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Higgs field, QFT in curved spacetime, and spinfoams

  1. Aug 12, 2006 #1
    How related are the concepts of the Higgs field and QFT in curved spacetime? As I understand it, The Higgs mechanism is derived from a false vacuum where no particles exist yet, but the Higgs field contains potential energy at an unstable equilibrium. This unstable potential is what drives inflationary expansion of spacetime at first. And then at some point the Higgs field of the false vacuum collapses to a more stable equilibrium, and in the process creates massive particles.

    But R. M. Wald describes how particles in curved spacetime is not a well defined concept - that fields are defined in curved spacetime but not particles. This seems similar to the Higgs mechanism. Is it the same thing? Matter is not defined when the universe's spacetime was very curved and expanding very fast. Then when spacetime flattens out enough, particles appear, with mass. Could the "undefinedness" of particles in curved space be the "unstable" quantum field in the Higgs mechanism? Both seem to have a field to begin with and then particles appear after some flatness is achieved.

    Are these concepts also related to spinfoam theories where there seems to be a QFT defined which includes spacetime in the Feynman type graphs as though it were like any other type of particle? What circumstances give a higher expectation value for this spinfoam theory to produce more spacetime and not particles? Is this correspond to a more highly curved spacetime or faster expanding spacetime?
     
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  3. Aug 12, 2006 #2

    selfAdjoint

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    The original Higgs mechanism did not require particles as such. See this wiki article: http://en.wikipedia.org/wiki/Higgs_mechanism. The minimum energy of the field is not at the zero of the field, but at the minimum of the potential function, which is a continuum of equal energy states surrounding a peak at the field minimum. So if the field happens to BE at its own minimum value, it is "downhill" for it to morph into one of the potential minima - any one, but whichever one it goes to, breaks the symmetry of the field.

    Consider a pencil balanced on its end. As long as it stands up, all horizontal directions are the same for it; it has directional symmetry, or rotations-in-the-plane symmetry with group U(1). But it is unstable against small perturbations; any little puff of a breeze will blow it over. And when it falls, the U(1) symmetry is broken; it falls in SOME DISTINGUISHED DIRECTION. This is the instability of the "Higgs vacuum" that they are talking about; you see that it doesn't refer to particles.

    But the Higgs field when quantized, like any quantized field, expresses itself though quanta. The quanta are of scalar type (spin zero) and massive, and if sufficiently localized can be considered particles, and as particles, can be expressed by ladder operators and participate in Feynman diagrams, so that aspect of the quantized Higgs field is what particle physicsts focus on.

    But if Wald's restriction on particles in curved spacetime imust be to be applied, that iin itself won't inhibit the Higgs Mechanism.

    Your other question, whether the Higgs vacuum is connected to other kinds of vacuum instability , is beyond me, but note the wiki article's reference to tachyon condensation. This is the central topic of String Field Theory, and a strong conclusion about it may be in the offing.
     
    Last edited: Aug 12, 2006
  4. Aug 12, 2006 #3
    Correct me if I'm wrong. But in both cases, both Higgs and Wald's QFT in curved spacetime, don't both require the curvature of spacetime to flatten out before particles can be defined? I'm wondering how there can be two completely unrelated mechnisms to create massive particles. Intuitively, it seems to me that causes that result in the exact same effect must be somehow related, even somehow equal to each other.
     
  5. Aug 12, 2006 #4

    selfAdjoint

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    You told me that Wald asserted that quantum particles were undefined in curved spacetime, and my description was conditioned on that, as I don't have access to Wald's statement. If you are now saying that Wald's statement only applied to his own way of quantizing GR, then all bets are off. Maybe Higgs or any other particles can be defined in curved spacetime?
     
  6. Aug 12, 2006 #5

    Haelfix

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    Higgs fields and everything else standard modelish goes through in QFT in curved spacetime just fine, nothing really new or ground breaking therein, as the formalism explicitly truncates out all deep UV divergences and any weird gravitational interactions at super high energies... The theory is silent by design on that blackbox.

    But it is true the notion of particles alla Wigner is problematic and doesn't work anymore (arguably thats just technical), so you have to move to the more modern treatment of effective field theory.

    QFT in curved space is an interesting beast. In many ways things go through exactly as you would expect (your metric g now is varied in the action), and things more or less as they were before. The nasty things really only occur in interpretations of QM (what *is* a particle) and of course the technicalities on the nonrenormalizability of gravity (as well as a few new things, like conformal anomaly constraints and technical issues with canonical quantization)
     
  7. Nov 7, 2006 #6
    I understand that particles don't get mass until the reheating occurs after inflation has flattened out the universe. During inflation the Higgs potential gives rise to a larger vacuum energy and therefore a larger cosmological constant which causes the universe to accelerate dramtically in its expansion. And once that potential is spent, the false vacuum of the Higgs potential drops as mass is given to particles. But I have to wonder if there are any type of massless particles in existence when the universe's space was still quite curved, before it significantly flattened out? Do photons exist during Inflation? Or is it the case that there are no particles whatsoever until the universe flattens out? Thanks.

    We are told that particles have certain spatial symmetries, SU(2), U(1), etc. Do these symmetries only exist in flat spacetimes? Are there different symmetries in curved spacetime that breakdown to the familiar symmetries when space flattens out? Any help is appreciated.
     
    Last edited: Nov 7, 2006
  8. Nov 8, 2006 #7
    For example, is the Higgs boson something that exists in the early universe when spacetime was still curved during Inflation? Or did the graviton exist during inflation? Or is it that because of the Heisenbery uncertainty principle that inflation happened so fast that there was no time for particles to come into existence? Thanks.

    I'm wondering if in the spinfoam models spacetime is just another kind of particle that can pop into existence. But if particles can only exist after the universe flattens out, then this would seem to suggest that particles depend on some properties of spacetime, so that spacetime is the essential ingredient, and particles appear as configurations or symmetries of spacetime. What do ya think?
     
    Last edited: Nov 8, 2006
  9. Nov 8, 2006 #8

    hellfire

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    First, you should note that when talking about curvature in cosmology it is usually considered the curvature of space, but not the curvature of spacetime. Space gets flat very soon in the universe's evolution. Anyway, I think this is not really relevant here.

    It is not completely correct that it is not possible to define particles in a cosmological background. However, to define particles means basically to define the Fock representation with a notion of vacuum and a set of basic modes. The main problem in an expanding background is that the Hamiltonian depends on time and therefore there is no set of time-independent eigenstates to define a unique vacuum as the lowest energy state. Same for the basic modes, that are time-dependent.

    It is correct that this makes it clear that the field is the fundamental entity. Some of its excitations can be treated as particles, but not always all of them can. To define the notion of particles in an expanding background at least under some reasonable conditions there are various prescriptions depending on the type of background. Some are more natural than other, like for example the Bunch-Davies vacuum in an inflationary space-time. All of them imply that the vacuum at one cosmological time is not the same than at another cosmological time and that, therefore, as the universe evolves in time there exists particle production due to the mere effect of gravity.
     
    Last edited: Nov 9, 2006
  10. Nov 9, 2006 #9
    If there are no particles, then there are no interactions between particles. So either there are no particles, or they are all boson which don't interact. Does this sound correct? So perhaps during Inflation there exists only one non-self-interacting fleld, the unified field, that later degenerates into the various fields and particles.
     
  11. Nov 9, 2006 #10

    selfAdjoint

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    No. What makes you think only particles can interact? The field has interactions. If you look at any of the QFT Lagrangians, they all have an interaction term; you can spot it because it's the one with the coupling coefficient in it. And the field supports fermionic as well as bosonic excitations.
     
    Last edited: Nov 9, 2006
  12. Nov 9, 2006 #11
    I took it as a definition for "interaction" particular events in spacetime. How can you identify an interaction apart from occurrences (of some identifiable thing = particles) at a particular place in time and space?
     
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