2024/09/09 by Leqian Chen, Chen, Leqian, Sarben Sarkar +1 · 1 citation
Physics and Astronomy · #FOS: Physical sciences #High Energy Physics - Phenomenology (hep-ph) #Quantum Mechanics and Non-Hermitian Physics #Quantum Physics (quant-ph)
paper · pdf · doi:10.48550/arxiv.2409.05439
openalex publication_date 2024/09/09 · openalex created_date 2024/10/22 · openalex updated_date 2026/07/28
For quantum mechanical anharmonic oscillator-type Hamiltonians, it is shown that there is a relation between the energy eigenvalues of parity symmetric and PT-symmetric phases for weak coupling. The possibility of such a relation was conjectured by Ai, Bender and Sarkar on examining the imaginary part of the ground state energy using path integrals. In the weak coupling limit, we show that the conjecture is true also for the real part of the ground state energy and of the excited state energies. However, the conjecture is false for strong coupling. The analogous relation for partition functions in zero spacetime dimensions is valid for many cases. However O(N) symmetric multi-component scalar fields, with N>1 and a quartic interaction, do not satisfy the conjecture for zero and one dimensional spacetime. The possibility that the conjecture is valid, for a single component field theory in higher dimensional spacetimes, is discussed in a simplified model.