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Coupling constant and mass

  1. Sep 14, 2004 #1
    In Bohr's model of hydrogen atoms, a 1s electron would
    orbit the proton quicker than a 2s electron.If we slowed down the 1s electron slightly we would normally expect it to spiral towards the proton.But not if we could decrease the force acting on the slower moving electron.If the electric coupling constant gets smaller as electron speed decreases,then this would happen.
    The force acting on the electron does not have to be weaker because there is some new repulsive force acting on the electron - the slower speed of the electron could affect the probability of particles in the space around the electron absorbing force carrying photons.A slower moving electron has less mass and so we could postulate that the mass of the electron is linked to the
    absorption capabilities of the particles in the space around the electron.
    If the particles cause the electron's mass then when it has a smaller mass
    (slower speed) there would be more mass-causing particles free to promote photon absorption.Why isn't electron mass linked to the coupling constant in
    quantum field theory - and which mass does the mass term in the gravitational coupling constant refer to?
  2. jcsd
  3. Sep 14, 2004 #2
    Mass IS linked to the coupling constant in QFT, besides mass itself is a coupling constant in QFT expressing the strength of the interaction between an elementary particle and the Higgs-field.

  4. Sep 14, 2004 #3
    Besides, mass is also renormalized because mass can be generated dynamically. basically this means that the mass of a particle depends on it's speed.

    Similarly mass can vary through interactions with other particles (something like the effective mass of solid state physics).

    Just look at the concept of the polarization-insertion in QFT. This is the self-energy of the photon-propagator and intuitively you can interpret this as follows : replace the vacuum by some kind of dielectricum that influences present electromagnetic fields. Hence the name POLARIZATION-insertion.

    This insertion is closely linked to the concept of quasi-particles. If the interaction between the electrons is "not too strong", we put all (more technically : we renormalize) all of the interactions that a single electron experiences into the
    selfenergy. Just look at this as if we "gather or lump" all the interactions into the mass of the electron and then we look at this new particle as if it were a "free" particle.
    Thus we acquire a a free electron with a new mass called the effective mass. This new particle is called a quasiparticle.

    A quasiparticle is a particle that is a result when we incorporate the renormalized self-interaction into it. Like this we reduced a many-body-problem that we cannot solve into many one-body-problems that we CAN solve.

    The polarization-insertion has the same use in QFT.

    just as an illustration, ok???

    marlon :smile:
    Last edited: Sep 14, 2004
  5. Sep 14, 2004 #4


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    So, am I the only one who is seeing a problem here?

    The s-orbitals are for the l=0 angular momentum quantum number. It means that it has ZERO angular momentum in the classical sense. So then my question is, what is being "slowed" down or what quantity is being made "faster"? It already has zero angular momentum. So how can we have it "orbiting" faster or slower?

  6. Sep 14, 2004 #5
    hahaha,ZapperZ, you certainly are not...

    I was only answering to the question on mass and the coupling constant...

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