131.111.184.92 at 20:42, 14 May 2013

2013-05-14T20:42:39Z

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In [[physics]], '''Hamiltonian lattice gauge theory''' is a calculational approach to [[gauge theory]] and a special case of [[lattice gauge theory]] in which the space is discretized but time is not. The [[Hamiltonian_(quantum_mechanics)|Hamiltonian]] is then re-expressed as a function of degrees of freedom defined on a d-dimensional lattice.

Following Wilson, the spatial components of the [[vector potential]] are replaced with [[Wilson line]]s over the edges, but the time component is associated with the vertices. However, the [[temporal gauge]] is often employed, setting the [[electric potential]] to zero. The [[eigenvalue]]s of the Wilson line [[operator (mathematics)|operator]]s U(e) (where e is the ([[oriented]]) edge in question) take on values on the [[Lie group]] G. It is assumed that G is [[compact group|compact]], otherwise we run into many problems. The conjugate operator to U(e) is the [[electric field]] E(e) whose eigenvalues take on values in the Lie algebra <math>\mathfrak{g}</math>. The Hamiltonian receives contributions coming from the plaquettes (the magnetic contribution) and contributions coming from the edges (the electric contribution).

Hamiltonian lattice gauge theory is exactly dual to a theory of [[spin network]]s. This involves using the [[Peter-Weyl theorem]]. In the spin network basis, the spin network states are [[eigenstate]]s of the operator <math>Tr[E(e)^2]</math>.

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==References==
*Hamiltonian formulation of Wilson's lattice gauge theories, [[John Kogut]] and [[Leonard Susskind]], ''Phys. Rev. D'' 11, 395–408 (1975)

[[Category:Lattice models]]

E-folding - Revision history

131.111.184.92 at 20:42, 14 May 2013