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Yang-mills and standard model

  1. Jul 29, 2004 #1
    What in simple terms is a Yang-Mills field?
    What has it got to do with the standard model of particle physics
    and why are all particles in the standard model massless - is this something
    to do with getting the standard model to be consistent with the Higgs field?
    Do we need the standard model given that it doesn't go well with gravity,
    when in reality gravity fits in quite naturally with the rest of the world?
    Does the math of modern physics have to be so difficult or is this just
    a sign that modern physics is going wrong?Why is perturbation theory needed in quantum field theories - what probem does it solve - what problems does it cause?
  2. jcsd
  3. Jul 29, 2004 #2
    What is going wrong with GTR?

    Too many questions kurious,

    Should we not better ask why the General Theory of Relativity doesn't go well with the standard model?
    Why QM and GTR do not talk to each other?
    What is going wrong with GTR?
    Does it have to do with the fact Einstein used Tensor Analysis for it?
    Does it have to do with the fact QM start with the complex Schrodinger wave equation?
    Must not complexity be taken to a minimum - such as a basic unit system based on Euler relation- if we want to overcome such an incommesurability(as T.S.K put it) problem in our interpretation of the physical world?


  4. Jul 29, 2004 #3
    Yang-Mills fields are the fields of the Yang-Mills-theory, thats logic. Now this theory can be viewed as the general model according which QFT works. It describes the behaviour of all elementary particles like electrons or messengers like fotons or gluons. Basically one starts from a lagrangian like in the Hamilton-Lagrangre-mechanics.In this lagrangian one finds the fields describing the elemantary particles, together with kinetic and potential energy. Then you look for global symmetries (global = independent of position and time) which correspond to a conserved quantity (like electric charge for EM-interactions). This is called the theorem of Noether. Then you make these global symmetries local. In order to maintain covariance under Lorentztransformations, extra fields will have to be introduced. These extra fields will describe the messenger particles like fotons. The exact way interactions between particles via the messengers, will evolve is determend by the conserverd quantity. This quantity should be seen as the referee, determing what interactions are valid and what not.

    Tensors are needed because of the "limitations of the human mind". We always want to make are reference frame lorentzian in our near perimetre, because that is the way we are used to look at things. One says that are metric is locally lorentzian. Because of this demand tensors are used and Lorentzcovariance is needed. In general relativity there is no preferred reference frame, so every quantity has to behave in the exact same way in every frame. We can go from frame to frame via parallel transport of vectors.
    If we have info in frame one and we go to frame two via parallel transport, this info in frame two must behave in the same way as in frame one. This is covariance.

    All elementary particles are massless before the spontanious breakdown of symmetry. They are massless because mass mixes the left and right handed chiralities of particles. The chirality is a quantity that describes the relation between spindirection and direction of momentum.Same direction is right-handed chirality and opposite direction of spin and momentum is left-handed-chirality. Different chirality corresponds to fundamentally diffrent particles because the two chiralities do not couple in the same way to elektroweak interactions.

    Perturbationtheory is needed in order to get fysical (usefull) results out of the model. When an interaction between particles must be described , one takes the corresponding potential energy multiplied by the coupling constant and puts this in the lagrangian of the model. Now if the coupling constant is not too big one can calculate stuff by performing some kind of Taylor-expansion in function of the coupling constant. The first term in this expansion always is the socaled free theory. This means a theory without the interaction taken into account. Then one by one one adds the different terms of the expansion into the model in order to bring in the effects of the actual particle-interaction which is described by the potential energy. The coupling constant describes the strength of the interaction.

    Note that this constant does not always is a constant. It can vary on the speed of the interacting particles, like in QCD...Problems arise when the coupling constant is big, then expansion is invalid just as with taylor. In order to solve this one can make some kind of duality-transformation to a model that describes the same situation but with very low coupling constant.

    There are threads that i wrote which give such an example like quarkconfinement.

    black, out of inspiration

    i hope this clarifies some of your questions

  5. Jul 29, 2004 #4

    No gravity in QFT. One of the mean reasons. In QFT you have Heisenbergs-principle. So a particle's position is never exact. This does not count for general relativity.

    Gravity is not implemented in the Standard Model because its effects are very very small, they can be ignored at this scale (up to 10^-15meters)
  6. Jul 29, 2004 #5
    Are not there other ways of representing gravitational fields?

    Kurious was confused in the first place about the way QM is in conflict with the prevailing representation(GTR) of gravitational fields.
    Tensors is the tool used by Einstein to develope his ideas about the "generally covariant laws" of nature, but are you sure there are not other ways to develope the laws of gravitational fields that are not in conflict with QM representation?
    Are you sure there is not a tool that by definition includes uncertainty in its representation? If it is, then we have a language or tool that is not so complicated as the ones we have today, not accesible for the "normal minds", which I think was the feeling kurious expressed in his question:
    "Does the math of modern physics have to be so difficult or is this just a sign that modern physics is going wrong?"



    Last edited: Jul 29, 2004
  7. Jul 29, 2004 #6
    ok, that is a very interesting question. I don't have the answer whether there is a better mathematical language to describe things without them nasty tensors.

