Now I see that the contravariant and covariant metric tensor are not the same. x0 = x0 and xa = - xa with the (+,-,-,-) metric we used. The same lecturer also teaches classical mechanics and it was during this class, when I think he said there is no difference between the contravariant and...
Thanks very much, I have just finished that part of the question and it worked out. I was not confident of what I was doing but I am now.
The fact that there were only lower indices confused me too, I vaguely remember my lecturer saying because its Minkowski space, contravariant and covariant...
εikl εjmngkmMkn =
εikl εjknMkn = (in book it changed sign to -εikl εjknMkn - Why? )
By identity
εikl εnjkMln = (δinδkj - δijδkn)Mkn = ?
I then get ..
Mji - δij Mnn ( is this correct ?)
There 's more to the question but if can get this part right, I should be able to complete the...
It was a very unfocused question, sorry about that. After a lot of reading online, I think I found what I was looking for.
1. What is the difference (or connection) between them?
My attempt at answering Q_1.
The connection between a Lie group and its Lie algebra is the fact that the Lie algebra...
I am just starting a QM course. I hope these are reasonable questions. I have been given my first assignment. I can answer the questions so far but I do not really understand what's going on. These questions are all about so(N) groups, Pauli matrices, Lie brackets, generators and their Lie...
Yes, I see that now after researching online ( I read almost all real numbers are transcendental-that's news to me). I should probably have used a transcendental number in my argument.
Are transcendental numbers the reason why the set of irrational numbers is uncountable?
I was just using ##\sqrt{61}## as an example of an irrational number and a member of an uncountable set. I thought irrational numbers might cause problems in MW, specifically when the universe branches. I need to do a lot more work not just in QM but also on the underlying maths.
I have just...
Perok thanks for your reply. Your point that ' the wavefuction does not create universes; rather, it splits the one universe into multiple "worlds" is well taken. I am guessing this is to do with energy.
My question arose most likely because I do not understand enough about uncountable sets...
Schrodinger’s Cat and the many worlds interpretation states that the wave function collapse doesn’t happen at all; every possible outcome of an observation actually comes to pass in its own separate universe. We are presented with a binary (discrete) outcome (dead or alive) but what if there...