All Questions
5 questions
1
vote
0
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57
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If there is a spin-0 structure and i differentiate it with respect to a space dimension, does it become a spin-1 structure?
It might be a naive question but i was wondering what a derivative can do regarding spin. If there is a Riemann scalar it is clear that its an invariant object under tensor transformation and it does ...
- 153
2
votes
1
answer
634
views
Covariant derivative on $n$-forms
I am new to form notation. I have recently read that one can write (non-abelian) gauge theory in terms of forms. I am stuck and can't derive this equation below:
$$ \nabla_{A} \alpha_p = d \alpha_p + ...
- 882
2
votes
2
answers
164
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Is there a equivalent theorem for closed form/ exact form for derivative with respect to fields
For a vector (one-form) $A_\mu$, when
\begin{eqnarray}
\partial_{[\mu}A_{\nu]}=0
\end{eqnarray}
then, there exists a scalar $\phi$ such that
\begin{eqnarray}
A_\mu =\partial_\mu\phi
\end{eqnarray}
...
- 91
0
votes
2
answers
678
views
Derivative with respect to the spacetime derivative of a field $\phi$
I've encountered the following notation several times (for example, when discussing Noether's Theorem):
$$\frac{\partial L}{\partial(\partial_\mu \phi)}$$
And it's not immediately clear to me what ...
- 2,135
1
vote
1
answer
449
views
Covariant and contravariant derivatives in Klein-Gordon equation
Whilst exposing how a scalar product for the solutions of the Klein-Gordon equation (written as $(\Box + m^2)\varphi(x)=0$) can be derived, my textbook starts from the following system
\begin{cases} \...
- 245