Mihai, Daniela
(2007)
Mathematical Aspects of Twistor Theory: Null Decomposition of Conformal Algebras and Selfdual Metrics on Intersections of Quadrics.
Doctoral Dissertation, University of Pittsburgh.
(Unpublished)
Abstract
<p>The conformal algebra of an ndimensional affine space with a metric of arbitrary signature (p, q) with p + q = n is considered. The case of broken conformal invariance is studied, by considering the subalgebra of the enveloping algebra of the conformal algebra that commutes with the squaredmass operator. This algebra, denoted R, is generated by the generators of the Poincaré Lie algebra and an additional vector operator R which preserves the relevant information when the conformal invariance is broken. Due to the nonlinearity of the algebra, finding the Casimir invariants becomes extremely difficult. The Ralgebra is constructed for arbitrary dimensions, but the Casimir invariants are only determined for n ≤ 5. The second part of this thesis describes the geometric properties of metrics on the twistor space on intersections of quadrics. Consider a generic pencil of quadrics in a complex projective space ℂℙ⁵. The base locus of this pencil is considered as a threedimensional projective twistor space, such that each point of the associated spacetime is a projective twoplane lying inside one quadric of the pencil. The time coordinate can be described as a hyperelliptic curve of genus two, over which the space time is fibered. The metrics arising on the associated twistor space of the completely null twoplanes are studied. It emerges that for pencils generated by simultaneously diagonalizable quadrics, these metrics are always selfdual and, in certain cases, conformal to vacuum. </p>
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Details
Item Type: 
University of Pittsburgh ETD

Status: 
Unpublished 
Creators/Authors: 

ETD Committee: 

Date: 
31 January 2007 
Date Type: 
Completion 
Defense Date: 
26 October 2006 
Approval Date: 
31 January 2007 
Submission Date: 
4 December 2006 
Access Restriction: 
No restriction; Release the ETD for access worldwide immediately. 
Institution: 
University of Pittsburgh 
Schools and Programs: 
Dietrich School of Arts and Sciences > Mathematics 
Degree: 
PhD  Doctor of Philosophy 
Thesis Type: 
Doctoral Dissertation 
Refereed: 
Yes 
Uncontrolled Keywords: 
Casimir invariants; conformal algebra; selfdual metrics; twistors 
Other ID: 
http://etd.library.pitt.edu/ETD/available/etd12042006210854/, etd12042006210854 
Date Deposited: 
10 Nov 2011 20:07 
Last Modified: 
15 Nov 2016 13:53 
URI: 
http://dscholarship.pitt.edu/id/eprint/10016 
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