Anomalous Commutator Algebra for Conformal Quantum Mechanics
arXiv:hep-th/0205191 · doi:10.1103/PhysRevD.67.045018
Abstract
The structure of the commutator algebra for conformal quantum mechanics is considered. Specifically, it is shown that the emergence of a dimensional scale by renormalization implies the existence of an anomaly or quantum-mechanical symmetry breaking, which is explicitly displayed at the level of the generators of the SO(2,1) conformal group. Correspondingly, the associated breakdown of the conservation of the dilation and special conformal charges is derived.
23 pages. A few typos corrected in the final version (which agrees with the published Phys. Rev. D article)
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- Mixed States from Anomalies
- Atomic collapse in graphene and cyclic RG flow
- Proper time reparametrization in cosmology: Mobius symmetry and Kodama charges
- Scale Anomaly as the Origin of Time
- Spectral Properties of the Symmetry Generators of Conformal Quantum Mechanics: A Path-Integral Approach
- Quantum Structure of Space Near a Black Hole Horizon
- RG limit cycles
- On Dimensional Transmutation in 1+1D Quantum Hydrodynamics
- A Partially Gauged Fixed Hamiltonian for Scalar Field Collapse
- Emergent Infrared Conformal Dynamics in Strongly Interacting Quantum Gases
- Path-Integral Approach to Scale Anomaly at Finite Temperature
- Quantum aspects of spacetime: A quantum optics view of acceleration radiation and black holes
- Refined cyclic renormalization group in Russian Doll model
- Relationship between Fujikawa's Method and the Background Field Method for the Scale Anomaly
- Multichannel Framework for Singular Quantum Mechanics
- Quantum anomaly and thermodynamics of one-dimensional fermions with antisymmetric two-body interactions
- Analytic Structure of the S-Matrix for Singular Quantum Mechanics
- Efimov energy level rebounding off the atom-dimer continuum