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There is an interesting paper on Goldstone theorem of non-Hermitian QFT. arXiv:1808.00437.

On page page 8-9 equation (36)-(38), author says that having equations of motion that are NOT complex conjugate to each other is a potential problem.

What are the "potential problems?". Why are we not allowed to have equations of motions that are not complex conjugate to each other?

Thank you

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