Solving the Cosmology Constant Problem, is it too easy?
The previous progress on the subject tells this: if there is no upper limit of possible energy (so called Planck Energy), then the energy density of the vacuum is infinite. Then in this case there is no such thing as "vacuum wave function". But the Google for search "Wave function of the vacuum" gives quite several results. Therefore, there is no the energy divergency ("cosmology constant problem") in Quantum Electrodynamics, isn't it?
The problem consists in the fact that in postmodern physics words don't have a precise meaning and the same term can explain a thing and the opposite of that same thing. It happens for instance for the so-called "quantum vacuum" that would be a "vacuum that isn't empty". Classic physicists called "ether" the vacuum that wasn' t empty but many experiments proved ether didn't exist. Now postmodern physicists propose again ether with another name i.e. "quantum vacuum" and they think a few recent experiments prove the existence of quantum vacuum, like for instance the Casimir effect and the expansion of the universe. But it is possible to demonstrate those facts through different physico-mathematical models. Postmodern physics, also with the introduction of terms as wave function of the universe and cosmological constant, is generating a big confusion that decreases the level of our understanding of the nature. It is due to the fact postmodern physics doesn't have sound fundamentals.
Dmitri wave functions by construction are infinite. In case of QED the infinities are canceled out by renormalization. So QED is regarded as a final solution to EM interacting with charge particles, and is highly accurate in experiments.
Other parts of the standard model and related studies like QCD are probably not final and may not have been renormalized.
Notice that infinities are not observed in nature. They are artifacts of the mathematical tools, especially from Fourier series analysis of QM.
It is important to keep separate thoughts for physical science and the tool kit of math that is chosen to describe it.
The renormalization is a mathematical tool that is very used in postmodern physics and was used also in modern physics. It is applied to many physical questions because frequently it allows to solve physico-mathematical complex problems. Often nevertheless the renormalization hides mathematical errors. For instance I would propose here a renormalization that was used in modern physics. Supposing that SQRT means "square root", what do you think about this renormalization SQRT[-g]=SQRT[g]? Returning then to the concept of infinity, it is manifest that it doesn't exist and cannot be observed, in fact infinities for mathematical definition aren't relative to real situations but they indicate simply the tendency of a dependent mathematical variable or of a physical magnitude to preserve a regular trend when the independent variable increases, without that an objective limit exists to that increase. It is the case of transitory phenomena, in which the correct renormalization consists for instance in cutting off the graph after 4-5 time constants in the event that the independent variable is the time. In the event of wave functions, they for mathematical definition are defined on the whole independent axis (generally time or space or angle) and this can produce problems when wave functions are used like mathematical models for physical quantities. It happened when the mathematical model of wavefunction was applied to photon, through the wave packet, that led Heisenberg to formulate the Indeterminacy Principle applying the Fourier series to a physico-mathematical model that was substantially wrong. Consequently I would be very carefull to apply the mathematical concept of wavefunction to complex concepts as the universe that cannot be reduced to a wavefunction.
I totally agree with Daniele who correctly addressed the problems of postmodern physics. We should strongly oppose to the use of words that don't have a meaning. An illuminating analysis of this widespread practice can be found in the link below.
http://www.physics.nyu.edu/faculty/sokal/transgress_v2/transgress_v2_singlefile.html
@Dmitri
What do you mean by "finite state"? For the free em field, the Fock space is well defined, and all infinities are due to improper operator orderings. This is not so for the interacting field, but this does not seem to be your question.
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