# Tag Info

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Related answer: http://math.stackexchange.com/a/532746/24293 Looking at the comments, you seem to be asking why there are chiral 'pairs' and not chiral multiplets. Looking at the tag, it looks like you want an analysis of higher dimensions as well. TL;DR Short answer: In any number of dimensions, chiral objects come in pairs. This is because numbers ...

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For spin measurements the original experiment was the Stern-Gerlach experiment in which you will see that a prior unpolarized beam will split up in two (Spin up and down) orientations. see: http://en.wikipedia.org/wiki/Stern%E2%80%93Gerlach_experiment For helicity, a very ingenious and fascinating experiment is the famours Goldhaber experiment that uses a ...

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No, it really is arbitrary. The reason we use the right hand rule today (although it may have been chosen for different reasons of convenience in the past) is simply that our coordinate system of choice is right-handed. Mathematically, this means that we define the directions of the axes so that you have to use the right-hand rule to evaluate this cross ...

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The clockwise direction is normally defined by the right hand grip rule. When your thumb is pointing away from you, your fingers are curled clockwise. So when you look at a clock the axis of rotation is away from you through the clock. I'd guess the downvotes are because people believe your question is not physics related, but in fact this rule is how ...

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Presumably you are asking about the communication ambiguity in physics: can we unambiguously specify what we mean by "a right handed coordinate system" to a correspondent far away without a pre-arrnage communications channel (i.e. using SETI)? For a long time the answer seemed to be "no", but the discovery of parity violation in 1957 changed the answer to ...

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Your confusion arises because the term (anti)clockwise, when used by itself, is ambiguous, and should always be used with a statement like "as seen from the top" (unless that is absolutely obvious$^1$). The reason for this is that "clockwise" defines a direction of rotation within a plane, but does not specify which side the plane is observed from. (In more ...

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At first glance, chirality and helicity seem to have no relationship to each other. Helicity, as you said, is whether the spin is aligned or anti aligned with the momentum. Chirality is like your left hand versus your right hand. Its just a property that makes them different than each other, but in a way that is reversed through a mirror imaging - your left ...

