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arXiv · 2512.06501

Finite-rank conformal quantum mechanics

Maxim Gritskov·Saveliy Timchenko
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Abstract

In this work, we study the simplest example of the landscape of conformal field theories: one-dimensional CFTs with finite-dimensional state space. Following the definition of quantum field theory given by G. Segal, we formulate the condition under which a one-dimensional QFT (quantum mechanics) possesses conformal symmetry, and we give a complete classification of conformal Hamiltonians with finite rank. It turns out that correlation functions in such theories are polynomial functions of the underlying geometric data. Moreover, the one-dimensional conformal Ward identities determine their scaling behavior, so that the correlators of the conformal observables are, in fact, homogeneous polynomials.

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Maxim Gritskov, Saveliy Timchenko. 2025-12-06. Finite-rank conformal quantum mechanics. https://arxiv.org/abs/2512.06501

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