We extend results on Grassmann scalar fields, demonstrating implications for fermionic composites and asymptotic behavior.
We extend previous results about scalar fields whose Fourier components are even elements of a Grassmann algebra with given index of nilpotency. Their main interest in Particle Physics is related to the possibility that they describe fermionic composites analogous to the Cooper pairs of superconductivity. We evaluate the free propagators for arbitrary index of nilpotency and we investigate a F4 model to one loop. Due to the nature of the integral over even Grassmann fields such a model exists for repulsive as well as attractive selfinteraction. In the first case the b-function is equal to that of the ordinary theory, while in the second one the model is asymptotically free. The bare mass has a peculiar dependence on the cutoff, being quadratically decreasing/increasing for attractive/repulsive selfinteraction.
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Palumbo F. (1996) studied this question.
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