Gauge transformation effect

We now describe the relation between a purely formal calculational device, like a gauge transformation that merely admixes the basis states, and observable effects. 

Another example of a physical effect of this type is the Aharonov-Bohm effect, which is supported by a multiply connected vacuum configuration such as that described by the 0(3) gauge group [6]. The Aharonov-Bohm effect is a gauge transform of the true vacuum, where there are no potentials. In our notation, therefore the Aharonov-Bohm effect is due to terms such as (1/ )8 , depending on the geometry chosen for the experiment. It is essential for the Aharonov-Bohm effect to exist such that (1/ )8 be physical, and not random. It follows therefore that the vacuum configuration defined by the... 

The effect of a local gauge transformation (Sction II) on the classical B(3 field is described as... 

The problem of gauge transform also surfaces when Schrodinger s equation is employed to study the Aharonov-Bohm effect. If the transform = oejv is performed within Schrodinger s equation ... 

The Sagnac effect is therefore due to a gauge transformation and a closed loop in Minkowski spacetime with 0(3) covariant derivatives. 

The properties of the phase factor (548) on 0(3) gauge transformation have been shown [47] to explain the Sagnac effect with platform in motion. In condensed notation, gauge transformation produces the results... 

The effect of the local gauge transform is to introduce an extra term 8M A in the transformation of the derivatives of fields. Therefore, 8 A does not transform covariantly, that is, does not transform in the same way as A itself. These extra terms destroy the invariance of the action under the local gauge transformation, because the change in the Lagrangian is... 

In the 0(3) invariant theory of the Aharonov-Bohm effect, the holonomy consists of parallel transport using 0(3) covariant derivatives and the internal gauge space is a physical space of three dimensions represented in the basis ((1),(2),(3)). Therefore, a rotation in the internal gauge space is a physical rotation, and causes a gauge transformation. The core of the 0(3) invariant explanation of the Aharonov-Bohm effect is that the Jacobi identity of covariant derivatives [46]... 

The electric and magnetic fields are invariant under gauge transformations, 4 X(x) i—>A (x) + cM A(x). The effect of these transformations on the helicity has been treated by Marsh [49]. The variation of the magnetic helicity under a gauge transformation 8A = —VA is... 

In an environment of atoms in collision, interatomic contacts consist of interacting negative charge clouds. This environment for an atom is approximated by a uniform electrostatic held, which has a well-defined effect on the phases of wave functions for the electrons of the atom. It amounts to a complex phase (or gauge) transformation of the wave function ... 

If the physical results are to remain unchanged under a unitary transformation, it is necessary to transform the operators as well as the state functions (eqns (8.28) and (8.29)). A gauge transformation has no effect on a coordinate operator but the momentum operator p is changed into p + [e/c) x- Thus, to maintain gauge invariance in properties determined by the momentum operator, p must be replaced by a new operator. In the presence of an electromagnetic field or just a magnetic field, the momentum operator is replaced by the expression... 

Solvent-induced effects on NMR shielding of 1,2,4,5-tetrazine and two isomeric tetrazoles are calculated using density functional theory combined with the polarizable continuum model and using the continuous set gauge transformation/ Direct and indirect solvent effects on shielding are also calculated. 

The effect of (12) on the vector (p is that gauge transformations, that leave (15) invariant, exist, we no longer have a projective geometry, but only an affine geometry. Because of the tensor gij this affine geometry is metrical. 

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