Two- and Three-Particle Systems in Relativistic Schrödinger Theory

Beck, Thomas L.; Sorg, M.

doi:10.1007/s10701-007-9145-5

Cited by 4 publications

(29 citation statements)

References 17 publications

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“…For such a situation, the original nine-dimensional structure group U(3) for three identical particles is reduced to the product group U(1) × U(2) (for the reduction process, see ref. [14]). Accordingly, the gauge potential A µ for such a threeparticle system can be decomposed into a five-dimensional Lie algebra basis {τ a , χ, χ}…”

Section: Matter Fieldsmentioning

confidence: 99%

“…With respect to these identifications, the operator form of the charge conservation law (II. 14) transcribes to the corresponding component form in the following way:…”

Section: Gauge Fieldsmentioning

confidence: 99%

“…Therefore the electric Poisson equation (V. 16) for the common electric potential (b/p) A 0 reads for both positronium configurations…”

Section: Ortho/para Dichotomy In Rstmentioning

confidence: 99%

“…where the upper/lower sign refers to the ortho/para-case, resp. The solutions for both requirements (V.23)-(V.24) are [14,16] ortho-positronium:…”

Section: Ortho/para Dichotomy In Rstmentioning

confidence: 99%

“…Furthermore, this common current k * ( r) could be eventually taken from the solution of the electrostatic (and therefore truncated) RST eigenvalue problem. Indeed, such a philosophy was put forward in two preceding papers [15,16]; and by such presumptions the ortho/para energy difference ∆ (m) E T (V.38) would be finally found in the following form…”

Section: Ortho/para Dichotomy In Rstmentioning

confidence: 99%

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Gauge-Invariant Energy Functional in Relativistic Schroedinger Theory

Mattes,

Sorg

2009

Preprint

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The non-invariant energy functional of the preceding paper is improved in order to obtain its gauge-invariant form by strictly taking into account the non-Abelian character of Relativistic Schrödinger Theory (RST). As an application of the results, the dichotomy of positronium with respect to singlet and triplet states is discussed (ortho-and para-positronium). The degeneracy of the ortho-and para-states occurs in RST if (i) the magnetic interactions are neglected (as in the conventional theory) and (ii) the anisotropy of the electric interaction potential is disregarded.In view of such a very crude approximation procedure, the non-relativistic positronium spectrum in RST agrees amazingly well with the conventional predictions.Indeed using here a very simple trial function with only two variational parameters yields deviations from the conventional predictions of some 10% (or less) up to large principal quantum numbers (n ≃ 100). This hints at the possibility that the exact RST calculations could yield predictions for the bound systems which come very close to (or even coincide with) those of the conventional quantum theory. Such a numerical correctness of the RST predictions supports a fluid-dynamic picture of quantum matter where any single particle appears as the carrier of a wave-like 1 structure (such a structure, however, is generally believed to be associated exclusively with statistical ensembles but not with single particles). Here, more detailed predictions of the positronium spectrum would be desirable but this will necessitate to first elaborate more exact solutions of the RST eigenvalue problem, especially with regard to the anisotropic and magnetic effects.

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Section: Matter Fieldsmentioning

confidence: 99%

“…With respect to these identifications, the operator form of the charge conservation law (II. 14) transcribes to the corresponding component form in the following way:…”

Section: Gauge Fieldsmentioning

confidence: 99%

“…Therefore the electric Poisson equation (V. 16) for the common electric potential (b/p) A 0 reads for both positronium configurations…”

Section: Ortho/para Dichotomy In Rstmentioning

confidence: 99%

“…where the upper/lower sign refers to the ortho/para-case, resp. The solutions for both requirements (V.23)-(V.24) are [14,16] ortho-positronium:…”

Section: Ortho/para Dichotomy In Rstmentioning

confidence: 99%

Section: Ortho/para Dichotomy In Rstmentioning

confidence: 99%

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Gauge-Invariant Energy Functional in Relativistic Schroedinger Theory

Mattes,

Sorg

2009

Preprint

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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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Non-Relativistic Positronium Spectrum in Relativistic Schroedinger Theory

Mattes,

Sorg

2008

Preprint

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The lowest energy levels of positronium are studied in the nonrelativistic approximation within the framework of Relativistic Schrödinger Theory (RST). Since it is very difficult to find the exact solutions of the RST field equations (even in the non-relativistic limit), an approximation scheme is set up on the basis of the hydrogen-like wave functions (i.e. polynomial times exponential). For any approximation order N (N = 0, 1, 2, 3, . . .) there arises a spectrum of approximate RST solutions with the associated energies, quite similarly to the conventional treatment of positronium in the standard quantum theory (Appendix). For the lowest approximation order (N = 0) the RST prediction for the groundstate energy exactly agrees with the conventional prediction of the standard theory. However for the higher approximation orders (N = 1, 2, 3), the corresponding RST prediction differs from the conventional result by (roughly) 0, 9 [eV ] which confirms the previous estimate of the error being due to the use of the spherically symmetric approximation. The excited states require the application of higher-order approximations (N >> 3) and are therefore not adequately described by the present orders (N ≤ 3).

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Two- and Three-Particle Systems in Relativistic Schrödinger Theory

Cited by 4 publications

References 17 publications

Gauge-Invariant Energy Functional in Relativistic Schroedinger Theory

Gauge-Invariant Energy Functional in Relativistic Schroedinger Theory

Density functional theory and multicomponent wave functions

Non-Relativistic Positronium Spectrum in Relativistic Schroedinger Theory

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