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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.
Diagrams with loops (in graph theory, these kinds of loops are called cycles, while the word loop is an edge connecting a vertex with itself) correspond to the quantum corrections to the classical field theory. Because one-loop diagrams only contain one cycle, they express the next-to-classical contributions called the semiclassical contributions.
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)
Using perturbation theory in quantum field theory in curved spacetime geometry is known as the semiclassical approach to quantum gravity. This approach studies the interaction of quantum fields in a fixed classical spacetime and among other thing predicts the creation of particles by time-varying spacetimes [5] and Hawking radiation. [6]
An example of a continuum theory that is widely studied by lattice models is the QCD lattice model, a discretization of quantum chromodynamics. However, digital physics considers nature fundamentally discrete at the Planck scale, which imposes upper limit to the density of information , aka Holographic principle .
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
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 ...
Semiclassical gravity is an approximation to the theory of quantum gravity in which one treats matter and energy fields as being quantum and the gravitational field as being classical. In semiclassical gravity, matter is represented by quantum matter fields that propagate according to the theory of quantum fields in curved spacetime .