Levi-Civita and Kronecker delta notation
I was wondering how to do the following
$epsilon_{ijk}sigma_{jk}=epsilon_{iji}=0$
I get this is $0$ but don't understand how they got the $epsilon_{iji}$
calculus kronecker-delta
edited Dec 2 at 18:02
Bernard
118k639112
asked Dec 2 at 17:11
Vicem0n
223
add a comment |
I was wondering how to do the following
$epsilon_{ijk}sigma_{jk}=epsilon_{iji}=0$
I get this is $0$ but don't understand how they got the $epsilon_{iji}$
calculus kronecker-delta
edited Dec 2 at 18:02
Bernard
118k639112
asked Dec 2 at 17:11
Vicem0n
223
1
To get more than one character in subscript in Mathmode, surround all of the things you want to be in subscript with {}. e.g. $epsilon_{ijk}$ is written epsilon_{ijk}. I've made these edits in your question.
– Rhys Steele
Dec 2 at 17:15
1
What is the $sigma_{Jk}$ here ?
– Emilio Novati
Dec 2 at 17:19
add a comment |
I was wondering how to do the following
$epsilon_{ijk}sigma_{jk}=epsilon_{iji}=0$
I get this is $0$ but don't understand how they got the $epsilon_{iji}$
calculus kronecker-delta
edited Dec 2 at 18:02
Bernard
118k639112
asked Dec 2 at 17:11
Vicem0n
223
I was wondering how to do the following
$epsilon_{ijk}sigma_{jk}=epsilon_{iji}=0$
I get this is $0$ but don't understand how they got the $epsilon_{iji}$
calculus kronecker-delta
calculus kronecker-delta
edited Dec 2 at 18:02
Bernard
118k639112
asked Dec 2 at 17:11
Vicem0n
223
edited Dec 2 at 18:02
Bernard
118k639112
asked Dec 2 at 17:11
Vicem0n
223
edited Dec 2 at 18:02
Bernard
118k639112
edited Dec 2 at 18:02
Bernard
118k639112
edited Dec 2 at 18:02
Bernard
118k639112
118k639112
asked Dec 2 at 17:11
Vicem0n
223
asked Dec 2 at 17:11
Vicem0n
223
asked Dec 2 at 17:11
Vicem0n
223
223
1
To get more than one character in subscript in Mathmode, surround all of the things you want to be in subscript with {}. e.g. $epsilon_{ijk}$ is written epsilon_{ijk}. I've made these edits in your question.
– Rhys Steele
Dec 2 at 17:15
1
What is the $sigma_{Jk}$ here ?
– Emilio Novati
Dec 2 at 17:19
add a comment |
1
To get more than one character in subscript in Mathmode, surround all of the things you want to be in subscript with {}. e.g. $epsilon_{ijk}$ is written epsilon_{ijk}. I've made these edits in your question.
– Rhys Steele
Dec 2 at 17:15
1
What is the $sigma_{Jk}$ here ?
– Emilio Novati
Dec 2 at 17:19
1
1
To get more than one character in subscript in Mathmode, surround all of the things you want to be in subscript with {}. e.g. $epsilon_{ijk}$ is written epsilon_{ijk}. I've made these edits in your question.
– Rhys Steele
Dec 2 at 17:15
To get more than one character in subscript in Mathmode, surround all of the things you want to be in subscript with {}. e.g. $epsilon_{ijk}$ is written epsilon_{ijk}. I've made these edits in your question.
– Rhys Steele
Dec 2 at 17:15
1
1
What is the $sigma_{Jk}$ here ?
– Emilio Novati
Dec 2 at 17:19
What is the $sigma_{Jk}$ here ?
– Emilio Novati
Dec 2 at 17:19
add a comment |
1 Answer
1
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votes
We have $epsilon_{ijk}delta_{jk}=epsilon_{ijj}=epsilon_{jij}$, where the second $=$ uses cyclic invariance. The statements $epsilon_{iji}=0,,epsilon_{jij}=0$ are really the same statement twice, differently indexed. Any source that wrote $epsilon_{ijk}delta_{jk}=epsilon_{iji}$ has effected an $ileftrightarrow j$ relabelling, which shouldn't have been done, not least because it changes which index isn't contracted.
answered Dec 2 at 18:10
J.G.
22.5k22035
add a comment |
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1 Answer
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active
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1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
We have $epsilon_{ijk}delta_{jk}=epsilon_{ijj}=epsilon_{jij}$, where the second $=$ uses cyclic invariance. The statements $epsilon_{iji}=0,,epsilon_{jij}=0$ are really the same statement twice, differently indexed. Any source that wrote $epsilon_{ijk}delta_{jk}=epsilon_{iji}$ has effected an $ileftrightarrow j$ relabelling, which shouldn't have been done, not least because it changes which index isn't contracted.
answered Dec 2 at 18:10
J.G.
22.5k22035
add a comment |
We have $epsilon_{ijk}delta_{jk}=epsilon_{ijj}=epsilon_{jij}$, where the second $=$ uses cyclic invariance. The statements $epsilon_{iji}=0,,epsilon_{jij}=0$ are really the same statement twice, differently indexed. Any source that wrote $epsilon_{ijk}delta_{jk}=epsilon_{iji}$ has effected an $ileftrightarrow j$ relabelling, which shouldn't have been done, not least because it changes which index isn't contracted.
answered Dec 2 at 18:10
J.G.
22.5k22035
add a comment |
We have $epsilon_{ijk}delta_{jk}=epsilon_{ijj}=epsilon_{jij}$, where the second $=$ uses cyclic invariance. The statements $epsilon_{iji}=0,,epsilon_{jij}=0$ are really the same statement twice, differently indexed. Any source that wrote $epsilon_{ijk}delta_{jk}=epsilon_{iji}$ has effected an $ileftrightarrow j$ relabelling, which shouldn't have been done, not least because it changes which index isn't contracted.
answered Dec 2 at 18:10
J.G.
22.5k22035
We have $epsilon_{ijk}delta_{jk}=epsilon_{ijj}=epsilon_{jij}$, where the second $=$ uses cyclic invariance. The statements $epsilon_{iji}=0,,epsilon_{jij}=0$ are really the same statement twice, differently indexed. Any source that wrote $epsilon_{ijk}delta_{jk}=epsilon_{iji}$ has effected an $ileftrightarrow j$ relabelling, which shouldn't have been done, not least because it changes which index isn't contracted.
answered Dec 2 at 18:10
J.G.
22.5k22035
answered Dec 2 at 18:10
J.G.
22.5k22035
answered Dec 2 at 18:10
J.G.
22.5k22035
answered Dec 2 at 18:10
J.G.
22.5k22035
22.5k22035
add a comment |
add a comment |
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1
To get more than one character in subscript in Mathmode, surround all of the things you want to be in subscript with {}. e.g. $epsilon_{ijk}$ is written epsilon_{ijk}. I've made these edits in your question.
– Rhys Steele
Dec 2 at 17:15
1
What is the $sigma_{Jk}$ here ?
– Emilio Novati
Dec 2 at 17:19