Lattice field theory with only spatial discretization
This article relies largely or entirely on a single source. Relevant discussion may be found on the talk page. Please help improve this article by introducing citations to additional sources. Find sources: "Hamiltonian lattice gauge theory" – news · newspapers · books · scholar · JSTOR(October 2022)
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 vector potential are replaced with Wilson lines 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 eigenvalues of the Wilson line operators 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, 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 . 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 networks. This involves using the Peter–Weyl theorem. In the spin network basis, the spin network states are eigenstates of the operator .
and 26 Related for: Hamiltonian lattice gauge theory information
physics The theory of quark confinement The development of Hamiltonianlatticegaugetheory known as Kogut–Susskind fermions The theory of scaling violations...
In physics, a gaugetheory is a type of field theory in which the Lagrangian, and hence the dynamics of the system itself, do not change under local transformations...
constraint Hamiltonian fluid mechanics Hamiltonian operator, see Hamiltonian (quantum mechanics) Hamiltonianlatticegaugetheory In both mathematics and physics...
quantum Hamiltonian constraint is the operator introduced by Thiemann. The constraints define a constraint surface in the original phase space. The gauge motions...
development of gaugetheory and the completion of the Standard Model in the 1970s led to a renaissance of quantum field theory. Quantum field theory results...
act as waves of lattice displacement.[citation needed] This technique is readily generalized to three dimensions, where the Hamiltonian takes the form:...
Landau pole Higgs mechanism Wilson line Wilson loop Tadpole (physics) Latticegaugetheory BRST charge Anomaly (physics) Chiral anomaly Braid statistics Plekton...
Jean-Michel (1989), Statistical field theory, Volume 1: From Brownian motion to renormalization and latticegaugetheory, Cambridge University Press, ISBN 978-0-521-40805-9...
\mathbf {A} .} There is some gauge freedom in the choice of vector potential for a given magnetic field. The Hamiltonian is gauge invariant, which means that...
proton, neutron and pion. QCD is a type of quantum field theory called a non-abelian gaugetheory, with symmetry group SU(3). The QCD analog of electric...
energies is by a supersymmetric gaugetheory, and found geometrical interpretations of mathematical structures in gaugetheory that he and Nathan Seiberg had...
In the physics of gaugetheories, gauge fixing (also called choosing a gauge) denotes a mathematical procedure for coping with redundant degrees of freedom...
Numerous fixed points appear in the study of lattice Higgs theories, but the nature of the quantum field theories associated with these remains an open question...
Davydov Hamiltonian. The mathematical techniques that are used to analyze Davydov's soliton are similar to some that have been developed in polaron theory. In...
of an electron to the electromagnetic field. In a non-abelian gaugetheory, the gauge coupling parameter, g {\displaystyle g} , appears in the Lagrangian...
example is the BCS theory of superconductivity. Here the underlying theory is the theory of electrons in a metal interacting with lattice vibrations called...
three-dimensional spatial slices in terms of a SU(2) gauge field and its complementary variable. The Hamiltonian was much simplified in this reformulation. This...
adding an interaction Hamiltonian. For a φ4 theory, this corresponds to adding a Wick ordered term g:φ4:/4! to the Hamiltonian, and integrating over x...
forces of nature. Beginning in 1954, the parallel was found by way of gaugetheory, leading by the late 1970s, to quantum field models of strong nuclear...
another spatial point (x) at a later time (t). Consider a system with Hamiltonian H. The Green's function G (fundamental solution) for the Schrödinger...
Principles of Quantum Mechanics. The word canonical arises from the Hamiltonian approach to classical mechanics, in which a system's dynamics is generated...
analog of a mass gap in many-body physics on a discrete lattice arises from a gapped Hamiltonian. For a given real-valued quantum field ϕ ( x ) {\displaystyle...
polymer physics, quantum field theory, string theory and cosmology. In physics, it is a foundation for latticegaugetheory and quantum chromodynamics. It...