- #1

- 167

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How do I expand

[tex]i\hbar \gamma^0[/tex]

the matrix in this term, I am a bit lost. All the help would be appreciated!

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- Thread starter help1please
- Start date

- #1

- 167

- 0

How do I expand

[tex]i\hbar \gamma^0[/tex]

the matrix in this term, I am a bit lost. All the help would be appreciated!

- #2

- 12

- 0

How do I expand

[tex]i\hbar \gamma^0[/tex]

the matrix in this term, I am a bit lost. All the help would be appreciated!

It's itself.Using Mathematica.

- #3

- 167

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Expanding that, gives back that?

What is mathematica??

What is mathematica??

- #4

Bill_K

Science Advisor

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- #5

- 167

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so you don't know how to expand the terms I asked of?

- #6

Bill_K

Science Advisor

- 4,155

- 201

I thought the Wikipedia article explained it pretty clearly. It gives the explicit form of γso you don't know how to expand the terms I asked of?

But if that's not what you mean by "expanding" it, the only other thing to do is this...

iħγ

- #7

- 167

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I thought the Wikipedia article explained it pretty clearly. It gives the explicit form of γ^{0}in the Dirac, Weyl and Majorana representations. Isn't that what you want?

But if that's not what you mean by "expanding" it, the only other thing to do is this...

iħγ^{0}

Why have that when I started off with that... my equation I really thought was simple. HOW do you expand [tex]i \hbar \gamma^0[/tex]

The answer I was looking for was not a go to wiki one! And no wiki does not explain it well for me, I am new at this stuff.

- #8

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Can you show me, in plane mathematical language, in an equation, how to expand it please.

- #9

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- #10

- 642

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Do you mean this? [itex]\qquad \gamma^0 =

\begin{pmatrix}

1 & 0 & 0 & 0\\

0 & 1 & 0 & 0\\

0 & 0 & -1 & 0\\

0 & 0 & 0 & -1

\end{pmatrix} \qquad \qquad

[/itex] (which is the Dirac representation)

so that [itex]\ \ \qquad \qquad i \hbar \gamma^0 =

\begin{pmatrix}

i \hbar & 0 & 0 & 0\\

0 & i \hbar & 0 & 0\\

0 & 0 & -i \hbar & 0\\

0 & 0 & 0 & -i \hbar

\end{pmatrix} \qquad \qquad

[/itex]

\begin{pmatrix}

1 & 0 & 0 & 0\\

0 & 1 & 0 & 0\\

0 & 0 & -1 & 0\\

0 & 0 & 0 & -1

\end{pmatrix} \qquad \qquad

[/itex] (which is the Dirac representation)

so that [itex]\ \ \qquad \qquad i \hbar \gamma^0 =

\begin{pmatrix}

i \hbar & 0 & 0 & 0\\

0 & i \hbar & 0 & 0\\

0 & 0 & -i \hbar & 0\\

0 & 0 & 0 & -i \hbar

\end{pmatrix} \qquad \qquad

[/itex]

Last edited:

- #11

- 167

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Do you mean this? [itex]\qquad \gamma^0 =

\begin{pmatrix}

1 & 0 & 0 & 0\\

0 & 1 & 0 & 0\\

0 & 0 & -1 & 0\\

0 & 0 & 0 & -1

\end{pmatrix} \qquad \qquad

[/itex] (which is the Dirac representation)

so that [itex]\ \ \qquad \qquad i \hbar \gamma^0 =

\begin{pmatrix}

i \hbar & 0 & 0 & 0\\

0 & i \hbar & 0 & 0\\

0 & 0 & -i \hbar & 0\\

0 & 0 & 0 & -i \hbar

\end{pmatrix} \qquad \qquad

[/itex]

Why is then when [tex]\gamma^{0}^2[/tex] is equal to 1?

- #12

- 642

- 15

\begin{pmatrix}

1 & 0 & 0 & 0\\

0 & 1 & 0 & 0\\

0 & 0 & -1 & 0\\

0 & 0 & 0 & -1

\end{pmatrix}

\begin{pmatrix}

1 & 0 & 0 & 0\\

0 & 1 & 0 & 0\\

0 & 0 & -1 & 0\\

0 & 0 & 0 & -1

\end{pmatrix} =

\begin{pmatrix}

1 & 0 & 0 & 0\\

0 & 1 & 0 & 0\\

0 & 0 & 1 & 0\\

0 & 0 & 0 & 1

\end{pmatrix}

[/tex]

- #13

- 167

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I don't know what I read earlier but this didn't immediately pop out to me! ty

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