NDLI: Cyclic Structures of Cliffordian Supergroups and Particle Representations of Spin+(1, 3)

Content Provider	Springer Nature Link
Author	Varlamov, V. V.
Copyright Year	2014
Abstract	Supergroups are defined in the framework of $${\mathbb{Z}_2}$$ 2-graded Clifford algebras over the fields of real and complex numbers, respectively. It is shown that cyclic structures of complex and real supergroups are defined by Brauer-Wall groups related with the modulo 2 and modulo 8 periodicities of the complex and real Clifford algebras. Particle (fermionic and bosonic) representations of a universal covering (spinor group Spin +(1, 3)) of the proper orthochronous Lorentz group are constructed via the Clifford algebra formalism. Complex and real supergroups are defined on the representation system of Spin +(1, 3). It is shown that a cyclic (modulo 2) structure of the complex supergroup is equivalent to a supersymmetric action, that is, it converts fermionic representations into bosonic representations and vice versa. The cyclic action of the real supergroup leads to a much more high-graded symmetry related with the modulo 8 periodicity of the real Clifford algebras. This symmetry acts on the system of real representations of Spin +(1, 3).
Starting Page	849
Ending Page	874
Page Count	26
File Format	PDF
ISSN	01887009
Journal	Advances in Applied Clifford Algebras
Volume Number	24
Issue Number	3
e-ISSN	16614909
Language	English
Publisher	Springer Basel
Publisher Date	2014-02-08
Publisher Place	Basel
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Clifford algebras supergroups spinor representations Mathematical Methods in Physics Theoretical, Mathematical and Computational Physics Applications of Mathematics Physics
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics

Sl.	Authority	Responsibilities	Communication Details
1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
2	Indian Institute of Technology Kharagpur	Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project	https://www.iitkgp.ac.in
3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
5	Website/Portal (Helpdesk)	Queries regarding NDLI and its services	support@ndl.gov.in
6	Contents and Copyright Issues	Queries related to content curation and copyright issues	content@ndl.gov.in
7	National Digital Library of India Club (NDLI Club)	Queries related to NDLI Club formation, support, user awareness program, seminar/symposium, collaboration, social media, promotion, and outreach	clubsupport@ndl.gov.in
8	Digital Preservation Centre (DPC)	Assistance with digitizing and archiving copyright-free printed books	dpc@ndl.gov.in
9	IDR Setup or Support	Queries related to establishment and support of Institutional Digital Repository (IDR) and IDR workshops	idr@ndl.gov.in

Spin and Clifford Algebras, an Introduction

Spinor spaces of Clifford algebras

The Structure of the Clifford Algebra

Cyclic structures of Cliffordian supergroups and particle representations of Spin+(1, 3). arXiv: 1207.6162 [math-ph (2012)

Some Topics in Clifford Analysis

Clifford Algebras of Forms of Higher Degrees

Degenerate Spin Groups as Semi-Direct Products

Bilinear Forms and Fierz Identities for Real Spin Representations

ELKO, Flagpole and Flag-Dipole Spinor Fields, and the Instanton Hopf Fibration

Cyclic Structures of Cliffordian Supergroups and Particle Representations of Spin+(1, 3)

Similar Documents

Spin and Clifford Algebras, an Introduction

Spinor spaces of Clifford algebras

The Structure of the Clifford Algebra

Cyclic structures of Cliffordian supergroups and particle representations of Spin+(1, 3). arXiv: 1207.6162 [math-ph (2012)

Some Topics in Clifford Analysis

Clifford Algebras of Forms of Higher Degrees

Degenerate Spin Groups as Semi-Direct Products

Bilinear Forms and Fierz Identities for Real Spin Representations

ELKO, Flagpole and Flag-Dipole Spinor Fields, and the Instanton Hopf Fibration

Cyclic Structures of Cliffordian Supergroups and Particle Representations of Spin+(1, 3)