Sigma matrices question Group theory

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Homework Help Overview

The discussion revolves around the properties of 2x2 Hermitian matrices in the context of group theory. The original poster questions why every 2x2 Hermitian matrix must satisfy a specific equation mentioned in a textbook, expressing confusion about the reasoning behind it.

Discussion Character

  • Exploratory, Conceptual clarification

Approaches and Questions Raised

  • The original poster seeks clarification on the necessity of a particular equation for Hermitian matrices, questioning whether the reasoning is obvious or requires extensive calculation. Another participant suggests that the properties of Hermitian matrices, such as having real diagonal elements and complex conjugate off-diagonal elements, make the equation seem apparent.

Discussion Status

The discussion includes expressions of uncertainty and attempts to clarify the properties of Hermitian matrices. While one participant acknowledges the apparent nature of the equation, there is no explicit consensus on the reasoning, and the conversation remains open-ended.

Contextual Notes

Participants reference a specific equation from a textbook, but the details of this equation are not provided in the discussion. There is an indication of a lack of detailed explanation in the textbook regarding the equation's necessity.

helpcometk
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Homework Statement


I have read the following text in a textbook(look the attaxhement) ,and i have a
simple question .WHY every 2x2 hermitian matrix would have to satisfy this Equation.It is not obvious to me why.Does anyone know the answer?
The textbook stops there without giving any answer.Is it something obvious?
Is there any lengthy calculation to show this?


Homework Equations





The Attempt at a Solution

 

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helpcometk said:

Homework Statement


I have read the following text in a textbook(look the attaxhement) ,and i have a
simple question .WHY every 2x2 hermitian matrix would have to satisfy this Equation.It is not obvious to me why.Does anyone know the answer?
The textbook stops there without giving any answer.Is it something obvious?
Is there any lengthy calculation to show this?


Homework Equations





The Attempt at a Solution


It's sort of obvious just looking at the expression (5.27). Hermitian matrices have real diagonal elements and the two off-diagonal elements are complex conjugates. By selecting values of x0,x1,x2,x3 you can get any such matrix.
 
Yes its sort of obvious that I am stupid.
Thanks
 
helpcometk said:
Yes its sort of obvious that I am stupid.
Thanks

Hey, I miss the obvious too sometimes. Doesn't make you stupid.
 

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