Physics Help Forum Particle Physics
 User Name Remember Me? Password

 General Physics General Physics Help Forum

 Apr 11th 2014, 07:49 AM #1 Junior Member   Join Date: Dec 2013 Posts: 10 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?
Apr 11th 2014, 12:39 PM   #2
Forum Admin

Join Date: Apr 2008
Location: On the dance floor, baby!
Posts: 2,777
 Originally Posted by lekha 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
__________________
Do not meddle in the affairs of dragons for you are crunchy and taste good with ketchup.

See the forum rules here.

 Apr 11th 2014, 02:06 PM #3 Junior Member   Join Date: Dec 2013 Posts: 10 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?
Apr 11th 2014, 05:14 PM   #4
Forum Admin

Join Date: Apr 2008
Location: On the dance floor, baby!
Posts: 2,777
 Originally Posted by lekha 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
__________________
Do not meddle in the affairs of dragons for you are crunchy and taste good with ketchup.

See the forum rules here.

 Apr 11th 2014, 09:54 PM #5 Junior Member   Join Date: Dec 2013 Posts: 10 In that case, does the tensor mesons also has a wavefunction which transforms as a tensor under Lorentz transformation?
Apr 12th 2014, 06:57 AM   #6
Forum Admin

Join Date: Apr 2008
Location: On the dance floor, baby!
Posts: 2,777
 Originally Posted by lekha 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.

-Dan
__________________
Do not meddle in the affairs of dragons for you are crunchy and taste good with ketchup.

See the forum rules here.

 Tags particle, physics

 Thread Tools Display Modes Linear Mode

 Similar Physics Forum Discussions Thread Thread Starter Forum Replies Last Post roger Quantum Physics 2 Apr 4th 2013 11:24 AM RAz Periodic and Circular Motion 1 Oct 25th 2010 11:25 AM Apprentice123 Kinematics and Dynamics 2 Apr 11th 2009 10:05 AM joker1 Nuclear and Particle Physics 0 Mar 12th 2009 01:10 PM