# Anomalies and renormalization of mixed states in quantum theories

@article{Gupta2013AnomaliesAR, title={Anomalies and renormalization of mixed states in quantum theories}, author={Kumar S. Gupta and Amilcar R. de Queiroz}, journal={Modern Physics Letters A}, year={2013}, volume={29}, pages={1450064} }

In a Hamiltonian approach to anomalies, parity and time-reversal symmetries can be restored by introducing suitable impure (or mixed) states. However, the expectation values of observables such as the Hamiltonian diverges in such impure states. Here, we show that such divergent expectation values can be treated within a renormalization group (RG) framework, leading to a set of β-functions in the moduli space of the operators representing the observables. This leads to well-defined expectation…

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## References

SHOWING 1-10 OF 30 REFERENCES

### Hamiltonian interpretation of anomalies

- Physics
- 1985

A family of quantum systems parametrized by the points of a compact space can realize its classical symmetries via a new kind of nontrivial ray representation. We show that this phenomenon in fact…

### Quantum gravity: mixed states from diffeomorphism anomalies

- Physics
- 2011

A bstractIn a previous paper, we discussed simple examples like particle on a circle and molecules to argue that mixed states can arise from anomalous symmetries. This idea was applied to the…

### Mixed states from anomalies

- Physics
- 2012

There are several instances where quantum anomalies of continuous and discrete classical symmetries play an important role in fundamental physics. Examples come from chiral anomalies in the Standard…

### EDGE STATES IN GAUGE THEORIES: THEORY, INTERPRETATIONS AND PREDICTIONS

- Physics
- 1994

Gauge theories on manifolds with spatial boundaries are studied. It is shown that observables localized at the boundaries (edge observables) can occur in such models irrespective of the…

### Renormalization in quantum mechanics.

- PhysicsPhysical review. D, Particles and fields
- 1993

We implement the concept of Wilson renormalization in the context of simple quantum-mechanical systems. The attractive inverse square potential leads to a $\ensuremath{\beta}$ function with a…

### Z2 topological order and the quantum spin Hall effect.

- PhysicsPhysical review letters
- 2005

The Z2 order of the QSH phase is established in the two band model of graphene and a generalization of the formalism applicable to multiband and interacting systems is proposed.

### Origin of the anomalies: The modified Heisenberg equation

- Physics
- 2002

The origin of the anomalies is analyzed. It is shown that they are due to the fact that the generators of the symmetry do not leave the domain of definition of the Hamiltonian invariant and thus a…