The Maxwell algebra: Symmetries of a particle in an electromagnetic field

Neeling, Dijs de (2020) The Maxwell algebra: Symmetries of a particle in an electromagnetic field. Master's Thesis / Essay, Physics.

Preview	Text mPHYS_2020_deNeelingDW.pdf Download (781kB) | Preview
	Text Toestemming.pdf Restricted to Registered users only Download (94kB)

Abstract

The Maxwell algebra is an extension of the Poincar´e algebra. When it is nonlinearly realised in a particle Lagrangian, the dynamics are that of a charged particle in a constant electromagnetic field. The algebra can be extended further, in an iterative way, up to an infinitely large Z-graded algebra (with empty negative levels) containing a free Lie algebra. Truncations to a finite level of the infinite algebra can be considered, giving dynamics consistent with a particle travelling through a field to which a higher order term in a Taylor expansion is added every level, but this is not all it describes. After giving an overview of the Maxwell algebra and some of its quotients, we describe how to nonlinearly realise its symmetries in Lagrangians and interpret theories built in this way. We show that a Lagrangian nonlinearly realising Maxwell up to and including the third level describes an induced dipole in a linear electromagnetic field. This dipole has the property that its electric and magnetic polarisability are equal and opposite, which can be realised by a perfect superconductor. Additionally, an attempt is made to establish a classification of classical electromagnetic particle theories, by using an analogy between the soft limit classification of scalar effective field theories and the Maxwell level structure.

Item Type:	Thesis (Master's Thesis / Essay)
Supervisor name:	Roest, D. and Bergshoeff, E.A.
Degree programme:	Physics
Thesis type:	Master's Thesis / Essay
Language:	English
Date Deposited:	27 Jul 2020 13:35
Last Modified:	27 Jul 2020 13:35
URI:	https://fse.studenttheses.ub.rug.nl/id/eprint/22700

Actions (login required)

View Item