Quantum field theory predicts a value for the cosmological constant that is 123 orders of magnitude larger than the observed value (if one assumes the Standard Model to be correct up to the Planck scale of 10^19 GeV)! To theoretically predict the value of the cosmological constant, one must, I suppose, add up all the ground state energies of the quantum fields corresponding to the particles of the Standard Model. By introducing some cut-off to the integral over frequencies, one obtains a finite answer. I would like to understand where this (horrible) prediction exactly comes from. I am a graduate student in particle physics and have had just a little on QFT so far. I have a few questions about quantum fields and it would be great if anyone could help!(adsbygoogle = window.adsbygoogle || []).push({});

I understand that within the QFT framework particles are interpreted as excited states of fields. I have seen that photons, for example, are the quanta of the electromagnetic field.

(1) But doeseveryparticle of the Standard Model correspond (uniquely) to some field? So do we have, say, a down quark field for the down quark, a charm quark field for the charm quark, a tau neutrino field for the tau neutrino, a Z boson field for the Z boson and so on... ? Or do some particles, in a way, correspond to the same field?

(3) Does the concept of a quantum field only makes sense for the elementary particles of the Standard Model? Or can one also speak of fields corresponding to composed particles, like mesons?

(2) And is there justonequantum field of each type in the whole Universe? So is the vacuum filled with all different types of quantum fields that exist? Is the vacuum hence identical for all points in spacetime? Perhaps I do not understand very well what a quantum field is...

I have seen that one can write the Hamiltonian of the electromagnetic field as an infinite sum of quantum harmonic oscillators. Then you immediately see that this field has some non-zero ground state energy which must contribute to the energy of the vacuum and in turn contribute to the cosmological constant.

(4) Do all quantum fields corresponding to the particles of the Standard Model have a non-zero ground state energy? If yes, then I suppose this follows from the Heisenberg uncertainty principle. Can this contribution also be negative?

(5) Caneveryquantum field be thought of as a collection of harmonic oscillators of all possible frequencies?

I have quite a lot of questions... I still just miss the conceptual part of QFT. Any help would be greatly appreciated!

Thanks in advance:)

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# Interpretation of quantum fields and their ground state energies.

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