0
$\begingroup$

I'm following my professor's notes on QFT, and I cannot understand this passage. It's about an infinitesimal transformation for the coordinates of a scalar field $\phi$. The passage reads:

Let us consider an infinitesimal spacetime translation $$x^{\nu} \to x^{' \nu} = x^{\nu} - \epsilon^{\nu}$$ whence $$\phi_i (x) \to \phi'_i (x) = \phi'_i (x' + \epsilon) = \phi_i (x) + \epsilon^{\nu} \partial_{\nu} \phi_i(x)$$

I really don't get why he goes to $\phi'$ and I don't get the very last two terms of the equality (the scalar fields plus the derivative).

Can you help me?

Improve this question
$\endgroup$
3
  • 1
    $\begingroup$ Does this answer your question? Coordinate Transformation of Scalar Fields in QFT $\endgroup$
    – Tobias Fünke
    Commented Jan 19 at 23:22
  • $\begingroup$ @TobiasFünke I was indeed reading that answer. It's still not clear to me why $\phi' = \phi$ though $\endgroup$
    – Heidegger
    Commented Jan 19 at 23:25
  • 1
    $\begingroup$ By definition, scalar fields transform under a Poincare transformations as $\phi'(x):=\phi(\Lambda^{-1}x)$, so if $\Lambda x:=x-\lambda$, then $\phi'(x)=\phi(x+\lambda)$. This is the active view point. $\endgroup$
    – Tobias Fünke
    Commented Jan 19 at 23:29

0

Reset to default