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WS24/25 – Abstract
Jeffrey Kuntz
(MPIK Heidelberg)
23.1.2025
Unitarity in Pseudo-Hermitean Quadratic Gravity
Theories described by non-Hermitian Hamiltonians are known to possess strictly positive energy eigenvalues and exhibit unitary time evolution if their Hamiltonian possesses an anti-linear symmetry or, equivalently, is pseudo-Hermitian. We review these claims and demonstrate how quantum quadratic gravity, a theory that generally violates unitarity when viewed as a Hermitian QFT, can be complex-deformed into an anti-linear PT-symmetric theory with an action that consists of a ghost-less Hermitian free part and non-Hermitian interactions. We also show compelling evidence that the quantized theory possesses a unitary inner product and a sensible interpretation of quantum probability, thus avoiding the ghost problem present in the Hermitian formulation of quadratic gravity.
