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Algorithmic boundedness-from-below conditions for generic scalar potentials

Ivanov, Igor P.; Köpke, Marcel; Mühlleitner, Margarete

Checking that a scalar potential is bounded from below (BFB) is an ubiquitous and notoriously difficult task in many models with extended scalar sectors. Exact analytic BFB conditions are known only in simple cases. In this work, we present a novel approach to algorithmically establish the BFB conditions for any polynomial scalar potential. The method relies on elements of multivariate algebra, in particular, on resultants and on the spectral theory of tensors, which is being developed by the mathematical community. We give first a pedagogical introduction to this approach, illustrate it with elementary examples, and then present the working Mathematica implementation publicly available at GitHub. Due to the rapidly increasing complexity of the problem, we have not yet produced ready-to-use analytical BFB conditions for new multi-scalar cases. But we are confident that the present implementation can be dramatically improved and may eventually lead to such results.

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Verlagsausgabe §
DOI: 10.5445/IR/1000083170
Veröffentlicht am 04.06.2018
DOI: 10.1140/epjc/s10052-018-5893-y
Zitationen: 4
Web of Science
Zitationen: 4
Zugehörige Institution(en) am KIT Institut für Theoretische Physik (ITP)
Publikationstyp Zeitschriftenaufsatz
Jahr 2018
Sprache Englisch
Identifikator ISSN: 1434-6044, 1434-6052
KITopen-ID: 1000083170
Erschienen in The European physical journal / C
Band 78
Heft 5
Seiten Article: 413
Bemerkung zur Veröffentlichung Gefördert durch SCOAP3
Vorab online veröffentlicht am 25.05.2018
Nachgewiesen in Scopus
Web of Science
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