Relativistic many-electron Hamiltonians

A review, not intended for experts, is given of a systematic approach to a relativistic theory of many-electron atoms which starts from first principles, i.e., from quantum electrodynamics. It is based on the construction of a relativistic configuration-space Hamiltonian Hrel, which is bona fide, i.e., possesses normalizable eigenstates which may be associated with atomic bound states. In this respect it differs drastically from the Dirac-Coulomb Hamiltonian, HDC, which has been the traditional starting point for the investigation of relativistic effects in heavy atoms but which suffers from "continuum dissolution" (CD). Hrel may be chosen in a variety of ways but all choices have in common the presence of positive-energy projection operators bracketing the Coulomb or Coulomb plus Breit interaction between electrons. Topics which are discussed within this context include mathematical aspects of these projection oeprators, the CD phenomenon, the field-theoretic interpretation of calculations based on the relativistic configuration-interaction method, and the effects of virtual electron-positron pairs on atomic energy levels. The problem of renormalization is briefly considered and a method for organizing the calculation of radiative corrections is sketched.

[1]  G. E. Brown,et al.  On the interaction of two electrons , 1951, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[2]  Hess,et al.  Applicability of the no-pair equation with free-particle projection operators to atomic and molecular structure calculations. , 1985, Physical review. A, General physics.

[3]  Approximation methods for many-electron atoms from a field theory point of view , 1987 .

[4]  G. Brown.  Relativistic effects in nuclear physics , 1987 .

[5]  J. Sucher,et al.  Relativistic wave equations in momentum space , 1984 .

[6]  Sucher,et al.  Critical coupling constants for relativistic wave equations and vacuum breakdown in quantum electrodynamics. , 1985, Physical review. A, General physics.

[7]  H. P. Kelly.  Many Body Calculations of Photoionization Cross Sections , 1987 .

[8]  B. A. Hess,et al.  Relativistic ab initio CI study of the X1Σ+ and A1Σ+ states of the AgH molecule , 1987 .

[9]  Sucher.  Continuum dissolution and the relativistic many-body problem: A solvable model. , 1985, Physical review letters.

[10]  Jonathan Sapirstein,et al.  Quantum electrodynamics of many-electron atoms , 1987 .

[11]  K. Dietz.  Relativistic Quantum Electrodynamics of Atoms , 1987 .

[12]  Yong-ki Kim,et al.  Atomic Theory Workshop on Relativistic and QED Effects in Heavy Atoms (National Bureau of Standards, Gaithersburg, MD, 1985) , 1985 .

[13]  Marvin H. Mittleman,et al.  Theory of relativistic effects on atoms: Configuration-space Hamiltonian , 1981 .

[14]  Ingvar Lindgren,et al.  Atomic Many-Body Theory , 1982 .

[15]  I. Balitsky.  On the virtual γγ annihilation to hadrons , 1982 .

[16]  P. Dirac.  Principles of Quantum Mechanics , 1982 .