Species Quantum Mechanics

Abstract

In this note we introduce some concepts of Species Quantum Mechanics. Specifically, we consider quantum operators that correspond to the species number $N_s$ and the tower mass scale $m_t$ 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 ${\cal N}=2$ Calabi-Yau compactifications to explore other aspects of the CRV pattern, including its possible connection to the Ooguri-Vafa-Verlinde black hole quantization procedure.