Relativistic Runge-Lenz vector: from $ \mathcal{N}=4 $ SYM to SO(4) scalar field theory - INSPIRE

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Relativistic Runge-Lenz vector: from $\mathcal{N}=4$ SYM to SO(4) scalar field theory

J. Alvarez-Jimenez
(
- Mexico U., ICN
)
,
I. Cortese
(
- Mexico U., ICN
)
,
J. Antonio García
(
- Mexico U., ICN
)
,
D. Gutiérrez-Ruiz
(
- Mexico U., ICN
)
,
J. David Vergara
(
- Mexico U., ICN
)

May 30, 2018

17 pages

Published in:

JHEP 10 (2018) 153

Published: Oct 25, 2018

e-Print:

1805.12165 [hep-th]

DOI:

10.1007/JHEP10(2018)153

View in:

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Abstract: (Springer)

Starting from

\mathcal{N}=4

SYM and using an appropriate Higgs mechanism we reconsider the construction of a scalar field theory non-minimally coupled to a Coulomb potential with a relativistic SO(4) symmetry and check for scalar field consistency conditions. This scalar field theory can also be obtained from a relativistic particle Lagrangian with a proper implementation of the non-minimal coupling. We provide the generalization of the non-relativistic construction of the Runge-Lenz vector to the relativistic case and show explicitly that this new vector generates the SO(4) algebra. Using the power of the SO(4) symmetry, we calculate the relativistic hydrogen atom spectrum. We provide a generalization of the Kustaanheimo-Stiefel transformation to the relativistic case and relate our results with the corresponding relativistic oscillator. Finally, in the light of these results, we reconsider the calculation of the hydrogen atom spectrum from the cusp anomalous dimension given in [2].

Note:

17 pages. Enhaced version matching the published JHEP version. Typos corrected. The argument of concistence at the end of section 2 was corrected

Duality in Gauge Field Theories
Global Symmetries
Spontaneous Symmetry Breaking
field theory: scalar
symmetry: SO(4)
hydrogen: atom
oscillator: relativistic
particle: relativistic
algebra: SO(4)
coupling: nonminimal

References(25)

Figures(0)

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