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1D QED on a lattice, how much information?

  1. Dec 1, 2011 #1
    Suppose we were to simulate 1D QED on a 1D lattice. How much information do we need at each lattice site given the mass, charge, and spin of the particles (does spin make sense in 1-1D spacetime?)?

    The links between lattice sites represent the gauge field? How much information is needed at each link?

    I'm guessing this lattice could be used to calculate whether oppositely charged particles moving towards each other with momentum p1 and p2, scattered or annihilated in one space dimension?

    Do we have "braking radiation" or Bremsstrahlung in 1D


    Edit, do we need a lattice of both time and space?

    Can the lattice accommodate any number of particles?

    Thanks for any help!
     
    Last edited: Dec 1, 2011
  2. jcsd
  3. Dec 2, 2011 #2
    Start here,

    http://www.scidacreview.org/0702/html/qcd.html [Broken]

    From there,

    QCD on the Lattice
    The good news is that QCD has been studied quantitatively in high energy collisions where the interactions are weak, providing overwhelming evidence for its validity. The bad news is that at the large distances and low energies governing the binding and structure of hadrons, the interactions become so strong and nonlinear that, unlike the case of QED, no known analytical technique can quantitatively describe them. Theoretical physicists have turned to large-scale computation to solve QCD numerically in order to unlock the secrets of the strong interaction. The inspiration and techniques come from Feynman’s path integral formulation of field theory that sums over all possible time histories contributing to a process, with appropriate weighting. To implement this idea in a practical calculation, scientists replace the space-time continuum with a discrete lattice in space and time that possesses a finite lattice spacing, a, and a finite volume. Quark fields are defined on the sites of the lattice, and the gluon fields are defined on the links connecting lattice sites. A discrete action is written for this lattice with the property that it approaches the QCD action in the limit as a goes to zero. The integral over the gluon fields is evaluated by Monte Carlo methods, so that as the number of time histories, N, sampled with a weight given by the discrete QCD action increases, the exact path integral is approximated with controlled errors that decrease as the reciprocal of √N.
     
    Last edited by a moderator: May 5, 2017
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