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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 821))

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The static quark potential arises from vacuum fluctuations of the gauge fields; this is clear from the fact that the potential is extracted from the vacuum expectation value of a Wilson loop. In a Euclidean functional integral, the orientation of a rectangular R × T loop is obviously irrelevant to the expectation value, and in particular it can be oriented in a plane at a fixed time.

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  1. 1.

    As already mentioned in Chapter 9, 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.

    For a recent attempt to overcome this difficulty by inclusion of monopole fields, cf. [12].

  3. 3.

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

  4. 4.

    The subtraction of λ0 is introduced so that spectrum of D 2 − λ0 + 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 [14].

  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 [19], 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. (2010). The Vacuum Wavefunctional. In: An Introduction to the Confinement Problem. Lecture Notes in Physics, vol 821. Springer, Berlin, Heidelberg.

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