Topic
Anticommutativity
About: Anticommutativity is a research topic. Over the lifetime, 174 publications have been published within this topic receiving 1247 citations.
Papers published on a yearly basis
Papers
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TL;DR: In this article, the authors introduce a new symmetry for algebras with one operation called dihedrality, responsible for the existence of dihedral cohomology, and analyze the Koszulness and cyclicity of the corresponding operads.
Abstract: We investigate algebras with one operation. We study when these algebras form a monoidal category and analyze Koszulness and cyclicity of the corresponding operads. We also introduce a new kind of symmetry for operads, the dihedrality, responsible for the existence of the dihedral cohomology.
The main trick, which we call the polarization, will be to represent an algebra with one operation without any specific symmetry as an algebra with one commutative and one anticommutative operation. We will try to convince the reader that this change of perspective might sometimes lead to new insights and results.
This point of view was used by Livernet and Loday to introduce a one-parametric family of operads whose specialization at 0 is the operad for Poisson algebras, while at a generic point it equals the operad for associative algebras. We study this family and explain how it can be used to interpret the deformation quantization in a neat and elegant way.
63 citations
TL;DR: In this article, the effect of perturbative quantum gravity on supermanifolds with both non-commutative and non-anticommutative coordinates was analyzed using the Batalin-Vilkovisky (BV) formalism.
Abstract: In this paper we will study perturbative quantum gravity on supermanifolds with both noncommutative and non-anticommutative coordinates. We shall first analyses the BRST and the anti-BRST symmetries of this theory. Then we will also analyze the effect of shifting all the fields of this theory in background field method. We will construct a Lagrangian density which apart from being invariant under the extended BRST transformations is also invariant under on-shell extended anti-BRST transformations. This will be done by using the Batalin-Vilkovisky (BV) formalism. Finally, we will show that the sum of the gauge-fixing term and the ghost term for this theory can be elegantly written down in superspace with two Grassmann parameters.
44 citations
TL;DR: In this paper, the classification of all n-dimensional anticommutative complex algebras with (n − − 3)-dimensional annihilator is given, and all central extensions of all 3-dimensional acyclic complexes are described.
Abstract: We give the classification of all n-dimensional anticommutative complex algebras with (n − 3)-dimensional annihilator. Namely, we describe all central extensions of all 3-dimensional anticommutativ...
42 citations
TL;DR: In this paper, the classical theory of fermionic (anticommuting) fields, which fits into the general framework proposed by Brunetti, Dutsch and Fredenhagen, is presented.
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, Dutsch 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.
32 citations
TL;DR: In this article, a noncommutative and non-anticommutative quantum field theory is formulated in a superspace, in which the superspace coordinates satisfy non-commodity and nonsmutative relations.
25 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2022 | 1 |
| 2021 | 9 |
| 2020 | 14 |
| 2019 | 8 |
| 2018 | 8 |
| 2017 | 10 |