# Frame rotation

Consider CRE-filtered beam. The photons of the beam are characterized by its
momentum, second quantization axis, Lambda-variable and chi-variable. Introduce
laboratory right-hand coordinate system with *Y*-axis alond the photon
second quantization axis and *Z*-axis along the
photon 3-momentum.

The CRE-filtered beam passes through conerefringent element, denoted as CRE′. It has its own
coordinate system and
Lambda-parameter . is rotated relative about the *Z*-axis
by an angle .

The passage of CRE-filtered beam through CRE′ can be considered as a passage through one Stern-Gerlach filter. The passage does not change the photon 3-momentum.

# Fine splitting neglected

If the fine Poggendorff splitting is neglected, the photon state before the CRE′ filter can be denoted by . CRE′ filter splits the -beam in two beams, which are in basis states of CRE′. The second quantization axes of both beams is either along (up) or opposite (down) to the Y′- axis. The photons of one of the beams are always in up-state, denote it by . The photons from the other one can be in a down or in up state depending on the variable . They are in a down-state if and in up-state if ; denote this state by .

## Transition amplitudes

We are interested for the transition amplitudes from -state to the final - and -states. The experiment demonstrates that:

## Photon variables

We are interested for the values of the Lambda- and chi-variables of the photon final states. The experiment demonstrates that: