4
votes
2answers
84 views

Commutation relations of the generators of the conformal group

My question is from P.98 of the book by Di Francesco on Conformal Field theory. He gives the six non-vanishing commutation relations between the elements $P_{\mu}, D, L_{\mu \nu}$ and $K_{\mu}$ ...
0
votes
3answers
71 views

Commutator summation notation

I have the relation $ e^L M e^{-L}=\sum_{n=0}^\infty \frac 1{n!} [L,M]_{(n)}$ where $L$ and $M$ are operators. What does the subscript $n$ after the commutator bracket denote?
3
votes
1answer
296 views

What exactly is the connection between the Jacobi and Bianchi identities

While reviewing some basic field theory, I once again encountered the Bianchi identity (in the context of electromagnetism). It can be written as $$\partial_{[\lambda}\partial_{[\mu}A_{\nu]]}=0$$ ...
3
votes
1answer
464 views

What physical significance has the Heisenberg Group?

I read that the canonical commutation relation between momentum and position can be seen as the Lie Algebra of the Heisenberg group. While I get why the commutation relations of momentum and momentum, ...
3
votes
1answer
366 views

Commutator of Lorentz boost generators : visual interpretation

I have always struggled to visualize the correctness of the commutation relation for the generators of the boost in the Lorentz group. We have $$[K_i,K_j] = i \epsilon_{ijk} L_k$$ I fail to picture ...
1
vote
1answer
290 views

Commutators with a density matrix

The equation describing the evolution of our system is as follows: $ \dot{\rho} = u_1(t)(a^\dagger a \rho - 2a\rho a^\dagger +\rho a^\dagger a) + u_2(t)(a a^\dagger \rho - 2a^\dagger\rho a +\rho a ...