Hey there! Sign in to join this conversationNew here? Join for free
    • Thread Starter
    Offline

    14
    ReputationRep:
    Stuck on a question - seems like it must just be some manipulation but I can't seem to get it.

    A tensor of rank 4 satisfies Tjikl = -Tijkl = Tijlk and Tijij=0

    Show that Tijkl = -EijpEklqTrqrp

    Where those 'E's are Cevi Levita symbols.

    I've figured that the first two indices must be different than each other to give a non-zero value, and the same with the last two indices.

    Help would be much appreciated. Thanks.
    Offline

    1
    ReputationRep:
    Does anyone have a solution?
    Offline

    18
    ReputationRep:
    Will skip out the details but here's an outline: define S_{pq}=\varepsilon_{ijp} \varepsilon_{klq}T_{ijkl}

    Then \varepsilon_{abp}\varepsilon_{cd  q} S_{pq}=\varepsilon_{abp} \varepsilon_{cdq} \varepsilon_{ijp} \varepsilon_{klq}T_{ijkl} \Rightarrow \varepsilon_{abp}\varepsilon_{cd  q}S_{pq}=4T_{abcd}. Contracting a,c we get T_{abad}=-\frac{1}{4}S_{bd}

    Substitute back into the equality that preceded the contraction and you have the desired expression (with relabelling)
 
 
 
Poll
Do you agree with the PM's proposal to cut tuition fees for some courses?
Useful resources

Make your revision easier

Maths

Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

Equations

How to use LaTex

Writing equations the easy way

Student revising

Study habits of A* students

Top tips from students who have already aced their exams

Study Planner

Create your own Study Planner

Never miss a deadline again

Polling station sign

Thinking about a maths degree?

Chat with other maths applicants

Can you help? Study help unanswered threads

Groups associated with this forum:

View associated groups

The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE

Write a reply...
Reply
Hide
Reputation gems: You get these gems as you gain rep from other members for making good contributions and giving helpful advice.