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The Vacuum Wavefunctional

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An Introduction to the Confinement Problem

Part of the book series: Lecture Notes in Physics ((LNP,volume 972))

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Abstract

The Yang-Mills vacuum wavefunctional as a bridge to magnetic disorder in lower dimensions. Proposals for the Yang-Mills vacuum wavefunctional in 2+1 dimensions. Numerical tests in temporal gauge. The Karabali-Nair “new variables” approach.

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Notes

  1. 1.

    As already mentioned in Chap. 10, it may still be useful in a physical gauge to introduce Faddeev-Popov ghosts in the path integral, but the essential point is that in a physical gauge these ghosts do not propagate in time.

  2. 2.

    An attempt to overcome this difficulty by inclusion of monopole fields is in [11].

  3. 3.

    In quantum gravity this subspace of the set of all configurations is known as “minisuperspace.”

  4. 4.

    The subtraction of λ 0 is introduced so that spectrum of D 2 − λ 0 + m 2 begins at m 2, rather than infinity in the continuum limit. Apart from this subtraction, the proposal is the same as an earlier suggestion by Samuel [13].

  5. 5.

    More precisely, it is the eigenstate of the lattice transfer matrix \(T=\exp [-Ha]\) with the highest eigenvalue.

  6. 6.

    Recently some corrections to σ have been calculated [17], and they are small. At present it is not entirely clear why the correction is so small, since it involves a sum of rather large (positive and negative) contributing terms, which for some reason nearly cancel.

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Greensite, J. (2020). The Vacuum Wavefunctional. In: An Introduction to the Confinement Problem. Lecture Notes in Physics, vol 972. Springer, Cham. https://doi.org/10.1007/978-3-030-51563-8_13

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