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In 1906, he was also the first to write that quantum theory should replicate classical mechanics at some limit, particularly if the Planck constant h were infinitesimal. [ 1 ] [ 2 ] With this idea he showed that Planck's law for thermal radiation leads to the Rayleigh–Jeans law , the classical prediction (valid for large wavelength ).
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 the ...
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 .
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]
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 ...
In this new formulation of quantum gravity AQG semiclassical states always control the fluctuations of all present degrees of freedom. This makes the AQG semiclassical analysis superior over that of LQG, and progress has been made in establishing it has the correct semiclassical limit and providing contact with familiar low energy physics. [46 ...
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.
The Bose–Hubbard model gives a description of the physics of interacting spinless bosons on a lattice.It is closely related to the Hubbard model that originated in solid-state physics as an approximate description of superconducting systems and the motion of electrons between the atoms of a crystalline solid.