Graded gauge theory
type: Item
instance of: scholarly article
title: Graded gauge theory
zbMATH Open document ID: 0536.53069
DOI: 10.1007/BF01211159
author: R. Kerner
published in: Communications in Mathematical Physics
publication date: 1983-01-01T00:00:00Z
review text: The author deals with two things: first he defines a class of graded principal fibre bundles, secondly he introduces there some differential operators and studies a Lagrangian of the supergauge field theory. For the purpose of his graded bundles he presents a realization of a super Lie group in the case when a linear representation of its algebra is given. The total space of the supergroup is provided with a semigroup structure. Then the author constructs a graded fibre bundle. The resulting bundle contains both Lorentz spinors (at the base) and G- spinors (at the fibre). Note that there exist also non-trivial bundles of this type; an example is outlined by the reviewer in [Prepr., Inst. Math., Pol. Acad. Sci., Warsz. 277, 88 p. (1983; Zbl 0515.58013)]. In the second part the author tries to describe gauge fields in the above bundle and their Lagrangians. Commutation relations in some sectors of values of the fields are discussed. Physical phenomena like conformal symmetry breaking and mass in related fields are studied. Three coupling scale constants of length-dimension are pointed out. The number of variables is big as the author is unable to give an explicit form for the Lagrangian. On the other hand some physical fields cannot be described in this model. Note that the whole machinery of the first part is not used in the second one. For needs of the Lagrangian local coordinates of the bundle are quite sufficient. Formula 1.18 is not proved. 4.6 seems to be not true. Several notational mistakes can be noticed.
Mathematics Subject Classification ID: 53C80
Mathematics Subject Classification ID: 58H99
Mathematics Subject Classification ID: 55R99
Mathematics Subject Classification ID: 81T08
Mathematics Subject Classification ID: 17B70
zbMATH DE Number: 3851980
zbMATH Keywords: graded principal fibre bundles
zbMATH Keywords: Lagrangian
zbMATH Keywords: supergauge field theory
zbMATH Keywords: supergroup
zbMATH Keywords: Lorentz spinors
zbMATH Keywords: G-spinors
MaRDI profile type: Publication
cites work: Q4149922
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full work available at URL: https://doi.org/10.1007/bf01211159
OpenAlex ID: W2000094956
description: scientific article; zbMATH DE number 3851980