Quantum harmonic oscillator, index theorem and spectral asymmetry

Shunrui Li; Yang Liu

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arXiv · 2505.21348

Quantum harmonic oscillator, index theorem and spectral asymmetry

Shunrui Li·Yang Liu

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Abstract

We report a spectral asymmetry effect in the quantum harmonic oscillator, where its partition function is identified as the Chern character. This establishes a direct link between statistical mechanics, and topological invariants (Atiyah-Singer index theorem), revealing the internal energy as a non-SUSY manifestation of the index theorem. We show that the partition function can be interpreted as the Chern character of "virtual physical sheaf", namely, a Hermitian vector bundle encoding quantum states over spacetime. This work uncovers an underlying topological structure in bosonic quantum systems.

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Shunrui Li, Yang Liu. 2025-05-27. Quantum harmonic oscillator, index theorem and spectral asymmetry. https://arxiv.org/abs/2505.21348

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