Fundamental fields and vacuum energy

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Please forward to appropriate subforums as I wasn't sure where to post it.


In the standard model there are the composite particles and elementary particles, for the elementary particles there is said to be an associated field and the particle is the excitation of that field.
Apart from asking how many of these fundamental fields there are I would also like to know whether it is these fields that also make up the so called vacuum or zero point energy which is said to be permeating all of space-time even in the absence of any matter or is the vacuum energy the result of yet another independent field?
 

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vanhees71
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This posting should be pushed to the quantum mechanics or the High Energy, Nuclear, Particle Physics forum.

To begin with in the Standard Model there are fields for each kind of what's known to be elementary particles today, the quarks and leptons which are grouped into three families. In each family are one charged lepton with charge -1 and a neutral neutrino (+their antiparticles) and two sorts of quarks, one with a charge of +2/3 and one of -1/3 (+their antiparticles):

1. family: electron+electron neutrino, up+down quark
2. family: muon+muon neutrino, charm+strange quark
3. family: tau lepton+tau neutrino, top+bottom quark

Besides the already mentioned electric charge, the leptons and quarks carry also the charge of the weak interaction, and the quarks additionally the color charge of the strong interaction (each quark comes with 3 sorts of color charge and the antiquarks with the corresponding anti-color charges). All the quarks and leptons carry spin 1/2 and are described by socalled (quantized) Dirac fields.

The interaction between the particles is mediated by socalled gauge fields. The electromagnetic field is the only one which also plays a direct role in everyday life, and it couples to the electric charge of the quarks and leptons. In addition there is a somwhat more complicated field that mediates the weak interaction and the gluon field which mediates the strong interaction. As all these fields are quantized their elementary excitations (socalled "one-quantum Fock states") correspond to spin-1 (vector) bosons. For the em. field these are the photons for the gluon field the gluons (there are 8 gluons with different color-dipole combinations), and for the weak interaction there are the 2 W-bosons (one with charge +1 and one with charge -1) and the electrically neutral Z boson.

Finally in addition there is also the Higgs field, which gives all the leptons (in the plain vanilla SM only the charged leptons, while the neutrinos are modelled as massless) and quarks a mass and also the W- and Z-bosons, without violating the very important local gauge symmetry underlying the math of the model. To the Higgs field there corresponds also one more elementary scalar particle, the famous Higgs boson. Only the Higgs field as a non-zero vacuum expectation value, which makes the right pattern for providing masses to the three weak gauge bosons but not to the photon and the gluons.

Vacuum fluctuations, vacuum energy and, somwhat related, "virtual particles" have to be taken with a grain of salt. In most popular-science texts it's not accurately described, what's meant by this. You find a lot of discussions about it this forums and also some nice Insights articles.
 
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The thread is now in the particle physics forum.
Apart from asking how many of these fundamental fields there are
That depends on how you count. As an example from classical mechanics, is there one electromagnetic field or are there two, the electric and the magnetic field? Both are valid descriptions. You get the same ambiguity for the fields of quantum field theory.
 
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vanhees71
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It depends ;-)). From the point of view of Newtonian classical mechanics, I'd say there are an electric and a magnetic field, and that's why electricity and magnetism were distinct subjects for a long time. Only in the first half of the 19th century it was discovered that there is a close connection. I'd take Oersted's discovery of the deflection of a compass needle close to a current-conducting wire the point where this close connection was realized. Then it took till Einstein 1905 and Minkowski 1908 to understand that in relativistic mechanics there must be both electric and magnetic field components to form the field-strength tensor which makes it one and only one field, i.e., the one and only electromagnetic field.
 
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I agree @vanhees71 about the "grain of salt" comment.

So would the statement that we have never and can never interact with or observe fields directly instead we observe them through matter/particle interactions be true?
I am not doubting that the "action at a distance" is not mere magic but a real physical phenomenon but just that it seems that unlike particles with fields we can only "calculate" them but not observe or interact directly?


One other thing than seems intriguing to me is that the fields associated with elementary particles also seem to interact or should I say give certain properties to composite particles, like for example we consider the electron to be an elementary particle not made up of any smaller particles, it has an electric charge then again the proton is made up of quarks and it also has an electric charge so does the positron which again is elementary particle, this seems strange.
For the proton the charge is said to be the result of the quark charge addition but the electron has no smaller structure.

So the same field (electric) interacts with different types of particles or should I say creates different types of particles?



PS. I still look forward to hear thoughts from my OP question about what makes up the zero point energy or the vacuum fluctuations in empty space? Even if it's a speculation somewhat at this point are these thought to be the result of the fundamental particles fields or is there some other field thought to be associated with this phenomenon ?
 
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@vanhees71 besides my previous post, so from what I gather the so called vacuum energy is also understood as the dark energy candidate for the accelerated expansion of the universe?
Is this the same thing that Einstein referred to as the cosmological constant, aka energy that resists spacetime from collapsing back due to gravity ?
 
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vanhees71
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Yes, it's formally the same as a cosmological constant, but note that there's big trouble with this. The "vacuum energy" of the standard model is of course divergent as are any other loop diagrams in perturbation theory. Thus you have to renormalize it. In usual QFT (special relativity) this infinite additive constant of the total energy has no physical impact at all. It's just subtracted, and the vacuum energy is defined to be 0 by convention.

In GR of course the absolute value of the energy density has a physical meaning. Now if you renormalize at low energy scales and use the renormalization group to calculate the value of the vacuum energy at large energy scales, particularly up to the Planck scale you get a value for the cosmological constant that is by a factor of around ##10^{120}## (sic!) too large compared to what's observed using observations like the cosmic microwave background and the redshift-distance relation from measuring Type 1a Supernovae etc. Thus you need a finetuning procedure to get rid of this, and many physicists consider this as pretty unsatisfactory. One would rather expect from a really fundamental model that the scale of the vacuum energy is somehow "natural" without any need of fine tuning.

A famous review by Weinberg about the subject is

https://doi.org/10.1103/RevModPhys.61.1
 

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