I Noether's Theorem for Translation in Field Theory

[binbagsss]

I am trying to follow the following post.
[Mentors' note: The "following post" is from https://physics.stackexchange.com/q...onservation-law-corresponds-to-lorentz-boosts]

I dont understand how they have got the expression for the current for translations from the general expressions for the current. so from what I see from the $\delta x^{\mu}$ stated for a translation , they are saying into the above substitute $a^{\nu}=\delta^{\mu}_{\nu}$ into the general expression. But obviously this is not what it is saying as this would not give me the right expression.

Thanks

 

[haushofer]

I am trying to follow the following post.

I dont understand how they have got the expression for the current for translations from the general expressions for the current. so from what I see from the $\delta x^{\mu}$ stated for a translation , they are saying into the above substitute $a^{\nu}=\delta^{\mu}_{\nu}$ into the general expression.

How'd you figure that? That expression doesn't even make sense tensorially; the indices don't match. Don't you mean $\delta x^{\mu} = a^{\mu}$?

 

[binbagsss]

How'd you figure that? That expression doesn't even make sense tensorially; the indices don't match. Don't you mean $\delta x^{\mu} = a^{\mu}$?

they've wrote $\delta x^{\mu}=\delta^{\mu}_{\nu}$ haven't they?!

 

[renormalize]

they've wrote $\delta x^{\mu}=\delta^{\mu}_{\nu}$ haven't they?!

Not true. Can you show the specific line in the post where you think the author states or implies this?

 

[vela]

Not true. Can you show the specific line in the post where you think the author states or implies this?

Near the bottom of the image from the text, it says $m_\nu \leftrightarrow \delta x^\mu = \epsilon \delta_\nu^\mu$. The notation is confusing to say the least. Assuming it's not a typo, I'd guess the author means a translation along just one of the coordinate directions.

 

[haushofer]

they've wrote $\delta x^{\mu}=\delta^{\mu}_{\nu}$ haven't they?!

Yes, now I see it, I didn't see that expression yesterday. Anyway, it must be a typo, because that doesn't make sense, and again, you don't give the source of this text so we can't check to see what the author(s) is probably meaning.

 

[Nugatory]

A short digression on posting etiquette has been removed.
We're leaving this post open in case someone can post a clarification of what this stackexchange post is trying to say.
@binbagsss you could have saves yourself and us mentors some grief by providing more context from the beginning.

 

[binbagsss]

anyone able to help

 

[haushofer]

Do you want us to tell you what that author meant, or do you want us to explain how to obtain the Noether currents belonging to translation invariance of the action? Frankly, I still don't understand the notation of the author.