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Lattice perturbation theory can also provide results for condensed matter theory. One can use the lattice to represent the real atomic crystal . In this case the lattice spacing is a real physical value, and not an artifact of the calculation which has to be removed (a UV regulator), and a quantum field theory can be formulated and solved on ...
In quantum field theory, the theory of a free (or non-interacting) scalar field is a useful and simple example which serves to illustrate the concepts needed for more complicated theories. It describes spin-zero particles. There are a number of possible propagators for free scalar field theory. We now describe the most common ones.
semiclassical gravity: quantum field theory within a classical curved gravitational background (see general relativity). quantum chaos ; quantization of classical chaotic systems. magnetic properties of materials and astrophysical bodies under the effect of large magnetic fields (see for example De Haas–Van Alphen effect )
In some cases, the Schrödinger equation can be solved analytically on a one-dimensional lattice of finite length [6] [7] using the theory of periodic differential equations. [8] The length of the lattice is assumed to be L = N a {\displaystyle L=Na} , where a {\displaystyle a} is the potential period and the number of periods N {\displaystyle ...
Physical lattice models frequently occur as an approximation to a continuum theory, either to give an ultraviolet cutoff to the theory to prevent divergences or to perform numerical computations. An example of a continuum theory that is widely studied by lattice models is the QCD lattice model, a discretization of quantum chromodynamics.
In lattice field theory, the Nielsen–Ninomiya theorem is a no-go theorem about placing chiral fermions on a lattice.In particular, under very general assumptions such as locality, hermiticity, and translational symmetry, any lattice formulation of chiral fermions necessarily leads to fermion doubling, where there are the same number of left-handed and right-handed fermions.
In physics, lattice field theory is the study of lattice models of quantum field theory. This involves studying field theory on a space or spacetime that has been discretised onto a lattice . Details
In physics, lattice gauge theory is the study of gauge theories on a spacetime that has been discretized into a lattice. Gauge theories are important in particle physics , and include the prevailing theories of elementary particles : quantum electrodynamics , quantum chromodynamics (QCD) and particle physics' Standard Model .