Let ##Q_ik## be a symetric tensor, so that ##Q_ik= \frac{m}{2} \dot x_i \dot x_j + \frac{k}{2} x_i x_j## (here k is also a sub, couldn't do it better with LaTeX).
How do we derive such a tensor, with respect to time? And what could such a tensor mean in a physical sense? It really looks like the...
I'm self-studying field theory and trying to solidify my understanding of index manipulations. So I've been told that there is a general rule: " If the index is lowered on the 'denominator' then it's a raised index". My question is whether this is just a rule or something that can make sense...
Hello, I just want to clarify some things with a simple exercise: I have the equation ## \frac{\partial^2 f}{\partial A^\mu \,\partial A^\nu} = 0## and I want to integrate it once assuming that ## f=f(A^1,A^2,...,A^n)=f(A^\rho) ##.
I think the solution should be ## \frac{\partial f}{\partial...
Compare this with the definition of the inverse transformation Λ-1:
Λ-1Λ = I or (Λ−1)ανΛνβ = δαβ,............(1.33)
where I is the 4×4 indentity matrix. The indexes of Λ−1 are superscript for the first and subscript for the second as before, and the matrix product is formed as usual by...
Hi guys,
I have a very basic question about the WZ model. I want to show that it is invariant under SUSY transformations.
The action is \int{d^4 x} \partial^\mu \phi* \partial_\mu \phi +i\psi^† \bar{\sigma}^\mu \partial_\mu \psi
The SUSY transformations are \delta\phi = \epsilon \psi ...
Homework Statement
My question is regarding a single step in a solution to a given problem. The step begins at:
##\large \frac{\partial \alpha _j}{\partial x ^i}
\frac{\partial x^i}{y^p}
\frac{\partial x^j}{\partial y^q} -
\frac{\partial \alpha _j}{\partial x ^i}
\frac{\partial x^i}{\partial...