2
$\begingroup$

  1. What is exactly meant by "Global part of a Local symmetry"?

  2. What are its implications on a field theory at classical level?

  3. What are its implications at quantum level?

  4. How is it related to symmetry breaking?

Improve this question
$\endgroup$
8
  • 4
    $\begingroup$ A local symmetry is a transformation whose parameters depends on space-time coordinates. There is a very particular case when these parameters are constant, so it can be view as a "global" symmetry. So, you can speak, if you want, of "global part" of a local symmetry. $\endgroup$
    – Trimok
    Commented Jun 12, 2013 at 18:09
  • 1
    $\begingroup$ I don't believe that @Trimok's explanation is so incomplete or unclear that it would require an example before it's usable. If you need an example after Trimok's explanation, then it's because you misunderstand not only what is a "global part of a local symmetry" but you misunderstand what a local symmetry itself means, too. $\endgroup$
    – Luboš Motl
    Commented Jun 12, 2013 at 18:40
  • 1
    $\begingroup$ @Palash : Think about local symmetry as a set. There is a particular subset of this set when transformation parameters are constant. So the "global part" of local symmetries is a particular subset of the local symmetry set. More precisely, local symmetries transformation parameters are defined as $a_i(x,t)$. A particular case is $a_i(x,t)$ = Constant $a_i$. This very particular case corresponds to what you call the "global part" of the local symmetry. $\endgroup$
    – Trimok
    Commented Jun 12, 2013 at 18:50
  • 1
    $\begingroup$ I think 2, 3 and 4 are way too big to answer here. They would typically take up a chapter in a book. $\endgroup$
    – twistor59
    Commented Jun 12, 2013 at 19:24
  • 1
    $\begingroup$ @ twistor59 : Can you please suggest some references on these queries? I will be very helpful. $\endgroup$
    – layman
    Commented Jun 12, 2013 at 19:28

0

Reset to default