Sum rules for zeros of polynomials. II

1980 ◽  
Vol 21 (4) ◽  
pp. 709-714 ◽  
Author(s):  
K. M. Case
Keyword(s):  
Sum Rules ◽  
Zeros Of Polynomials

Sum rules for zeros of polynomials. I

1980 ◽  
Vol 21 (4) ◽  
pp. 702-708 ◽  
Author(s):  
K. M. Case
Keyword(s):  
Sum Rules ◽  
Zeros Of Polynomials

A Perturbation Theory for the Population of Atomic Energy Levels in Non-Lte Plasmas

1988 ◽  
Vol 102 ◽  
pp. 343-347
Author(s):  
M. Klapisch
Keyword(s):  
Perturbation Theory ◽  
Small Parameter ◽  
Classification Scheme ◽  
Sum Rules ◽  
Energy Levels ◽  
Natural Classification ◽  
Quantum Numbers ◽  
Formal Expansion ◽  
Atomic Energy Levels ◽  
As Effects

AbstractA formal expansion of the CRM in powers of a small parameter is presented. The terms of the expansion are products of matrices. Inverses are interpreted as effects of cascades.It will be shown that this allows for the separation of the different contributions to the populations, thus providing a natural classification scheme for processes involving atoms in plasmas. Sum rules can be formulated, allowing the population of the levels, in some simple cases, to be related in a transparent way to the quantum numbers.

KRAMERS--KRONIG RELATIONS AND SUM RULES.

1972 ◽  
Author(s):  
R Kubo ◽  
M Ichimura
Keyword(s):  
Sum Rules

scholarly journals Consistency of nucleon-transfer sum rules in well-deformed nuclei

2021 ◽  
Vol 103 (2) ◽  
Author(s):  
B. P. Kay ◽  
J. P. Schiffer ◽  
S. J. Freeman ◽  
T. L. Tang ◽  
B. D. Cropper ◽  
...  
Keyword(s):  
Sum Rules ◽  
Deformed Nuclei ◽  
Nucleon Transfer

scholarly journals |Vcb| and γ from B-mixing — Addendum to “Bs mixing observables and |Vtd/Vts| from sum rules”

2020 ◽  
Vol 2020 (3) ◽  
Author(s):  
Daniel King ◽  
Matthew Kirk ◽  
Alexander Lenz ◽  
Thomas Rauh
Keyword(s):  
Sum Rules ◽  
B Mixing

scholarly journals Unitarity in KK-graviton production, a case study in warped extra-dimensions

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
A. de Giorgi ◽  
S. Vogl
Keyword(s):  
Extra Dimensions ◽  
Sum Rules ◽  
Effective Theory ◽  
Higher Dimensional ◽  
Massive Spin ◽  
The Matrix ◽  
Dimensional Gravity ◽  
Warped Extra Dimensions ◽  
Kaluza Klein

Abstract The Kaluza-Klein (KK) decomposition of higher-dimensional gravity gives rise to a tower of KK-gravitons in the effective four-dimensional (4D) theory. Such massive spin-2 fields are known to be connected with unitarity issues and easily lead to a breakdown of the effective theory well below the naive scale of the interaction. However, the breakdown of the effective 4D theory is expected to be controlled by the parameters of the 5D theory. Working in a simplified Randall-Sundrum model we study the matrix elements for matter annihilations into massive gravitons. We find that truncating the KK-tower leads to an early breakdown of perturbative unitarity. However, by considering the full tower we obtain a set of sum rules for the couplings between the different KK-fields that restore unitarity up to the scale of the 5D theory. We prove analytically that these are fulfilled in the model under consideration and present numerical tests of their convergence. This work complements earlier studies that focused on graviton self-interactions and yields additional sum rules that are required if matter fields are incorporated into warped extra-dimensions.

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