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Theta term in a bounded region
High Energy Physics - Theory · Submitted 12 May 2011
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim The results of the present work suggest that the observable effects of the $\theta$-term could be very small even without assuming $\theta$ itself to be small.
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The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.
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The abstract, sentence by sentence
We analyse the physical implications of adding a topological density term $\theta Tr(F\wedge F)$ to a gauge theory in a bounded region. In particular, we calculate the Casimir effect on a spherical region and we show that the result is not periodic in $\theta$, contrary to what would be expected for a true topological density. The topological nature of the $\theta$-term can be restored if an additional boundary term required by the Atiyah-Patodi-Singer theorem is included. Then, the periodicity is trivially restored because the resulting Casimir energy is independent of $\theta$. The results of the present work suggest that the observable effects of the $\theta$-term could be very small even without assuming $\theta$ itself to be small.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We analyse the physical implications of adding a topological density term $\theta Tr(F\wedge F)$ to a gauge theory in a bounded region. | contribution 0.98 | 0.90 | 0.06 | asserted 0.86 |
| s1 | In particular, we calculate the Casimir effect on a spherical region and we show that the result is not periodic in $\theta$, contrary to what would be expected for a true topological density. | result 0.96 | 0.96 | 0.30 | asserted 1.00 |
| s2 | The topological nature of the $\theta$-term can be restored if an additional boundary term required by the Atiyah-Patodi-Singer theorem is included. | result 0.84 | 0.58 | 0.19 | asserted 0.94 |
| s3 | Then, the periodicity is trivially restored because the resulting Casimir energy is independent of $\theta$. | result 0.96 | 0.84 | 0.16 | asserted 1.00 |
| s4 | The results of the present work suggest that the observable effects of the $\theta$-term could be very small even without assuming $\theta$ itself to be small. | interpretation 0.99 | 0.64 | 0.54 | hedged possibility 1.00 |
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The paper
Original abstract
We analyse the physical implications of adding a topological density term $\theta Tr(F\wedge F)$ to a gauge theory in a bounded region. In particular, we calculate the Casimir effect on a spherical region and we show that the result is not periodic in $\theta$, contrary to what would be expected for a true topological density. The topological nature of the $\theta$-term can be restored if an additional boundary term required by the Atiyah-Patodi-Singer theorem is included. Then, the periodicity is trivially restored because the resulting Casimir energy is independent of $\theta$. The results of the present work suggest that the observable effects of the $\theta$-term could be very small even without assuming $\theta$ itself to be small.
Human review
How the literature uses it
5 arXiv papers cite this in 6 sentences
Papers citing it · 3 sentences without a confident label
Cites it as support 1 paper
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Another effect of such coupling is a modification of the Casimir energy inside an empty region surrounded by a “material" in which $θ≠0$ [ref] .
Chern-Simons Forms in Gravitation Theories · 3D-CS systems and condensed matter · 0.96
Cites it as background 2 papers
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There have been several interesting developments related to this kind of system: the Casimir effect for a spherical region, with C-S like boundary conditions due to the presence of a $θ$ term, has been considered in [ref] .
On the static Casimir effect with parity-breaking mirrors · Introduction · 0.98
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Some general aspects of gauge invariance of the Casimir energy in the presence of a parity breaking $θ$-term were considered in [ref] .
The quest for Casimir repulsion between Chern-Simons surfaces · Introduction · 0.99
What it cites · 13 sentences without a confident label
Uses the method or tool of 1 paper
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This can be done by different methods [ref] , probably the easiest is to use $ζ$ function.
Simple method for calculating the Casimir energy for sphere · Appendix A · 0.92
Compares with 2 papers
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Using $ζ$ function techniques, we find (see appendix), [equation] Finally, restoring the constants $ħ$ and $c$, the Casimir Energy is [equation] and in the limit $ξ→1$, $η=1$ we obtain, at this order in $ν$, [equation] in very good agreement with earlier results [ref] .
Simple method for calculating the Casimir energy for sphere · Casimir effect with a $θ$-term · 0.97
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Note that for $θ=0$ the usual result [ref] is recovered.
New Developments in the Casimir Effect · Appendix A · 0.88
Cites as background 3 papers
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This so-called strong CP problem has no satisfactory explanation up to now (for detailed reviews, see [ref] ).
Theta dependence of SU(N) gauge theories in the presence of a topological term · Introduction · 0.98
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This so-called strong CP problem has no satisfactory explanation up to now (for detailed reviews, see [ref] ).
The Strong CP Problem and Axions · Introduction · 0.98
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This so-called strong CP problem has no satisfactory explanation up to now (for detailed reviews, see [ref] ).
Theta Vacua, QCD Sum Rules, and the Neutron Electric Dipole Moment · Introduction · 0.98
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