On non-linear extensions of the Perron-Frobenius theorem

1986 ◽  
Vol 15 (1) ◽  
pp. 59-62 ◽  
Author(s):  
Kali Rath
Keyword(s):  
Linear Extensions ◽  
Frobenius Theorem ◽  
Non Linear

scholarly journals Accidental Gauge Symmetries of Minkowski Spacetime in Teleparallel Theories

Universe ◽  
2021 ◽  
Vol 7 (5) ◽  
pp. 143
Author(s):  
Jose Beltrán Jiménez ◽  
Tomi S. Koivisto
Keyword(s):  
General Relativity ◽  
Minkowski Spacetime ◽  
Linear Extensions ◽  
Gauge Symmetries ◽  
Linear Spectrum ◽  
Massless Spin ◽  
Non Linear ◽  
Common Framework ◽  
Local Symmetries ◽  
Quadratic Action

In this paper, we provide a general framework for the construction of the Einstein frame within non-linear extensions of the teleparallel equivalents of General Relativity. These include the metric teleparallel and the symmetric teleparallel, but also the general teleparallel theories. We write the actions in a form where we separate the Einstein–Hilbert term, the conformal mode due to the non-linear nature of the theories (which is analogous to the extra degree of freedom in f(R) theories), and the sector that manifestly shows the dynamics arising from the breaking of local symmetries. This frame is then used to study the theories around the Minkowski background, and we show how all the non-linear extensions share the same quadratic action around Minkowski. As a matter of fact, we find that the gauge symmetries that are lost by going to the non-linear generalisations of the teleparallel General Relativity equivalents arise as accidental symmetries in the linear theory around Minkowski. Remarkably, we also find that the conformal mode can be absorbed into a Weyl rescaling of the metric at this order and, consequently, it disappears from the linear spectrum so only the usual massless spin 2 perturbation propagates. These findings unify in a common framework the known fact that no additional modes propagate on Minkowski backgrounds, and we can trace it back to the existence of accidental gauge symmetries of such a background.

The non-linear Perron-Frobenius theorem

1994 ◽  
Vol 23 (1) ◽  
pp. 21-31 ◽  
Author(s):  
Erik Dietzenbacher
Keyword(s):  
Frobenius Theorem ◽  
Non Linear

Non‐linear extensions to shell models of ultrasound contrast agents: theory and experiment

2008 ◽  
Vol 123 (5) ◽  
pp. 3220-3220
Author(s):  
Nikos A. Pelekasis ◽  
Kostas Tsiglifis ◽  
Benjamin Dollet ◽  
Nico De Jong ◽  
Detlef Lohse ◽  
...  
Keyword(s):  
Contrast Agents ◽  
Ultrasound Contrast Agents ◽  
Linear Extensions ◽  
Ultrasound Contrast ◽  
Shell Models ◽  
Non Linear ◽  
Theory And Experiment

NON-LINEAR QUANTUM MECHANICS: TWO POSSIBILITIES

1990 ◽  
Vol 05 (02) ◽  
pp. 91-94
Author(s):  
CRAIG D. ROBERTS
Keyword(s):  
Quantum Mechanics ◽  
Linear Extensions ◽  
Non Linear ◽  
Linear Quantum

A comparative discussion of two possible non-linear extensions of quantum mechanics is presented. It is argued that the two extensions are mutually consistent but applicable to completely different phenomena and that, as a consequence, quantum mechanics will be demonstrated to be truly linear only if both extensions are precluded by experiment.

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