Comparison of different approaches of finding the positive definite metric in pseudo-Hermitian theories

Ananya Ghatak; Bhabani Prasad Mandal

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arXiv · 1305.2022

Comparison of different approaches of finding the positive definite metric in pseudo-Hermitian theories

Ananya Ghatak·Bhabani Prasad Mandal

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Abstract

To develop a unitary quantum theory with probabilistic description for pseudo- Hermitian systems one needs to consider the theories in a different Hilbert space endowed with a positive definite metric operator. There are different approaches to find such metric operators. We compare the different approaches of calculating pos- itive definite metric operators in pseudo-Hermitian theories with the help of several explicit examples in non-relativistic as well as in relativistic situations. Exceptional points and spontaneous symmetry breaking are also discussed in these models.

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Ananya Ghatak, Bhabani Prasad Mandal. 2013-05-09. Comparison of different approaches of finding the positive definite metric in pseudo-Hermitian theories. https://arxiv.org/abs/1305.2022

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