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Grassmann scalar fields and asymptotic freedom

Abstract

The authors 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 Copper pairs of superconductivity. The authors evaluate the free propagators for arbitrary index of nilpotency and they investigate a {phi}{sup 4} model to one loop. Due to the nature of the integral over even Grassmann fields such as a model exists for repulsive as well as attractive self interaction. In the first case the {beta}-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 self interaction.
Authors:
Palumbo, F [1] 
  1. INFN, Laboratori Nazionali di Frascati, Rome (Italy)
Publication Date:
Mar 01, 1996
Product Type:
Technical Report
Report Number:
LNF-P-96/016
Reference Number:
SCA: 662110; PA: ITA-97:000441; EDB-97:063922; NTS-97:010223; SN: 97001773839
Resource Relation:
Other Information: PBD: Mar 1996
Subject:
66 PHYSICS; QUANTUM FIELD THEORY; SCALAR FIELDS; FERMIONS; ALGEBRAIC FIELD THEORY
OSTI ID:
465197
Research Organizations:
Istituto Nazionale di Fisica Nucleare, Frascati (Italy). Lab. Nazionale di Frascati
Country of Origin:
Italy
Language:
English
Other Identifying Numbers:
Other: ON: DE97740690; TRN: IT9700441
Availability:
OSTI as DE97740690
Submitting Site:
ITA
Size:
22 p.
Announcement Date:
May 16, 1997

Citation Formats

Palumbo, F. Grassmann scalar fields and asymptotic freedom. Italy: N. p., 1996. Web.
Palumbo, F. Grassmann scalar fields and asymptotic freedom. Italy.
Palumbo, F. 1996. "Grassmann scalar fields and asymptotic freedom." Italy.
@misc{etde_465197,
title = {Grassmann scalar fields and asymptotic freedom}
author = {Palumbo, F}
abstractNote = {The authors 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 Copper pairs of superconductivity. The authors evaluate the free propagators for arbitrary index of nilpotency and they investigate a {phi}{sup 4} model to one loop. Due to the nature of the integral over even Grassmann fields such as a model exists for repulsive as well as attractive self interaction. In the first case the {beta}-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 self interaction.}
place = {Italy}
year = {1996}
month = {Mar}
}