Wormholes in Quantum Mechanics

Abstract

We introduce a geometric path integral definition of wormhole partition functions in a general class of 1D quantum systems obtained by quantizing a phase space. We compute the wormhole partition function in a semi-classical limit and in some simple examples. The partition function of the n-fold wormhole is found to be identical to the n-th Renyi entropy of a thermal mixed state of the doubled system. This mixed state incorporates three types of quantum statistical behavior: classically correlated, quantum entangled, and classically uncorrelated. We apply our prescription to 2D CFTs with Virasoro symmetry and recover the holographic dual formulation in terms of AdS3 gravity.

arXiv comment15 pages plus Appendix, 10 figures

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• Geometric phases distinguish entangled states in wormhole quantum mechanics
• Factorizing Wormholes in a Partially Disorder-Averaged SYK Model
• Baby universes, ensemble averages and factorizations with matters