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The automatic calculation of particle interaction or decay is part of the computational particle physics branch. It refers to computing tools that help calculating the complex particle interactions as studied in high-energy physics, astroparticle physics and cosmology.
A treatment of the helicity of gravitational waves can be found in Weinberg. [4] In summary, they come in only two forms: +2 and −2, while the +1, 0 and −1 helicities are "non-dynamical" (they can be removed by a gauge transformation).
In meteorology, [2] helicity corresponds to the transfer of vorticity from the environment to an air parcel in convective motion. Here the definition of helicity is simplified to only use the horizontal component of wind and vorticity, and to only integrate in the vertical direction, replacing the volume integral with a one-dimensional definite integral or line integral:
These amplitudes are called MHV amplitudes, because at tree level, they violate helicity conservation to the maximum extent possible. The tree amplitudes in which all gauge bosons have the same helicity or all but one have the same helicity vanish. MHV amplitudes may be calculated very efficiently by means of the Parke–Taylor formula.
At equilibrium, the rate of net energy production in the system must equal the rate of energy loss due to frictional dissipation at the surface, i.e. W i n = W o u t {\displaystyle W_{in}=W_{out}} The rate of energy loss per unit surface area from surface friction, W o u t {\displaystyle W_{out}} , is given by
In the Standard Model, using quantum field theory it is conventional to use the helicity basis to simplify calculations (of cross sections, for example). In this basis, the spin is quantized along the axis in the direction of motion of the particle.
Where is the height of the level of free convection and is the height of the equilibrium level (neutral buoyancy), where , is the virtual temperature of the specific parcel, where , is the virtual temperature of the environment (note that temperatures must be in the Kelvin scale), and where is the acceleration due to gravity. This integral is ...
Magnetic helicity is a gauge-dependent quantity, because can be redefined by adding a gradient to it (gauge choosing).However, for perfectly conducting boundaries or periodic systems without a net magnetic flux, the magnetic helicity contained in the whole domain is gauge invariant, [15] that is, independent of the gauge choice.
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