# Implications of Conformal Symmetry in Quantum Mechanics

## TL;DR

This paper explores how conformal symmetry influences quantum mechanics, revealing monotonic behavior of dilatation expectations and bounds on scaling dimensions, with implications for understanding quantum state evolution.

## Contribution

It demonstrates the monotonic decrease of dilatation expectation values and establishes bounds on scaling dimensions in conformal quantum mechanics.

## Key findings

- Dilatation expectation values decrease monotonically from UV to IR.
- Bounds on physical state and gauge operator scaling dimensions.
- Implications for state evolution under conformal symmetry.

## Abstract

In conformal quantum mechanics with the vacuum of a real scaling dimension and with a complete orthonormal set of energy eigenstates which is preferable under the unitary evolution, the dilatation expectation value between energy eigenstates monotonically decreases along the flow from the UV to the IR. In such conformal quantum mechanics there exist bounds on scaling dimensions of the physical states and the gauge operators.