Hamiltonian lattice gauge theory

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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 is then re-expressed as a function of degrees of freedom defined on a d-dimensional lattice.

Following Wilson, the spatial components of the

E(e) whose eigenvalues take on values in the Lie algebra ${\displaystyle {\mathfrak {g}}}$. 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

eigenstates

of the operator ${\displaystyle Tr[E(e)^{2}]}$.

References

• ISSN 0556-2821
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