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Species quantum mechanics

Luis A. Anchordoqui1,2,3, Dieter Lüst4,5, and Severin Lüst6

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Phys. Rev. D 113, 026021 – Published 23 January, 2026

DOI: https://doi.org/10.1103/vwjx-lrhl

Abstract

In this paper we take the initial steps toward a formulation of species quantum mechanics. Specifically, we consider quantum operators that correspond to the species number Ns and the tower mass scale mt in the context of the swampland distance conjecture. We discuss the commutation relations, a possible wave function, and symplectic duality transformations on the conjugate variables. Furthermore, we argue that the Castellano-Ruiz-Valenzuela (CRV) pattern is a consequence of the canonical commutation rules of moduli space quantum mechanics. We also connect the canonical quantization to the periods of N=2 Calabi-Yau compactifications to explore other aspects of the CRV pattern, including its possible connection to the Ooguri-Vafa-Verlinde black hole quantization procedure.

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Outline

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Phys. Rev. D 113, 026021– Published 23 January, 2026
  • Received 7 November 2025
  • Accepted 2 January 2026
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