# Tag Info

0

There are some ways to get the symmetry factors correct. If it is an easy diagram like this one you can actually imagine it. For example here, by flipping the loop you get the identical diagram and that means dividing by two. However, there are more difficult diagrams. Then, you have to follow set of rules which are described in many field theory books. I ...

1

The symmetry factor should be $2$. This comes from the fact that exchanging the derivatives at the vertex is the same symmetry operation as swapping the endpoints of the propagator in the loop. Each of them amounts for a multiplication by 2, but since they are identical we are essentially overcounting. Dividing by $2$ corrects this error.

5

To be honest, I think that the route you describe (and which is also used in many textbooks) is not physically well motivated at all. You have begun with a theory of a fermion with a global symmetry which maps physical states to different physical states. This theory has the property that specifying initial conditions on a spacelike surface completely ...

7

You are right, it is wrong to think that in gauge theory "gauge transformations are just a redundancy". This becomes true only if one abandons locality, ignores all boundary effects, all instanton effects, hence most of what is interesting about gauge theory. Of course forming gauge equivalence classes (say of observables) is something one wants to do every ...

2

This is how I understand this issue. First, I believe you may agree that imposing gauge invariance is a sensible thing to do. If we want our fields to be invariant under some kind of transformation it better be local, since two separate space-time points shouldn't be related in any unnecessary way, otherwise we may violate causality. A different issue is ...

0

Electric charge conservation is a "discrete" symmetry. Quarks and anti-quarks have discrete fractional electric charges (±1/3, ±2/3) electrons, positrons and protons have integer charges.

7

When it comes to fundamental charges, the (left-handed) up-type quarks actually have either the same values of the charge as the down-type quarks, or exactly the opposite ones. It just happens that the electric charge isn't a fundamental charge in this sense. Let me be more specific. All the quarks carry a color – red, green, or blue – the charge of the ...

0

If you are looking for symmetry, I think one should point out that there IS a particle with a -2e/3 charge and a particle with a +e/3 charge. They are the up antiquark and down antiquark respectively. Now, following that, you would very reasonably ask the question why we observe more up quarks than up antiquarks, and other follow-up questions like ...

-1

for an analysis of anomalies via quantum impedances, see http://vixra.org/author/peter_cameron the paper on the pizero, eta, and etaprime branching ratios gives another perspective

1

I know to introduce a more mathematical description of your quest, based on Operator Algebraic methods. If your speculation also regards the gauge symmetries of this 2-d model, the global gauge symmetry may be described by a compact Abelian gauge group that results to be the Bohr Compactification of $\mathbb{R}^2$. This is a quite a large group that, in ...

5

The Virasoro algebra is a centrally extended algebra. This means that in every representation, its central element must be represented by the unit operator. Thus (for a nonvanishing central charge) it cannot fully implemented at the quantum level as a symmetry of the vacuum, otherwise one can get a contradiction of the type $1 |0\rangle = 0 |0\rangle$. ...

0

I recommend you "Symmetries" by Griffiths, or "Symmetry" by Roy McWeeny (it's a Dover book). "Geometry, Topology and Physics" by Nakahara is a good option.

5

What is a physical theory/model? A given physical theory is typically mathematically modeled by some set $\mathscr O$ of mathematical objects, and some rules that tell us how these objects correspond to a physical system and allow us to predict what will happen to that system. For example, many systems in classical mechanics can be described by a pair ...

2

Symmetries indeed have a broad and powerful impact in physics, and I will only be able to scratch the surface of the subject in this answer, but I will try to give you a glimpse of the subject. In the most simple framework, you mention an electrostatic problem. In such a problem, the key factor is the geometric symmetries which apply to the charged ...

6

Symmetry is present when something $x$ doesn't change under some transformation $T$: $$T(x)=x$$ In an infinite cylinder, there is radial symmetry because if you move at constant height and radius, you see the same figure. In the Lagrangian case, if you change coordinates, the Lagrangian doesn't change. $L(x') =L(x)$ In group theory, group elements will ...

Top 50 recent answers are included