Mihai, Daniela
(2007)
Mathematical Aspects of Twistor Theory: Null Decomposition of Conformal Algebras and Self-dual Metrics on Intersections of Quadrics.
Doctoral Dissertation, University of Pittsburgh.
(Unpublished)
Abstract
<p>The conformal algebra of an n-dimensional 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 squared-mass 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 R-algebra 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 three-dimensional projective twistor space, such that each point of the associated space-time is a projective two-plane 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 two-planes are studied. It emerges that for pencils generated by simultaneously diagonalizable quadrics, these metrics are always self-dual and, in certain cases, conformal to vacuum. </p>
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Details
| Item Type: |
University of Pittsburgh ETD
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| Status: |
Unpublished |
| Creators/Authors: |
|
| ETD Committee: |
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| 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; self-dual metrics; twistors |
| Other ID: |
http://etd.library.pitt.edu/ETD/available/etd-12042006-210854/, etd-12042006-210854 |
| Date Deposited: |
10 Nov 2011 20:07 |
| Last Modified: |
15 Nov 2016 13:53 |
| URI: |
http://d-scholarship.pitt.edu/id/eprint/10016 |
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