# Nonperturbative Adler-Bardeen theorem

## Abstract

The Adler-Bardeen theorem has been proven only as a statement valid at all orders in perturbation theory, without any control on the convergence of the series. In this paper we prove a nonperturbative version of the Adler-Bardeen theorem in d=2 by using recently developed technical tools in the theory of Grassmann integration. The proof is based on the assumption that the boson propagator decays fast enough for large momenta. If the boson propagator does not decay, as for Thirring contact interactions, the anomaly in the WI (Ward Identities) is renormalized by higher order contributions.

- Authors:

- Dipartimento di Matematica, Universita di Roma 'Tor Vergata', via della Ricerca Scientifica, Rome I-00133 (Italy)

- Publication Date:

- OSTI Identifier:
- 20929634

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Journal of Mathematical Physics; Journal Volume: 48; Journal Issue: 2; Other Information: DOI: 10.1063/1.2436731; (c) 2007 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; BOSONS; CHIRAL SYMMETRY; CONVERGENCE; PARTICLE DECAY; PERTURBATION THEORY; PROPAGATOR; RENORMALIZATION; THIRRING MODEL; WARD IDENTITY

### Citation Formats

```
Mastropietro, Vieri.
```*Nonperturbative Adler-Bardeen theorem*. United States: N. p., 2007.
Web. doi:10.1063/1.2436731.

```
Mastropietro, Vieri.
```*Nonperturbative Adler-Bardeen theorem*. United States. doi:10.1063/1.2436731.

```
Mastropietro, Vieri. Thu .
"Nonperturbative Adler-Bardeen theorem". United States.
doi:10.1063/1.2436731.
```

```
@article{osti_20929634,
```

title = {Nonperturbative Adler-Bardeen theorem},

author = {Mastropietro, Vieri},

abstractNote = {The Adler-Bardeen theorem has been proven only as a statement valid at all orders in perturbation theory, without any control on the convergence of the series. In this paper we prove a nonperturbative version of the Adler-Bardeen theorem in d=2 by using recently developed technical tools in the theory of Grassmann integration. The proof is based on the assumption that the boson propagator decays fast enough for large momenta. If the boson propagator does not decay, as for Thirring contact interactions, the anomaly in the WI (Ward Identities) is renormalized by higher order contributions.},

doi = {10.1063/1.2436731},

journal = {Journal of Mathematical Physics},

number = 2,

volume = 48,

place = {United States},

year = {Thu Feb 15 00:00:00 EST 2007},

month = {Thu Feb 15 00:00:00 EST 2007}

}

DOI: 10.1063/1.2436731

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