I've read in the wikipedia supersymmetry page,that supersymmetry is a symmetry which relates fermions to bosons. Can we tell that this means there is aOne-to-One Correspondence between fermions and bosons and we can substitute a fermion with its corresponding boson and vice versa,to get a similar interaction? thanks
Supersymmetry is an extention of the standard model which says that to each fundamental particle that we know of, there exists a supersymmetric corresponding particle. Specifically for each fundamental fermion, there is a supersymmetric boson, while for each fundamental boson there is a supersymmetric fermion. To date no such particles have been found. Examples: electron partner is called selectron, while photon partner is called photino.
To elaborate just a little, if the universe was exactly supersymmetric you could perform this switcharoo and swap each fundamental particle with its superpartner and the universe would stay exactly the same. However there are many experimental reasons why this cannot be the case, so the solution is to assume the world is only supersymmetric at very high energies, and that there is a supersymmetry breaking mechanism which gives all the superpartners a large mass at low energies so that they would not have been seen in any current experiments.
Is the symmetry breaking,which causes the electromagnetic and weak forces emerge from electroweak force,the same thing as you mentioned kurros? Thanks to both
No it is a seperate thing, although somewhat similar in that there is a symmetry of the fundamental theory which needs to be broken. The electroweak unification scale is around the terascale, i.e. 10^3 GeV, whereas the scale at which SUSY breaking is often theorised to occur is at something more like the grand unification scale, way up at 10^19 GeV or so usually.
So up to now,considering GUTs,after big bang,our universe is supersymmetric until it cools down to [itex] 10^{19} \ GeV [/itex].At this energy,supertsymmetry breaks and as a result,electroweak and strong forces become distinct.Then when the energy reaches [itex] 10^3 \ GeV [/itex] , The electroweak force divides to electromagnetic and weak forces and we have three fundamental interactions.right?
Something like that, as far as I know. I am not an expert on GUT's though :). Actually I think the breaking of the GUT group is generally separate to the SUSY breaking (the SUSY breaking occurring at an even higher scale I think), but I am not very familiar with it, and there are various different GUTs that all do things a bit differently.
Actually, there is a nice connection between the SUSY breaking and electroweak symmetry breaking that I neglected to mention. In the Standard Model there is a parameter in the higgs potential which gives the potential a non-zero minima if it is negative, often called μ^2, and the fact that the minima is non-zero is what causes electroweak symmetry breaking to occur. In SUSY models it is possible for this parameter to start out positive at high scales (so the higgs potential has no non-zero minima and no symmetry breaking is possible) and then due to radiative corrections that arise due to the existence of the massive superpartners this parameter can be dynamically flipped to negative as you go down in energy scale, pushing the minima of the Higgs potential out to non-zero values and triggering electroweak symmetry breaking. This is a pretty cool thing to have happen. It is called radiative electroweak symmetry breaking, or "REWSB" if you want to read more about it.