Theory of Group Representations and Applications

Barut, A. O.; Rączka, R.

doi:10.1142/0352

Cited by 988 publications

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“…It follows then from the transformation laws (2) and from the fact that dµ(g) = dµ(f −1 g f ) for any group element f that the amplitude ψ(g; γ) should actually be the function on the group classes [13,14], that is:…”

Section: Distribution Of Parallel Transporters On the Group Manifoldmentioning

confidence: 99%

“…for any element f of the gauge group G. It is known from the theory of harmonic analysis on compact groups that the characters of irreducible unitary representations of simple compact group build full orthonormal basis in the Hilbert space of functions on the group classes [13,14], therefore the function ψ(g; γ) can be decomposed as:…”

Section: Distribution Of Parallel Transporters On the Group Manifoldmentioning

confidence: 99%

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Asymptotic behavior of Wilson loops from Schrödinger equation on the gauge group

Buividovich

Kuvshinov

2006

Physics Letters B

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Probability distribution of non-Abelian parallel transporters on the group manifold and the corresponding amplitude are investigated for quantum Yang-Mills fields. It is shown that when the Wilson area law and the Casimir scaling hold for the quantum gauge field, this amplitude can be obtained as the solution of the free Schrödinger equation on the gauge group. Solution of this equation is written in terms of the path integral and the corresponding action term is interpreted geometrically. We also note that the partition function of two-dimensional pure Yang-Mills theory living on the surface spanned on the loop solves the obtained equation.

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Section: Distribution Of Parallel Transporters On the Group Manifoldmentioning

confidence: 99%

Section: Distribution Of Parallel Transporters On the Group Manifoldmentioning

confidence: 99%

Asymptotic behavior of Wilson loops from Schrödinger equation on the gauge group

Buividovich

Kuvshinov

2006

Physics Letters B

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“…Let ( , ) be any hermitian product on V. Since T is compact, there exists a left invariant (Haar) measure p on T (see x [3]). For v,w e V we define <v,w> := J (rt(g)v, T jt(g)w)dy (g).…”

Section: Jm Myezewskimentioning

confidence: 99%