Recent content by ferret123

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    Determine condition on invariants under transformation

    The lecturer made the decision to extend the deadline until Friday midday due to a typo in the second question
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    Determine condition on invariants under transformation

    Its a homework problem that does count for credit but I doubt there would be any problem so long as the solution isn't being handed to us, after all we are encouraged to work together and ask for help at tutorials etc so long as the final submitted piece of work reflects our understanding, so...
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    Determine condition on invariants under transformation

    Yeah I'll repost the entire question should be able to access it here http://www2.ph.ed.ac.uk/~rzwicky2/SoQM/Ast_SoQM_14_3.pdf [Broken] with the lecture notes here http://www2.ph.ed.ac.uk/~rzwicky2/SoQM/notes.pdf [Broken] I've also had doubts about what the first part of this question means...
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    Determine condition on invariants under transformation

    Ok, \delta'_{ij}\rho_{ik}\rho_{jl}a_{k}b_{l} = \delta_{ij}a_{i}b_{j} then to me factoring out the a and b terms should require all terms being summed over together so we have \delta'_{ij}\rho_{ik}\rho_{jl}a_{k}b_{l} - \delta_{ij}a_{i}b_{j} = 0 the relabeling i=k,\ j=l I get...
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    Determine condition on invariants under transformation

    So we start with \delta'_{ij}\rho_{ik}\rho_{jl}a_{k}b_{l} = \delta_{ij}a_{i}b_{j} I feel like I then want subract the RHS to give me an expression equal to 0 from which I can then factor out the a and b terms letting what's left become X_{ij} although I'm not particularly confident this is...
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    Determine condition on invariants under transformation

    Surely by the supposition method you have to make the assumption that \rho\rho^{T} = I\ \&\ det(\rho) = 1 to gain the equalities for the transformed tensors?
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    Determine condition on invariants under transformation

    Ok, so with a'_{i} = \rho_{ij}a_{j} I find that \delta'_{ij}a'_{i}b'_{j} = \delta'_{ij}\rho_{ik}a_{k}\rho_{jl}b_{l} which then I'm not sure if I can then just equate the delta dashed with the rho's to the non transformed delta I assume not due to the summation?
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    Determine condition on invariants under transformation

    Well for the first I getRR^{T} = r_{ij}r{ji} = \delta_{ij} is this the condition? Then we have \epsilon_{imr}det(R) = \epsilon_{jns}r_{ij}r_{mn}r_{rs} with det(R) = 1 leaving the equation invariant. However the second part of the problem asks: Show that these conditions are related to the...
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    Determine condition on invariants under transformation

    Not OP but also working on this problem and having a similar problem in getting started so thought I'd post in here rather than start my own thread. Anyway, from what I've seen on the Wikipedia page the condition is that RR^{T} = I? Which goes along with det(R) = 1 in defining SO(3).
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    Expansions of Functions Analytic at Infinity

    Ok I've really over complicated it then, thanks! So then when I change back to f I get the desired result analytic outside of a disk with radius 1/radius of the g disk. The next part of the question is looking for an expansion of this form for for \frac{z-1}{z+1} \& \frac{z^{2}}{z^{2} - 1}. I...
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    Expansions of Functions Analytic at Infinity

    Homework Statement Prove that if f(z) is analytic at infinity, then it has expansion of the form f(z) = \sum_{n=0}^{+\infty} \frac{a_{n}}{z^{n}} converging outside some disk.2. The attempt at a solution I know that for f(z) to be analytic at infinity we want to consider the composite...
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    Character Table Soduku Homework Statement

    Homework Statement Complete the character table giving a brief explanation of each step. Hint: You should use the fact that some representations are one dimensional. 2. The attempt at a solution Reading through Mathematical Methods for Physics and Engineering by Riley, Hobson &...
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    Complex Square Root Analyticity

    Ok thanks for all help and clarification
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    Complex Square Root Analyticity

    No so the branch is analytic there, thanks. The next part of the question asks for analyticity on the exterior of the disk with the hint ##z^{2} - 1 = z^{2}(1-z^{-2})##. I assume I approach this in a similar way except a branch cut from 1 to -1 now makes more sense?
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    Complex Square Root Analyticity

    Ok because then it would be crossing the branch cut? So if I express each of the parts as mentioned there that will give me an analytic branch on the interior of the unit disk?
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