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Q1. A unitary matrix is defined by the requirement UtU = 1. a. A unitary matrix can be written as U = exp(io"T). Show that a 'generator' Ta is a IHermitian matrix. b. Find an explicit representation of the generators when U is a 2 x 2 unitary matrix. c. Consider an N x N unitary matrix. Ilow many lincarly independent generators are there?

Q1. A unitary matrix is defined by the requirement UtU = 1. a. A unitary matrix can be written as U = exp(io"T). Show that a 'generator' Ta is a IHermitian matrix. b. Find an explicit representation of the generators when U is a 2 x 2 unitary matrix. c. Consider an N x N unitary matrix. Ilow many lincarly independent generators are there?

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Q1. A unitary matrix is defined by the requirement UtU = 1. a. A unitary matrix can be written as U = exp(ia"T"). Show that a 'generator' T" is a IHermitian matrix. b. Find an explicit representation of the generators when U is a 2 x 2 unitary matrix. c. Consider an N x N unitary matrix. Ilow many linearly independent generators are there? d. A grand unified theory (GUT) is based on a gauge group U(5). Ilow many gauge bosons exist in this theory?
Transcribed Image Text:Q1. A unitary matrix is defined by the requirement UtU = 1. a. A unitary matrix can be written as U = exp(ia"T"). Show that a 'generator' T" is a IHermitian matrix. b. Find an explicit representation of the generators when U is a 2 x 2 unitary matrix. c. Consider an N x N unitary matrix. Ilow many linearly independent generators are there? d. A grand unified theory (GUT) is based on a gauge group U(5). Ilow many gauge bosons exist in this theory?
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