- #1
ChrisVer
Gold Member
- 3,378
- 464
If I am not mistaken, the change of the minkowski metric to:
[itex] n_{\mu\nu} \rightarrow g_{\mu\nu}(x)[/itex]
will violate the Poincare invariance of (example) the Electromagnetism Action.
However it allows us to define a wider set of arbitrary transformations (coordinate transformations).
The last line confuses me. If I can choose a general coordinate system without a problem (since everything will remain invariant) what restricts my choice not to be of the form:
[itex] x'^{a}(x^{b})= Λ^{a}_{b}x^{b}+p^{a}[/itex]?
[itex] n_{\mu\nu} \rightarrow g_{\mu\nu}(x)[/itex]
will violate the Poincare invariance of (example) the Electromagnetism Action.
However it allows us to define a wider set of arbitrary transformations (coordinate transformations).
The last line confuses me. If I can choose a general coordinate system without a problem (since everything will remain invariant) what restricts my choice not to be of the form:
[itex] x'^{a}(x^{b})= Λ^{a}_{b}x^{b}+p^{a}[/itex]?