Speaker
Description
The equal-time Bethe–Salpeter (Salpeter–Sucher) equation is the exact QED wave equation for a two-fermion system $[1, 2, 3, 13, 14]$. The equation containing only the instantaneous part of the interaction is the with-pair Dirac–Coulomb(–Breit) equation (wpDC(B)), which includes the double-pair correction to the no-pair DC(B) equation (npDC(B)). The numerical results for these equations can be converged within ppb to ppt relative precision using an explicitly correlated Gaussian (ECG) basis set approach $[4]–[12]$.
While the double-pair correction is a non-hermitian, but ‘algebraic’ term, which leaves the DC(B) equation linear in energy, the single-pair correction, represented by the irreducible crossed–Coulomb(–Breit) interaction kernel, appears within a complicated, energy dependent operator in the Salpeter–Sucher equation. The inclusion of the crossed–Coulomb(–Breit) and other higher-order irreducible interaction kernels through this term renders the wave equation non-linear in energy.
A novel perturbative approach is therefore being considered for the treatment of these contributions, using the npDC(B) and wpDC(B) results as high-precision relativistic reference energies and wave functions $[13, 14]$. The results of this new relativistic QED (rQED) approach, including the single-pair correction, are expected to serve as a useful comparison to the well established non-relativistic QED (nrQED) methodologies, and the highest precision experimental results.
References
$[1]$ E. E. Salpeter and H. A. Bethe, Phys. Rev. A 84, 1232 (1951).
$[2]$ E. E. Salpeter, Phys. Rev. A 87, 328 (1952).
$[3]$ J. Sucher, Ph. D. Thesis (1958), Columbia University.
$[4]$ P. Jeszenszki, D. Ferenc, E. Mátyus, J. Chem. Phys. 154, 224110 (2021).
$[5]$ P. Jeszenszki, D. Ferenc, E. Mátyus, J. Chem. Phys. 156, 084111 (2022).
$[6]$ D. Ferenc, P. Jeszenszki, E. Mátyus, J. Chem. Phys. 156, 084110 (2022).
$[7]$ D. Ferenc, P. Jeszenszki, E. Mátyus, J. Chem. Phys. 157, 094113 (2022).
$[8]$ P. Jeszenszki and E. Mátyus, J. Chem. Phys. 158, 054104 (2023).
$[9]$ D. Ferenc and E. Mátyus, Phys. Rev. A. 107, 052803 (2023).
$[10]$ P. Hollósy, P. Jeszenszki, E. Mátyus, under review (2024).
$[11]$ P. Jeszenszki and E. Mátyus, in preparation (2024).
$[12]$ Á. Nonn, Á. Margócsy, E. Mátyus, under review (2024).
$[13]$ E. Mátyus, D. Ferenc, P. Jeszenszki, Á. Margócsy, ACS Phys. Chem. Au 3, 222 (2023).
$[14]$ Á. Margócsy and E. Mátyus, arXiv:2312.13887 (2024)
