Topological currents in relativistic Schrödinger theory

Sorg, M.

doi:10.1088/0305-4470/30/15/033

Cited by 15 publications

(4 citation statements)

References 14 publications

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“…relativistic Schrödinger theory (RST), which has been put forward in some preceeding papers. (7)(8)(9) The first numerical tests of the theory referred to the groundstate and ionization energies of the helium-like ions (with arbitrary nuclear charge number) and yielded predictions close enough to the experimental data (9)(10)(11) in order that a further theoretical elaboration of the new framework seems desirable. Subsequently, there will be treated certain fundamental questions which are induced by experimental evidence and which therefore must be taken into account by any theory of quantum matter.…”

Section: Introduction and Survey Of Resultsmentioning

confidence: 92%

Two- and Three-Particle Systems in Relativistic Schrödinger Theory

Beck

Sorg

2007

Found Phys

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The relativistic Schrödinger theory (RST) for N-fermion systems is further elaborated with respect to three fundamental problems which must emerge in any relativistic theory of quantum matter: (i) emergence/suppression of exchange forces between identical/non-identical particles, (ii) self-interactions, (iii) non-relativistic approximation. These questions are studied in detail for two-and three-particle systems but the results do apply to a general N-particle system. As a concrete demonstration, the singlet and triplet configurations of the positronium groundstate are considered within the RST framework, including a discussion of the corresponding hyperfine splitting.KEY WORDS: relativistic wave equations; solutions of wave equations; bound states; semiclassical theories and applications; matter waves.

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Section: Introduction and Survey Of Resultsmentioning

confidence: 92%

Two- and Three-Particle Systems in Relativistic Schrödinger Theory

Beck

Sorg

2007

Found Phys

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“…Furthermore, the well-known Noether-theorems (due to the external and internal symmetries of the action integral) yield the associated conservation laws for energy-momentum and charge, which were previously deduced directly from the RST dynamics itself. (12)(13)(14) Clearly, the existence of an action principle opens now a wide field of variational methods for approximately solving the RST field equations.…”

Section: Introduction and Survey Of Resultsmentioning

confidence: 99%

“…The internal part L D,in looks quite similar to the original L D (243), however with the internal connection (S) A µ ( 12 ) being used in place of the original A µ (10).…”

Section: Euler-lagrange Equationsmentioning

confidence: 98%

“…However, for our variational purposes we will treat the total electromagnetic potential A µ (31) as an independent field so that the total Maxwell equation formally appears also as an independent variational equation. Thus, the independent RST field degrees of freedom consist of the two-particle matter field (1), the external gauge potential (ex) A µ ( 11 ), the internal gauge potentials A α µ (12), and the total potential A µ (31). The quantity fixed from the outside is the external current (ex) j µ (60).…”

Section: Euler-lagrange Equationsmentioning

confidence: 99%

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Self-Energy and Action Principle in Relativistic Schrödinger Theory

et al. 2005

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The mathematical framework of Relativistic Schrödinger Theory (RST) is generalized in order to include the self-interactions of the particles as an integral part of the theory (i.e. in a non-perturbative way). The extended theory admits a Lagrangean formulation where the Noether theorems confirm the existence of the conservation laws for charge and energy-momentum which were originally deduced directly from the dynamical equations. The generalized RST dynamics is applied to the case of some heavy helium-like ions, ranging from germanium (Z = 32) to bismuth (Z = 83), in order to compute the interaction energy of the two electrons in their ground-state. The present inclusion of the electron self-energies into RST yields a better agreement of the theoretical predictions with the experimental data.

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Density functional theory and multicomponent wave functions

Karwowski¹

2012

Int J of Quantum Chemistry

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Some consequences of using multicomponent wave functions are analyzed. In particular, paradoxical properties of a density functional derived from Dirac and Lévy‐Leblond equations are discussed. The application of a recently formulated N‐electron “relativistic Schrödinger theory,” based on a 4N‐component wave function, to the construction of a Lorentz and gauge covariant density functional theory is suggested. © 2012 Wiley Periodicals, Inc.

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Topological currents in relativistic Schrödinger theory

Cited by 15 publications

References 14 publications

Two- and Three-Particle Systems in Relativistic Schrödinger Theory

Two- and Three-Particle Systems in Relativistic Schrödinger Theory

Self-Energy and Action Principle in Relativistic Schrödinger Theory

Density functional theory and multicomponent wave functions

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