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Упражнение по физике
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Dear ...,
I am attaching a short note related to the renormalization problem in QFT that I think you might be interested in. Consider the standard construction (as in Assumption 0 of Streater & Wightman (p.97)) of the vacuum wavestate in QFT. This defines a translationally (Poincare) invariant vector in an infinite-dimensional Hilbert space (unlike any other state in QFT, it is not in "Fock" space and doesn't depend on any fields). The invariance implies the vacuum depends on nothing and must be a constant function in Hilbert space. This leads to a contradiction because it is impossible to construct a constant function in Hilbert space with a finite norm. The renormalization problem of modern particle physics, the "problem of the infinities", is a direct consequence of this problem. The energy of the vacuum turns out to diverge because norm of the vacuum wavestate itself is divergent. The impossibility of a vacuum also gives rise to vacuum polarization, which as has recently been shown in anti-desitter space gives rise to a nonzero cosmological constant. It is now clear that this is a direct manifestation of the fact that there cannot be a vacuum state. The minimal energy level of a physical state is greater than zero.
(Author: some professor of finance in Texas)
Dear ...,
I am attaching a short note related to the renormalization problem in QFT that I think you might be interested in. Consider the standard construction (as in Assumption 0 of Streater & Wightman (p.97)) of the vacuum wavestate in QFT. This defines a translationally (Poincare) invariant vector in an infinite-dimensional Hilbert space (unlike any other state in QFT, it is not in "Fock" space and doesn't depend on any fields). The invariance implies the vacuum depends on nothing and must be a constant function in Hilbert space. This leads to a contradiction because it is impossible to construct a constant function in Hilbert space with a finite norm. The renormalization problem of modern particle physics, the "problem of the infinities", is a direct consequence of this problem. The energy of the vacuum turns out to diverge because norm of the vacuum wavestate itself is divergent. The impossibility of a vacuum also gives rise to vacuum polarization, which as has recently been shown in anti-desitter space gives rise to a nonzero cosmological constant. It is now clear that this is a direct manifestation of the fact that there cannot be a vacuum state. The minimal energy level of a physical state is greater than zero.
(Author: some professor of finance in Texas)