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There is no chiral anomaly/gauge anomaly if the spacetime dimension $2\ell+1$ is odd, partly because $SO(2\ell+1)$ has real or pseudo-real representations, but no complex representations. There may instead be parity anomalies in odd spacetime dimensions. In fact, there is a dimensional ladder of related anomalies $$\text{Abelian chiral anomaly in}~ ... 4 You seem want to introduce gauge invariance into a theory that doesn't appear to have the global symmetry need in the first place. One way to think of gauge invariance is that you 'gauge' the global symmetry, then you just change your derivative terms to covariant derivatives like you mentioned. In other words, we can only concern ourselves with the global ... 4 Simply think of a Weyl Spinor as a Dirac spinor where the other two components are set to zero. Equivalently, a Weyl spinor (of chirality +1) belongs to the two-dimensional subspace with eigenvalue 1 under the action of the projection operator P_+=\frac{(1-\gamma^5)}2. For negative chirality, use the other projection operator, i.e., ... 3 I think its really important to differentiate between helicity and chirality. Helicity is the spin angular momentum of a particle projected onto its direction of motion. For a massive particle this quantity is frame dependent. Furthermore, since angular momentum is conserved, as a particle propagates helicity is conserved. On the other hand, chirality is an ... 3 The statement you cited does not imply that a complex representation of a gauge group implies a chiral gauge theory in general. This only holds true if the gauge group corresponds to a chiral symmetry in the first place. A chirally symmetric theory contains massless fermions. Regarding your counterexample: it is true that QCD contains fermions in the ... 3 I agree with the answer of Quantum physicist , that zero mass for neutrinos was an input to the standard model , not a prediction, because measurements showed a mass compatible with zero. But I will add that the discovery that neutrinos must have mass does not destroy the Standard Model, just different Lagrangian for the neutrinos has to be included. ... 3 Standard model doesn't predict that neutrinos are massless. It's a "Model", where initially neutrinos are considered massless, because no mass was observed. The way we know, now, that neutrinos have masses, is through the mixing between the different neutrino types, through a matrix called the PMNS matrix (similar to the CKM matrix for quarks). This mixing ... 3 Tarek (OP) e-mailed me to contribute to this thread. Here's the response that I gave him (slightly edited for clarity). I see why this was confusing, my apologies! I was perhaps too glib in the post. Iwas implicitly talking about a chiral rotation but wanted to present it somewhat more intuitively. Let me try to spell it out more carefully, and hopefully ... 3 The Majorana bound state inside a vortex of a topological superconductor is, indeed, not a chiral edge state. It does not follow that the topological superconductor does not have a chiral edge state. It does! Solve, for example, the BdG equations for a p+ip superconductor with open boundary conditions, and you'll see it. The existence of edge modes is ... 3 The importance of chiral symmetry breaking is a point that e.g. David Gross, a co-father of Quantum Chromodynamics, likes to make whenever some people suggest that the mass is entirely due to the Higgs field. In fact, most of the mass of visible matter is due to the QCD, especially chiral symmetry breaking, and it has nothing to do with the Higgs field. The ... 3 No, it's not true. Suppose I'm floating in outer space (presumably in a space suit or something else to keep me alive). I'm still me, and I still know that, for example, my left hand is the one on the left, and my right hand is the one I can write with. Even on Earth, we don't need environmental clues to distinguish left from right; it's more a matter of ... 3 Dear lurscher, the quote is the kind of C-physics described by the C-word which is a favorite word of mine but is discouraged on this server, so I won't use it - but you have used it. You don't misunderstand anything - quite on the contrary, you're right on the money. These comments about a non-existent test of parity in the equivalence principle are due to ... 3 You are correct that for a massive spinor, helicity is not Lorentz invariant. For a massless spinor, helicity is Lorentz invariant and coincides with chirality. Chirality is always Lorentz invariant. Helicity defined$$ \hat h = \vec\Sigma \cdot \hat p, $$commutes with the Hamiltonian,$$ [\hat h, H] = 0, $$but is clearly not Lorentz invariant, because ... 2 I think what your frien talked about was chiral symmetry breaking, which was observe in particle physics experiments. In this sense, "right" and "left" may be absolutely defined, much like how positive and negative charges are absolutely defined although the names are arbitrary. 2 There is a very simple and enlightening explanation due to N.V.Gribov given in his following conference article and also beautifully explained by Dmitri Kharzeev in the following arxiv article(section 1). Gribov's argument doesn't involve the heavy machinery of quantum field theory. He actually proves that in the case of colinear electric and magnetic ... 2 Let me add a few comments to Michael Brown's answer/comment. As he mentioned, a QFT is well defined with an action and a regulator. We always wish to use regulators that preserve gauge invariance, since that is a redundancy of our description and should not be removed in our quantum theory. However, any regulator that preserves gauge invariance, ... 2 It is simply the fact that if the g is large,$$ g \cos(\hat{\phi}) \to g(1- \frac{1}{2}\hat{\phi}^2 +\dots) $$the ground state will be trapped in one of the vacuum sectors, at the minimum of the potential energy. (Please check S Coleman's book \it{Aspects\; of\; symmetry} or his Phys Rev D paper on quantum sine-Gordon eq. It may offer differ views than ... 2 The charged current part of the Lagrangian of the electoweak interaction, for the first generation of leptons, is :$$L_c = \frac{g}{\sqrt{2}}(\bar \nu_L \gamma^\mu e_L W^+_\mu + \bar e_L \gamma^\mu \nu_L W^-_\mu )$$The first part corresponds to different versions of the same vertex : e_L + W^+ \leftrightarrow \nu_L \tag{1a} (\bar\nu)_R + W^+ ... 1 Based on the paper, the answer is |m|^2. They suggest in their p.8, Eq.36, the effective theory is a Chern-Simons theory$$ \frac{1}{4\pi}\int K_{IJ} a_I \wedge d a_J $$with the  K_{IJ} bilinear K matrix as$$K_{IJ}={\begin{pmatrix}m & 0\\ 0 & -m\end{pmatrix}}$$. The up m labels one sector and the lower m labels the other sector. The ... 1 Apparently, there seems to be no agreed upon definition of clockwise in 3D space - but an a clear agreement regarding the meaning in a plane "seen from above" As I am starting to answer, I have no idea what is the correct answer, if any. It is the "if any" that gets me started on this topic. I am certainly not an expert, I never could tell my left from my ... 1 The angle 120 degrees is calculated as$$ \frac{360^\circ}{3} = 120^\circ because the full angle 360 degrees in the hexagon is divided to three equal parts. One may draw the "Mercedes logo" triplet of arms into the hexagon network in several ways – one of the arms may be vertical; or one of them may be horizontal, and so on – and one of these ways explains ...

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The operator $S=\bar{q}\lambda_a q$ is the so-called scalar quark density, and together with its pseudoscalar counterpart, it enters the expressions for the divergence of the vector and axial-vector currents (see section 2.3.6). Spontaneous symmetry breaking occurs if $n$ generators of a symmetry transformation do not annihilate the ground state, resulting ...

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