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What is helicity?by Mk
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#1
Jan805, 08:21 AM

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It is quite difficult to understand, can someone explain what is helicity?



#2
Jan805, 08:38 AM

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It has the physical meaning of the projection of the total angular momentum on the direction of the linear momemntum of the particle.It is denoted by "lambda": [tex] \lambda=:\frac{\vec{J}\cdot\vec{P}}{P^{0}} [/tex] It can take only positive/negative integer/semiinteger values. For the photon:[itex] \lambda=\pm 1[/itex];for the scalar boson it is zero,for the graviton it is [itex] \pm 2 [/tex] Daniel. 


#3
Jan805, 08:39 AM

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In QM you can measure the spin of some particle by using the spin quantum operator S' and the momentum is expressed by some vector p. Now if you want to measure the helicity of some particle you just apply a new operator (the helicityoperator) onto the particle's wavefunction. This new operator is defined as p.S' and it measures the components of the spin operator along the direction of momentum p (this is the direction along which the particle moves). p.S' is the scalar product of some vector with an operator and suppose for example that p is along the zaxis then the helicity operator is nothing else then the length of vector p (this is the momentumvalue of the particle) multiplyed with the zcomponent of the spin operator S'. So you measure the spin along the zaxis. Positive helicity means that the rotationaxis of the spin is in the same direction as the direction in which the particle moves. If helicity is negative, it is the other way around regards marlon these concepts are very important in QFT, and more specifically the weak interactions because particles of different helicity behave totally different under such interactions. Only left handed fermions will feel the weak force and therefore are fundamentally different as right handed fermions... 


#4
Jan805, 08:43 AM

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What is helicity?
This is wrong... What you are referring to is the eigenvalue of this helicity operator, not the operator itself... GROUPTHEORY dextercioby... Besides, i don't think that this definition will bring much clarity... And besides, also i this case the direction of the spin can be defined in terms of the direction of momentum... marlon 


#5
Jan805, 08:53 AM

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Yes,it's not a fortunate exprimation.That relation should include "hats",of course.It is the operator:
[tex] \hat{\lambda} =\frac{\hat{\vec{J}}\cdot\hat{\vec{P}}}{P^{0}} [/tex] [tex] \hat{W}^{\mu}=:\hat{\lambda}\hat{P}^{\mu} [/tex] Yields the comutation relations with the generators of the Poincaré group [tex] [\hat{\lambda},\hat{M}_{\mu\nu}]_{}=\hat{0} [/tex] [tex] [\hat{\lambda},\hat{W}_{\mu}]_{}=\hat{0} [/tex] [tex] [\hat{\lambda},\hat{P}_{\mu}]_{}=\hat{0} [/tex] Daniel. PS.What i said about its eigenvalues is correct. 


#6
Jan805, 08:57 AM

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Are u inventing new physics and i don't see it...??? Daniel. PS.Since these particles are pointlike,how would u define their rotation ?? 


#7
Jan805, 09:02 AM

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And yes, your definition is wrong in this sense that you are referring to the actual eigenvalues of the helicity operator, not the operator itself... Tell me, what do you think this operator expresses, HMMM?? marlon 


#8
Jan805, 09:17 AM

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I said what it represents.The projection of the total angular momentum on the direction of movement.If u come up with another definiton,u're free to do so,as long as it is correct. Daniel. 


#9
Jan805, 10:32 AM

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marlon 


#10
Jan805, 09:05 PM

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I'll just wait till you guys figure it out...



#11
Jan805, 09:23 PM

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My advice:take Sakurai "Modern Quantum Mechanics" for helicity in QM and Bailin & Love "Weak Interactions" for helicity in QFT. Learn as much math is possible. Daniel. 


#12
Jan905, 05:35 AM

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Hi, MK, just read my first post and do feel free to ask more questions if something is not clear. All my other posts here, you must disregard, because they are waiste of time... Besides, don't do any QFT not yet. That is a stupid advice. First start out with any thorough book on QM and there you will also find some explanation for the helicityoperator. I always used Bransden and Joachain "QUANTMMECHANICS" regards marlon 


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