    I think the biggest problem to overcome, in order to achieve this goal is a very spectacular one : WE HAVE TO GET RID OF THE CONCEPT OF DISTANCE !!!!

    Remember that tensors are born in the geometry of Riemann. One can calulate the Riemanntensor on a locally flat space (like we right now) and yet still be able to conclude he or she is on a global curved space. i think this intrinsic property of differentialgeometry is marvelous.

    But to give you my view : I think some twisted mind could develop a theory without a distance in it. But the problem that remains is, what is the use ??? We would not be able to interprete such a theory, right ???

    Tensors and a of this calculation-horror comes directly from the fact that we always want to measure are local - lorentzian-space ...
  8. Jul 29, 2004 #7
    It's nothing to do with the fact GR uses tensors. Tensors are also used quantum field theory.
  9. Jul 29, 2004 #8
    I think these difficulties in calculation or not a sign of fysics going wrong. They are the sound of brain - inevitability !!!

    There is no other option for our limited minds !!!

  10. Jul 29, 2004 #9
    Two different languages in conflict?

    Evidently you are using two different languages that do not talk to each other, that of QM and that of GTR. What has prevailed since QM is a dual concept of wave-particle, and this concept is impossible to be expressed by GTR, which is then, in certain sense, a classic representation of physical reality, classic in the sense it cannot rationalize duality. This is what is wrong in modern physics.


  11. Jul 29, 2004 #10

    Yep, yep

    tensors are widely used. Even the engineers use them to express the directional dependence of some quantities like pressure or mass. or to express anisotropic properties of cristals
  12. Jul 29, 2004 #11
    Tensor not an ideal too for covariant laws of nature

    Nobody is talking about tensors are not widely used. My central point is that they are not the better tool for representing the covariant laws of nature, as with them as I put it before, we cannot represent a concept such as wave-particle concept



  13. Jul 29, 2004 #12

    Ehh, so what ???

    Why would we wanna do that ?

    What is the advantage ???

    The concept of dualities is very well known in QFT.

    But this is not the case for GRT, right... so ???
    Are you saying they cannot be unified ? I think not ... what about strings...

    greetz marlon,
  14. Jul 29, 2004 #13

    What wave - particle concept ??? You mean in general relativity??

    What about the fields-particle relation ???
  15. Jul 29, 2004 #14
    getting rid of a fundamental concept?

    No, why should we have to get rid of such a fundamental concept?
    Why we think that Riemann geometries have to be used for representing physical reality? because Einstein used it with Tensor Analysis?
    Why don't we use sort of complex differential geometry in which duality is rationalized?



  16. Jul 29, 2004 #15
    no they cannot be unified

    No, QM and GRT cannot be unified, they talk different languages...strings is a noble intent, let us wait what it gives us


  17. Jul 29, 2004 #16

    Different languages, but they both use tensors, so they can not be the cause of problems.

    Indeed strings are not yet a certainty
    But we are forgetting one fine concept of from topology. What about compactification and wrapped up dimensions? Maybe this is taking us to far.

    Don't just say they talk different languages just because of the difficulties we have in unifying them. Both models use tensors extensively because of the same reason. It has nothing to do with the fact that one uses fields and the other uses curvature of spacetime
  18. Jul 30, 2004 #17
    Some great answers to my original question.Thanks a lot.
    Why is the uncertainty in a particle's position not used in General relativity -
    couldn't we just say that a particle has a probability of being at a given
    point in a distance range and a certain probability for its momentum in a small range of momenta and work out a relativity theory that has a stress energy tensor that reflects this i.e a theory that yields a stress energy tensor that has a certain probability of existing with a certain numerical value?
    Noether's theorem relates symmetry laws to conserved physical quantities.
    are any physical quantities conserved together: for example is the conservation of electric charge conjugate with the conservation of
    Last edited: Jul 30, 2004
  19. Jul 30, 2004 #18
    The main reason is that general relativity is a classical theory, not a quantum theory. There have been attempts to develop a gravitational uncertainty principle. You may be interested in http://arXiv.org/abs/gr-qc/9904026

    It's worth noting that inside the infinite density singularity inside the event horizon of a black hole, we are uncertain of even the uncertainty principle :yuck:
  20. Jul 30, 2004 #19
    Something very, very wrong in modern physics???

    Hi Lonewolf and everybody,

    Thank you! At last we find an akin point of view of the way I see physical reality.
    In the first place what is needed, IMHO, is not just necessarely to develop a "gravitational uncertainty principle", but to use a tool such as complex numbers that permits us to rationalize that duality of time and space, wave and particle, ect.

    And your important second point about black holes is not again one of those great contradictions that result by using the wrong tool?
    Not only with it is violated a fundamental law of nature such the conservation of energy-matter but additionally as you have pointed out "we are uncertain of even the uncertainty principle". Why at atomic levels the system cannot collapse but it can at large?
    Definitively as I have insisted, there is something very, very wrong with modern physics.



  21. Jul 30, 2004 #20
    What if we were able to perform an analogon of the Wick-rotation to some sort of complex time or distance-coordinate ???

    Shouldn't we be able to incorporated compex numbers.

    Besides I think the solution is to be found in the search for dualities between models with uncertainty and those that do not incorporate such a consept.
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