Generalized quantum dimensions from SymTFTs classify massless and massive RG flows in pseudo-Hermitian systems and relate coset constructions to domain walls.
Pseudo-Hermiticity versus PT-Symmetry III: Equivalence of pseudo-Her miticity and the presence of antilinear symmetries
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abstract
We show that a diagonalizable (non-Hermitian) Hamiltonian H is pseudo-Hermitian if and only if it has an antilinear symmetry, i.e., a symmetry generated by an invertible antilinear operator. This implies that the eigenvalues of H are real or come in complex conjugate pairs if and only if H possesses such a symmetry. In particular, the reality of the spectrum of H implies the presence of an antilinear symmetry. We further show that the spectrum of H is real if and only if there is a positive-definite inner-product on the Hilbert space with respect to which H is Hermitian or alternatively there is a pseudo-canonical transformation of the Hilbert space that maps H into a Hermitian operator.
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Analytic continuation produces a PT-invariant CFT state reproducing the Bunch-Davies Wightman function for dS, but entanglement entropy captures only real central charge, motivating a timelike geodesic-integrated dual for OPE block correlators and conformal defects from dS/CFT symmetry.
A density matrix approach to non-Hermitian two-flavor neutrino oscillations shows steady-state probabilities not necessarily 1/2, indicating non-Markovian behavior.
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Generalizing quantum dimensions: Symmetry-based classification of local pseudo-Hermitian systems and the corresponding domain walls
Generalized quantum dimensions from SymTFTs classify massless and massive RG flows in pseudo-Hermitian systems and relate coset constructions to domain walls.
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Two flavor neutrino oscillations in presence of non-Hermitian dynamics
A density matrix approach to non-Hermitian two-flavor neutrino oscillations shows steady-state probabilities not necessarily 1/2, indicating non-Markovian behavior.