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Old Apr 11th 2014, 07:49 AM   #1
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Particle Physics

Why the W mesons are called 'vector' mesons? I know that its spin is 1, but what vector properties does it show to be called so?
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Old Apr 11th 2014, 12:39 PM   #2
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Originally Posted by lekha View Post
Why the W mesons are called 'vector' mesons? I know that its spin is 1, but what vector properties does it show to be called so?
Just a quick note...The Ws (and Z) are not made up of quarks, so they can't be mesons. They are what is called "mediator" particles ie. those that are carriers of a given force. (In this case the weak nuclear force.) All mediator particles are bosons, as far as I know.

First the Lorentz group: this is the group for Special Relativity. We say that a particle has a certain property if it stays the same under a (Lorentz) transformation.

To give you a quick (and simpler) example, consider the cross product. Let us take the vector A and the vector B and look at C = A X B. If we do a "parity" transformation we take (x, y, z)
--> (-x, -y, -z). So the vector A goes to -A and the vector B goes to -B. What happens to A X B? Well we get (-A) X (-B) = C. But that means that the "vector" C does not go to -C under a parity transformation. So C isn't really a vector, it is a pseudo-vector.

So (finally!) to your question. Vectors transform in a certain way under Lorentz transformations. In this case the wavefunction for a W transforms as a vector does under Lorentz transformations.

-Dan
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Old Apr 11th 2014, 02:06 PM   #3
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Yes W are vector bosons. I misprinted!
W wavefunction means? Just like electron wavefunction in a potential?
We say particles are representations of the field. So can we say that the field itself is a vector field, quantizing which we get the vector particle?
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Old Apr 11th 2014, 05:14 PM   #4
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Originally Posted by lekha View Post
Yes W are vector bosons. I misprinted!
W wavefunction means? Just like electron wavefunction in a potential?
We say particles are representations of the field. So can we say that the field itself is a vector field, quantizing which we get the vector particle?
Yes, the W has a wavefunction just like for an electron. (The equation of the wavefunction of a spin 1 massive particle is called the "Proca equation.") It's just that, in this case, we can't actually solve the differential equation in general...and the form of the potential for the weak field is not known. Feynman diagrams get around that problem using perturbation techniques.

I'm not familiar with calling the field a vector field, but I can't see why not. Just as long as you carefully put some distance between this concept and the Mathematical definition of a vector field. The two would not be the same.

-Dan
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Old Apr 11th 2014, 09:54 PM   #5
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In that case, does the tensor mesons also has a wavefunction which transforms as a tensor under Lorentz transformation?
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Old Apr 12th 2014, 06:57 AM   #6
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Originally Posted by lekha View Post
In that case, does the tensor mesons also has a wavefunction which transforms as a tensor under Lorentz transformation?
"Tensor mesons?" I don't know the term. If I am remembering correctly all mesons are either scalars or pseudo-scalars. These are, in fact, tensors so I guess the answer to your question is yes.

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