Vacuum Stability Conditions and Potential Minima for a Matrix Representation in Lightcone Orbit Space

preprint2022arXivOpen access

The orbit space for a scalar field in a complex square matrix representation obtains a Minkowski space structure from the Cauchy-Schwarz inequality. It can be used to find vacuum stability conditions and minima of the scalar potential. The method is suitable for fields such as a bidoublet, an $SU(2)$ triplet or $SU(3)$ octet. We use the formalism to find the vacuum stability conditions for the left-right symmetric potential of a bidoublet and left and right Higgs doublets.

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Vacuum Stability Conditions and Potential Minima for a Matrix Representation in Lightcone Orbit Space

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