Negative energy, instability, and AdS–CFT This paper was presented at the Theory CANADA 4 conference, held at Centre de recherches mathématiques, Montréal, Québec, Canada on 4–7 June 2008.

Keith Copsey; Robert B. Mann

doi:10.1139/p08-135

Negative energy, instability, and AdS–CFT This paper was presented at the Theory CANADA 4 conference, held at Centre de recherches mathématiques, Montréal, Québec, Canada on 4–7 June 2008.

Canadian Journal of Physics ◽

10.1139/p08-135 ◽

2009 ◽

Vol 87 (3) ◽

pp. 285-292

Author(s):

Keith Copsey ◽

Robert B. Mann

Keyword(s):

Boundary Conditions ◽

Negative Energy ◽

Energy Instability

We consider a freely orbifolded AdS5 × S5 and demonstrate that standard boundary conditions allow states of arbitrarily negative energy. These states describe bubbles that are regular up to singularities due to smeared D3-branes. We discuss the evolution of this data and point out that if the usual boundary conditions are enforced such bubbles may never reach infinity.

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Negative energy states of an ‘‘inverted’’ delta potential: Influence of boundary conditions

American Journal of Physics ◽

10.1119/1.14310 ◽

1985 ◽

Vol 53 (8) ◽

pp. 768-773 ◽

Cited By ~ 11

Author(s):

A. Rabinovitch

Keyword(s):

Boundary Conditions ◽

Negative Energy ◽

Potential Influence ◽

Delta Potential ◽

Negative Energy States ◽

Energy States

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The critical transition of Coulomb impurities in gapped graphene

Journal of High Energy Physics ◽

10.1007/jhep08(2020)144 ◽

2020 ◽

Vol 2020 (8) ◽

Author(s):

M. Asorey ◽

A. Santagata

Keyword(s):

Boundary Conditions ◽

Bound States ◽

Energy Levels ◽

Bound State ◽

Negative Energy ◽

Spectral Flow ◽

Supercritical Regime ◽

Gapped Graphene ◽

Critical Charge ◽

Common Framework

AbstractThe effect of supercritical charge impurities in graphene is very similar to the supercritical atomic collapses in QED for Z > 137, but with a much lower critical charge. In this sense graphene can be considered as a natural testing ground for the analysis of quantum field theory vacuum instabilities. We analyze the quantum transition from subcritical to supercritical charge regimes in gapped graphene in a common framework that preserves unitarity for any value of charge impurities. In the supercritical regime it is possible to introduce boundary conditions which control the singular behavior at the impurity. We show that for subcritical charges there are also non-trivial boundary conditions which are similar to those that appear in QED for nuclei in the intermediate regime 118 < Z < 137. We analyze the behavior of the energy levels associated to the different boundary conditions. In particular, we point out the existence of new bound states in the subcritical regime which include a negative energy bound state in the attractive Coulomb regime. A remarkable property is the continuity of the energy spectral flow under variation of the impurity charge even when jumping across the critical charge transition. We also remark that the energy levels of hydrogenoid bound states at critical values of charge impurities act as focal points of the spectral flow.

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Use of the Magnetostatic Analogue In Electromagnetic Lens Engineering

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100068795 ◽

1970 ◽

Vol 28 ◽

pp. 360-361

Author(s):

John W. Coleman

Keyword(s):

Boundary Conditions ◽

High Performance ◽

Force Fields ◽

Optical Design ◽

Direct Conversion ◽

Design Engineering ◽

Design Data ◽

Scalar Potentials ◽

Geometric Elements ◽

At Will

In the design engineering of high performance electromagnetic lenses, the direct conversion of electron optical design data into drawings for reliable hardware is oftentimes difficult, especially in terms of how to mount parts to each other, how to tolerance dimensions, and how to specify finishes. An answer to this is in the use of magnetostatic analytics, corresponding to boundary conditions for the optical design. With such models, the magnetostatic force on a test pole along the axis may be examined, and in this way one may obtain priority listings for holding dimensions, relieving stresses, etc..The development of magnetostatic models most easily proceeds from the derivation of scalar potentials of separate geometric elements. These potentials can then be conbined at will because of the superposition characteristic of conservative force fields.

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