NDLI: Matrix Mechanics of the Relativistic Point Particle and String in Clifford Space

Content Provider	Springer Nature Link
Author	Borchsenius, Kaare
Copyright Year	2015
Abstract	We resolve the space-time canonical variables of the relativistic point particle into inner products of Weyl spinors with components in a Clifford algebra and find that these spinors themselves form a canonical system with generalized Poisson brackets. For N particles, the inner products of their Clifford coordinates and momenta form two N × N Hermitian matrices X and P which transform under a U(N) symmetry in the generating algebra. This is used as a starting point for defining matrix mechanics for a point particle in Clifford space. Next we consider the string. The Lorentz metric induces a metric and a scalar on the world sheet which we represent by a Jackiw–Teitelboim term in the action. The string is described by a polymomenta canonical system and we find the wave solutions to the classical equations of motion for a flat world sheet. Finally, we show that the $${SL(2.\mathbb{C})}$$ charge and space-time momentum of the quantized string satisfy the Poincaré algebra.
Starting Page	53
Ending Page	69
Page Count	17
File Format	PDF
ISSN	01887009
Journal	Advances in Applied Clifford Algebras
Volume Number	26
Issue Number	1
e-ISSN	16614909
Language	English
Publisher	Springer International Publishing
Publisher Date	2015-05-09
Publisher Place	Cham
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	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

Matrix mechanics of the relativistic point particle and string in Clifford space

Applications of Matrix Algebra to Clifford Groups

Spinor spaces of Clifford algebras

Matrix Representations of the Low Order Real Clifford Algebras

A Construction of Matrix Representation of Clifford Algebras

Explicit Matrix Realization of Clifford Algebras

Clifford Algebras and Matrix Factorizations

Progress in Clifford Space Gravity

RETRACTED ARTICLE: Matrix Representation of the Real Clifford Algebra

Matrix Mechanics of the Relativistic Point Particle and String in Clifford Space

Similar Documents

Matrix mechanics of the relativistic point particle and string in Clifford space

Applications of Matrix Algebra to Clifford Groups

Spinor spaces of Clifford algebras

Matrix Representations of the Low Order Real Clifford Algebras

A Construction of Matrix Representation of Clifford Algebras

Explicit Matrix Realization of Clifford Algebras

Clifford Algebras and Matrix Factorizations

Progress in Clifford Space Gravity

RETRACTED ARTICLE: Matrix Representation of the Real Clifford Algebra

Matrix Mechanics of the Relativistic Point Particle and String in Clifford Space