# Gauge forces and internal symmetries

1. Oct 31, 2013

### kye

gauge forces like electromagnetic, weak and strong forces have local gauge symmetry invariance in terms of u(1), su(2), su(3) because the em for example cant have the same global phase or global symmetry at all points of space. but is there no corresponding gauge forces for global symmetry?

2. Oct 31, 2013

### dauto

No, global symmetries have no gauge bosons or gauge forces associated with them. For instance, there is not gauge boson associated with baryon number conservation but there is a boson associated with electric charge conservation - the photon. That's because baryon conservation is a consequence from a global symmetry while charge conservation is a consequence from a local symmetry.

3. Oct 31, 2013

### kye

1. does global symmetry only have to do with conservations? what other conservations are there beside baryon conservation in global symmetry?

2. quantum is supposed to be random and even nonlocal. why does it have go obey local symmetry of phase for example when global simultaneous change of phase may not be problem since quantum mechanics is fundamentally nonlocal?

4. Nov 1, 2013

### K^2

Each symmetry has a conserved charge. There are four symmetries and four charges. U(1)xSU(2) gives you conserved electric and weak charges. SU(3) gives you conserved color-charge. And if you throw in a bit of GR and consider Poincare symmetry, you end up with stress-energy tensor as another conserved charge. The later is a generalization of energy, momentum, and angular momentum conservation from classical theory.

And Quantum Mechanics is actually very local. You shouldn't think of "delocalization" as particles starting to behave as diffuse clouds. They still behave as point objects. These point objects simply have ability to take all the possible paths at once, and therefore, interact at many different places at once. But interaction at each location is still strictly local.

5. Nov 1, 2013

### kye

i read the global symmetry is composed of

1. parity
2. charge conjugation
3. time reversal
4. flavor conservation laws - lepton and baryon numbers

are there others?
but you will notice all of them are not fields like em or weak fields. but why is there no global symmetry fields. what laws forbid them?

but in contextuality and bells theorem which discoung local realism, bill hobba for example in the other thread said particles dont exist before measurement, meaning the other entangled pair for example dont exist before measurement. maybe you subscribe to realism compared to others?

6. Nov 1, 2013

### K^2

Parity, charge, and time symmetries, individually, are broken. There are PC violations which suggest that T violations also exist. Together, PCT is a valid global symmetry, but since it follows from Poincare symmetry, I would expect it to have the same conservation law.

Flavors aren't strictly conserved either. Baryon and lepton numbers appear to be, but their conservation follows from super symmetry, and there is symmetry breaking there as well. Unfortunately, I know very little about the subject. You can try your luck in high energy section for that.

Because the corresponding force fields result from gauge comparators. If the gauge is global, comparator is unity throughout space, and the connection field vanishes. So you can say that there is a field corresponding to global symmetry, but it's zero everywhere. There is a bit of algebra in here that I'm glossing over. I can run through it if you are comfortable with multi-variable calculus.

7. Nov 2, 2013

### kye

K^2. I searched for "Gauge Comparators" and all references I can find are tire gauge comparators. What is the other name for this in gauge theory that I can find in the net? Anyway. I found this paper by David Gloss "Gauge: Past, Present and Future" and there is a line that mentioned "A local symmetry is much more in keeping with the lessons of field theory and relativity than a postulated global symmetry, which smells of action at a distance.". Now let me go back the quantum entanglement thing. Is quantum correlations or Bell's theorem not related to the global symmetry of Gauge theory? Or Is gauge theory nothing to do with quantum entanglement at all? It is not described by local symmetry nor global symmetry? Why? Hope others can comment too. Thanks.

8. Nov 2, 2013

### kye

Gauge Global Symmetry

I read that global symmetry is composed of

1. parity
2. charge conjugation
3. time reversal
4. flavor conservation laws - lepton and baryon numbers

Why is mass not a global symmetry? are there others global symmetry besides the above? Why them specifically?

I know local symmetry produced the gauge fields like em, electroweak, strong in the form of U(1), SU(2), SU(3)

9. Nov 3, 2013

### vanhees71

Since mass is not conserved within relativistic physics, there's no symmetry related to it.

In non-relativistic physics mass is a central charge of the Galilei group and thus not only conserved but there's also a superselection rule, according to which there are no superpositions of states with different mass. See, e.g.,

http://arxiv.org/abs/quant-ph/9508002

10. Nov 3, 2013

### fzero

Mass is a conserved quantity. The relevant global symmetry in relativistic physics is translation invariance of spacetime: $x^\mu \rightarrow x^\mu + \alpha^\mu$. Under this symmetry, 4-momentum $p_\mu$ (energy and spatial momentum) is conserved. Mass is the length squared of this 4-momentum, $p^\mu p_\mu = m^2$ and is a conserved, Lorentz-invariant quantity.