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The data below tabulates standard electrode potentials (E°), in volts relative to the standard hydrogen electrode (SHE), at: Temperature 298.15 K (25.00 °C; 77.00 °F); Effective concentration (activity) 1 mol/L for each aqueous or amalgamated (mercury-alloyed) species; Unit activity for each solvent and pure solid or liquid species; and
The potential equations can be simplified using a procedure called gauge fixing. Since the potentials are only defined up to gauge equivalence, we are free to impose additional equations on the potentials, as long as for every pair of potentials there is a gauge equivalent pair that satisfies the additional equations (i.e. if the gauge fixing ...
The concept and the name of gauge theory derives from the work of Hermann Weyl in 1918. [1] Weyl, in an attempt to generalize the geometrical ideas of general relativity to include electromagnetism, conjectured that Eichinvarianz or invariance under the change of scale (or "gauge") might also be a local symmetry of general relativity.
A particular choice of the scalar and vector potentials is a gauge (more precisely, gauge potential) and a scalar function ψ used to change the gauge is called a gauge function. [citation needed] The existence of arbitrary numbers of gauge functions ψ(r, t) corresponds to the U(1) gauge freedom of this theory. Gauge fixing can be done in many ...
In electromagnetism, the Lorenz gauge condition or Lorenz gauge (after Ludvig Lorenz) is a partial gauge fixing of the electromagnetic vector potential by requiring = The name is frequently confused with Hendrik Lorentz , who has given his name to many concepts in this field. [ 1 ] (
ϕ is known as a velocity potential for u. A velocity potential is not unique. If ϕ is a velocity potential, then ϕ + f(t) is also a velocity potential for u, where f(t) is a scalar function of time and can be constant. Velocity potentials are unique up to a constant, or a function solely of the temporal variable.
Note that, in contrast to the magnitude of an electric field due to a point charge, the electric potential scales respective to the reciprocal of the radius, rather than the radius squared. The electric potential at any location, r , in a system of point charges is equal to the sum of the individual electric potentials due to every point charge ...
There is some gauge freedom in the choice of vector potential for a given magnetic field. The Hamiltonian is gauge invariant, which means that adding the gradient of a scalar field to A changes the overall phase of the wave function by an amount corresponding to the scalar field. But physical properties are not influenced by the specific choice ...