'Lie group' presentation slideshows

8. The Group SU(2) and more about SO(3)

8. The Group SU(2) and more about SO(3). SU(2) = Group of 2 ?2 unitary matrices with unit determinant. Simplest non-Abelian Lie group. Locally equivalent to SO(3); share same Lie algebra. Compact & simply connected ? All IRs are single-valued.

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Intro to SUSY I: SUSY Basics

Archil Kobakhidze PRE-SUSY 2016 SCHOOL 27 JUNE -1 JULY 2016, MELBOURNE. Intro to SUSY I: SUSY Basics. What are these lectures about?

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FIRST (FP7/ Marie-Curie ) F ronts and I nterfaces in S cience & T echnlogy

FIRST (FP7/ Marie-Curie ) F ronts and I nterfaces in S cience & T echnlogy Adaptive and directional local processing in image processing Arpan Ghosh Supervisor: R.Duits. Directional processing image processing. neural fibers in brain. bone-structure. catheters. muscle cells.

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DARPA Oasis PI Meeting

DARPA Oasis PI Meeting. Hilton Head, SC March 2002. Network Classifications & Flows as Markov Lie Algebra Transformations. DARPA OASIS PI Meeting Hilton Head SC Tuesday March 12, 2002 Joseph E. Johnson, PhD. Introduction to Lie Groups & Algebras. Lie Groups and Lie Algebras.

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Ged Ridgway

CMIC Journal Club R. Woods (2003) Neuroimage Characterising Volume and Surface Deformations in an Atlas Framework. Ged Ridgway. About this paper. Very mathematical Sorry (a little bit) But few equations No results But a lot of novelty Many useful concepts/relations to other work

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Scale invariance

Scale invariance. Object of which a detail when enlarged becomes (approximately) identical to the object itself. Condition of self-similarity leads to properties defined in fractal dimensions. Examples of scale invariance . Snow flakes. Lungs. Trees. Neurons. Symmetry in art.

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Single-slew manoeuvres for spin-stabilized spacecraft

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Multi-Partite Squeezing and SU (1,1) Symmetry

Zahra Shaterzadeh Yazdi Institute for Quantum Information Science, University of Calgary with Peter S. Turner and Dr. Barry C. Sanders IICQI 2007 Conference, Kish University, Kish Island, Iran Sunday, 9 th September 2007.

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Mathematical Physics Seminar Notes Lecture 3 Global Analysis and Lie Theory

Mathematical Physics Seminar Notes Lecture 3 Global Analysis and Lie Theory. Wayne M. Lawton Department of Mathematics National University of Singapore 2 Science Drive 2 Singapore 117543. Email matwml@nus.edu.sg Tel (65) 6874-2749. 1. Commuting Vector Fields. Theorem. If. then there.

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GENERIC RELATIVITY

GENERIC RELATIVITY. David Ritz Finkelstein Georgia Institute of Technology FQXi Reykjavic, 2007.07.22. Thanks. Heinrich Saller (Heisenberg Institute) Andrei Galiautdinov, James Baugh, Mohsen Shiri-Garakani (Georgia Tech) Ruis Vilela Mendes (Lisbon) Tchavdar Palev (Sofia) Many others.

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Three-dimensional Lorentz Geometries

Three-dimensional Lorentz Geometries . Sorin Dumitrescu Univ. Paris 11 (Orsay). Joint work with Abdelghani Zeghib. Klein geometries. Definition: A Klein geometry (G,X=G/H) is a simply connected space X endowed with a transitive action of a Lie group G.

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Rotation Group

Rotation Group. A metric is used to measure the distance in a space. Euclidean space is delta An orthogonal transformation preserves the metric. Inverse is transpose Determinant squared is 1 The special orthogonal transformation has determinant of +1. Metric Preserving. x 3. x 2. x 1.

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Symplectic Group

Symplectic Group. The orthogonal groups were based on a symmetric metric. Symmetric matrices Determinant of 1 An antisymmetric metric can also exist. Transpose is negative Bilinear function. Antisymmetry. Dimension 2n. To have an inverse a matrix must be non-singular.

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Lie Generators

Lie Generators. Lie groups are continuous. Continuous coordinate system Finite dimension Origin is identity. The multiplication law is by analytic functions. Two elements x , y Consider z = xy There are N analytic functions that define the coordinates. Based on 2 N coordinates.

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