Abstract
The splitting of the massless (\(1+1\))-dimensional Dirac field into right- and left-handed components. The quantization of the right- and left-handed fields. Construction of the Hamiltonian and of the U(1) current operator. The non-conservation of the U(1) current in the presence of an external Abelian gauge field. Derivation of the U(1) anomaly equation. Cancelation of anomalies. Non-invariance of the fermionic path integral measure under the axial U(1) transformations. Derivation of the U(1) anomaly equation in the path integral formulation of the quantum theory of the massless Dirac Dirac field in four-dimensional Euclidean space. The index of the Dirac operator.
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Notes
- 1.
It is certainly simple when compared with other models, nonetheless we consider a system that has an infinite number of degrees of freedom. Simplicity is a relative notion.
- 2.
Let us recall that a term denoted as ‘h.c.’ is obtained by the Hermitian conjugation of the preceding term or terms.
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Arodź, H., Hadasz, L. (2017). Anomalies. In: Lectures on Classical and Quantum Theory of Fields. Graduate Texts in Physics. Springer, Cham. https://doi.org/10.1007/978-3-319-55619-2_14
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DOI: https://doi.org/10.1007/978-3-319-55619-2_14
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