# Dimensional regularization, abnormal amplitudes and anomalies

### Citation

Akyeampong, DA and Delbourgo, R, Dimensional regularization, abnormal amplitudes and anomalies, Nuovo Cimento A, 17, (4) pp. 578-586. ISSN 0369-3546 (1973) [Refereed Article]

### Abstract

Identifying axial vectors and pseudoscalars as antisymmetric 3-component and 4-component tensors in space-time of arbitrary dimensions, we discover a new PCAC law: [Kψ¯ΓLΓMΓN]=$\partial [_{K\bar \psi } \Gamma _L \Gamma _M \Gamma _{N]} =$ =2miψ¯Γ[KΓLΓMΓN]ψ15iψ¯(iJ+2eAJ)Γ[JΓKΓLΓMΓN]ψ=$= 2mi\bar \psi \Gamma _{[K} \Gamma _L \Gamma _M \Gamma _{N]} \psi - \frac{1}{5}i\bar \psi (\overleftrightarrow {i\partial }^J + 2eA^J )\Gamma _{[J} \Gamma _K \Gamma _L \Gamma _M \Gamma _{N]} \psi =$ , where the extra term on the right-hand side does not exist in 4 dimensions. However, when we do descend to 4 dimensions after dimensional regularization it is precisely the axial vector anomaly. In a parallel calculation we have also shown how to obtain the anomaly in the matrix elements of the trace of the stress tensor.

### Item Details

Item Type: Refereed Article Physical Sciences Atomic, Molecular, Nuclear, Particle and Plasma Physics Particle Physics Expanding Knowledge Expanding Knowledge Expanding Knowledge in the Physical Sciences Delbourgo, R (Professor Robert Delbourgo) 96927 1973 146 Mathematics and Physics 2014-11-26 2014-11-26 0

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