Fermionic fields in the functional approach to classical field theory

K. Rejzner

doi:10.1142/S0129055X11004503

Fermionic fields in the functional approach to classical field theory

K. Rejzner

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

In this paper, we present a formulation of the classical theory of fermionic (anticommuting) fields, which fits into the general framework proposed by Brunetti, Dütsch and Fredenhagen. It was inspired by the recent developments in perturbative algebraic quantum field theory and it also allows for a deeper structural understanding on the classical level. We propose a modification of this formalism that also allows to treat fermionic fields. In contrast to other formulations of classical theory of anticommuting variables, we do not introduce additional Grassman degrees of freedom. Instead the anticommutativity is introduced in a natural way on the level of functionals. Moreover, our construction incorporates the functional-analytic and topological aspects, which is usually neglected in the treatments of anticommuting fields. We also give an example of an interacting model where our framework can be applied.

Original language	English
Pages (from-to)	1009-1033
Number of pages	25
Journal	Reviews in Mathematical Physics
Volume	23
Issue number	9
DOIs	https://doi.org/10.1142/S0129055X11004503
Publication status	Published - 1 Oct 2011

Access to Document

10.1142/S0129055X11004503

Cite this

@article{c1691f21ca30449d846ba035f5e46cb8,

title = "Fermionic fields in the functional approach to classical field theory",

abstract = "In this paper, we present a formulation of the classical theory of fermionic (anticommuting) fields, which fits into the general framework proposed by Brunetti, D{\"u}tsch and Fredenhagen. It was inspired by the recent developments in perturbative algebraic quantum field theory and it also allows for a deeper structural understanding on the classical level. We propose a modification of this formalism that also allows to treat fermionic fields. In contrast to other formulations of classical theory of anticommuting variables, we do not introduce additional Grassman degrees of freedom. Instead the anticommutativity is introduced in a natural way on the level of functionals. Moreover, our construction incorporates the functional-analytic and topological aspects, which is usually neglected in the treatments of anticommuting fields. We also give an example of an interacting model where our framework can be applied.",

author = "K. Rejzner",

year = "2011",

month = oct,

day = "1",

doi = "10.1142/S0129055X11004503",

language = "English",

volume = "23",

pages = "1009--1033",

journal = "Reviews in Mathematical Physics",

issn = "0129-055X",

publisher = "World Scientific Publishing",

number = "9",

}

TY - JOUR

T1 - Fermionic fields in the functional approach to classical field theory

AU - Rejzner, K.

PY - 2011/10/1

Y1 - 2011/10/1

N2 - In this paper, we present a formulation of the classical theory of fermionic (anticommuting) fields, which fits into the general framework proposed by Brunetti, Dütsch and Fredenhagen. It was inspired by the recent developments in perturbative algebraic quantum field theory and it also allows for a deeper structural understanding on the classical level. We propose a modification of this formalism that also allows to treat fermionic fields. In contrast to other formulations of classical theory of anticommuting variables, we do not introduce additional Grassman degrees of freedom. Instead the anticommutativity is introduced in a natural way on the level of functionals. Moreover, our construction incorporates the functional-analytic and topological aspects, which is usually neglected in the treatments of anticommuting fields. We also give an example of an interacting model where our framework can be applied.

AB - In this paper, we present a formulation of the classical theory of fermionic (anticommuting) fields, which fits into the general framework proposed by Brunetti, Dütsch and Fredenhagen. It was inspired by the recent developments in perturbative algebraic quantum field theory and it also allows for a deeper structural understanding on the classical level. We propose a modification of this formalism that also allows to treat fermionic fields. In contrast to other formulations of classical theory of anticommuting variables, we do not introduce additional Grassman degrees of freedom. Instead the anticommutativity is introduced in a natural way on the level of functionals. Moreover, our construction incorporates the functional-analytic and topological aspects, which is usually neglected in the treatments of anticommuting fields. We also give an example of an interacting model where our framework can be applied.

UR - http://www.scopus.com/inward/record.url?scp=81255184581&partnerID=8YFLogxK

U2 - 10.1142/S0129055X11004503

DO - 10.1142/S0129055X11004503

M3 - Article

AN - SCOPUS:81255184581

SN - 0129-055X

VL - 23

SP - 1009

EP - 1033

JO - Reviews in Mathematical Physics

JF - Reviews in Mathematical Physics

IS - 9

ER -

Fermionic fields in the functional approach to classical field theory

Abstract

Access to Document

Other files and links

Cite this