A gauge transformation rotates the phase of the condensate by an amount which changes from point to point, and shifts the vector potential by a gradient:
42.
As our vector potential; this corresponds to a uniform and constant magnetic field " B " in the " z " direction.
43.
The line running upward represents the gauge orbit of the vector potential A ^ \ Lambda _ \ mu as the gauge transformation function \ Lambda varies.
44.
For example, in electromagnetism "'A o "'is typically the vector for the electric field, magnetic field, or vector potential.
45.
Together with the electric potential, the magnetic vector potential can be used to specify the electric field, "'E "'as well.
46.
The vector potential "'A "'is used when studying the Schr�dinger equation for charged particles, Dirac equation, Aharonov Bohm effect ).
47.
Using the standard trick of adjoint creation and annihilation operators, but with this quotient trick, one can formulate free field vector potential operator valued distribution A satisfying
48.
It is particularly useful for " semi-classical " calculations in quantum mechanics, in which the vector potential is quantized but the Coulomb interaction is not.
49.
Following Wilson, the spatial components of the vector potential are replaced with Wilson lines over the edges, but the time component is associated with the vertices.
50.
Where " e " is the electric charge of the particle and "'A "'the magnetic vector potential of the electromagnetic field.
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