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Gauge symmetry is said to be "unphysical" because the transformations - unlike changes of reference frame - do not correspond to real physical operations. But the consequences of gauge symmetries are bosonic gauge fields with their resulting forces! So how can gauge be a purely notational/unphysical phenomenon if it has real measurable effects such as forces on particles?

quantumorsch
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    Global symmetries, NOT gauge symmetries give rise to conserved charges. – Prahar Feb 06 '15 at 02:37
  • "Nowadays"? ...These kids today... – hft Feb 06 '15 at 02:37
  • Gauge fields are physical. Briefly, promoting a global symmetry to a local one requires the introduction of one or more gauge fields that possess both physical and non-physical (gauge) degrees of freedom. The gauge degrees of freedom 'absorb' local gauge transformations but the gauge field has physical consequences. – Alfred Centauri Feb 06 '15 at 02:49
  • Thank you all so much for your answers! Nima Arkani-Hamed has said in various talks/lectures that gauge symmetry is "nothing but a redundancy in our description" (quote). That is what I am getting at. If it were just a redundancy because of our notation, how can such redundant things have physical effects? – quantumorsch Feb 06 '15 at 03:02
  • Sigh... Gauge fields are physical. Briefly... https://en.wikipedia.org/wiki/Gauge_theory#Gauge_fields – Alfred Centauri Feb 06 '15 at 03:17
  • Folks, gauge transformation is a mathematical operation. It has no physical consequence except for someone has to think it and sometimes write it down. – Ján Lalinský Feb 06 '15 at 03:17
  • Yes thank you Alfred, I read that. But this is precisely what I dont understand! Something that is "nothing but a redundancy in our description", sth entirely in our heads gives rise to a physical field? – quantumorsch Feb 06 '15 at 03:20
  • You're conflating two distinctly different concepts. Gauge symmetry is not identical to gauge field. The electromagnetic four-potential is a gauge field with gauge (non-physical) degrees of freedom. The fact that a gauge transformation does not change the physics does not change the fact that photons, quanta of the four-potential, exist. – Alfred Centauri Feb 06 '15 at 03:23
  • @quantumorsch, it is the other way around. Experiments motivate people to develop mathematical models, one of which is the one with potential leading to predictions that are gauge invariant (the potential is not unique). Gauge invariance has no physical effects. It is a math. property of a model. – Ján Lalinský Feb 06 '15 at 03:25
  • @Alfred: of course gauge symmetry is not the same as gauge field. But as you stated, promoting a global symmetry to a local (gauge) one forces us to introduce gauge fields along with the covariant derivative. so in our mind we created sth that was not really there (local symmetry instead of global) - and get out a physical field! the "imagined" local symmetry somehow gave rise to real fields/forces... I just dont get it. Maybe my question is too metaphysical. Please excuse my confusion – quantumorsch Feb 06 '15 at 03:47
  • Forget how you were taught that gauge theories are introduced. Yes it makes sense that we start with a global symmetry, gauge it, need to add new degrees of freedom (the gauge fields), and Yang-Mills + matter lagrangians. Instead keep the following in mind:
    1. For these theories its possible to write down gauge invariant equations of motions involving only the current and the field strength tensor.
    2. The "conserved charges" that arise from a local symmetry actually vanish.
    3. A single theory can be described by lagrangian descriptions with different gauge groups.
     – David M Feb 06 '15 at 07:19
  • Possible duplicates: http://physics.stackexchange.com/q/13870/2451 and links therein. – Qmechanic Feb 06 '15 at 07:51

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