Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Group Theory and Physics .

  1. Mar 25, 2003 #1
    Group Theory and Physics.....

    Suppose we have a quantum field theory with a defined Lie Group of n-parameters, then if we calculated the invariants of the Lie Group...could we then determine the Lagrangian of the theory?.

    That is my opinion i think that given a group for a theory we could know all about the physics.....and when it comes to gravity and standard model..could they be unified by setting the unified theory group AxB where A would be the group for standard model and B the group for gravity (considered both of them as gauge theory), where "x" means direct product of the two groups.
  2. jcsd
  3. Mar 25, 2003 #2


    User Avatar
    Gold Member

    The first answer if yes, assuming that "the Lagrangian of the theory" translate to "The Lagrangian of the corresponding Yang-Mills theory".
  4. Mar 26, 2003 #3
    Re: Group Theory and Physics.....

    The first question reflects indeed the usual methods used to characterize states, the second is not true. The symmetry gives you valuable information, but not all. An example is given by the Poincaré group, where under certain circumstances there are other invariants which cannot be recovered from the group symmetry, but using distributions. Also discrete symmetries cannot usually be found from the Lie group. And then symmetry breakings can evaporate the efforts. Group theory is a powerful tool, but it does certainly do not answer to all questions.
  5. Mar 26, 2003 #4


    User Avatar
    Staff Emeritus
    Gold Member
    Dearly Missed

    The above two answers are not inconsistent, because it is not clear from the question whethere a gauge group was meant or not. I don't believe the Poincare group is the gauge group of a physical theory.
  6. Mar 27, 2003 #5
    Who has told that Poincaré is the gauge group? Indeed the special affine groups SA(n,R) where proposed to play the role of gauge groups (more concretely n=4).
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook