? 1 and ? 3 are symmetric with respect to the mirror plane as the sign of the p-orbital lobes is preserved under the symmetry transformation.
12.
Either the dipole moment stays invariant under the symmetry transformation ( " + 1 " ) or it changes its direction ( " " 1 " ):
13.
According to the theorem, any "'symmetry transformation "'of "'ray space "'is represented by a representation or a projective representation.
14.
The density matrix of a KMS state is related to unitary transformations involving time translations ( or time translations and an internal symmetry transformation for nonzero chemical potentials ) via the Tomita Takesaki theory.
15.
All multiplicative quantum numbers belong to a symmetry ( like parity ) in which applying the symmetry transformation twice is equivalent to doing nothing ( group called "'Z 2 " '.
16.
A system described by a given action might have multiple independent symmetries of this type, indexed by r = 1, 2, \ ldots N, so the most general symmetry transformation would be written as
17.
In supersymmetric quantum field theories, in which the action integral is invariant under a set of symmetry transformations ( known as supersymmetry transformations ) whose algebras are superalgebras, the supertrace has a variety of applications.
18.
Alluding to Klein's ( 1893 ) treatment of minimal projection, he pointed out that this group " is simply isomorphic with the group of all displacements and symmetry transformations in space of four dimensions ".
19.
According to this definition, supplemented with the constancy of the speed of light, inertial frames of reference transform among themselves according to the Poincar?group of symmetry transformations, of which the Lorentz transformations are a subgroup.
20.
During this period, Eckart developed his formulation of the Wigner-Eckart theorem a link between symmetry transformation groups applied to the Schr�dinger equation and the laws of conservation of energy, momentum, and angular momentum.
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