2S–2P transition frequencies in μ4He+ and μ3He+ by means of laser spectroscopy with an accuracy of 50 ppm. This will lead to a determination of the corresponding nuclear rms charge radii with a relative accuracy of 3 × 10−4, limited by the uncertainty of the nuclear polarization contribution. First, these measurements will help to solve the proton radius puzzle. Second, these very precise nuclear radii are benchmarks for ab initio few-nucleon theories and potentials. Finally when combined with an ongoing measurement of the 1S–2S transition in He+, these measurements will lead to an enhanced bound-state QED test of the 1S Lamb shift in He+.

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