Photon propagation

In CDAD, a chiral experimental geometry is created about a fixed molecular orientation, and the asymmetry in the electron distribution can be observed in directions mutually perpendicular to the photon propagation direction and the... 

The key prerequisite for optical amplification via stimulated emission is that the emitted photons propagate through the gain medium long enough to initiate further stimulated transitions. This condition can be expressed as... 

The photoelectric cross-section o is defined as the one-electron transition probability per unit-time, with a unit incident photon flux per area and time unit from the state to the state T en of Eq. (2). If the direction of electron emission relative to the direction of photon propagation and polarization are specified, then the differential cross-section do/dQ can be defined, given the emission probability within a solid angle element dQ into which the electron emission occurs. Emission is dependent on the angular properties of T in and Wfin therefore, in photoelectron spectrometers for which an experimental set-up exists by which the angular distribution of emission can be scanned (ARPES, see Fig. 2), important information may be collected on the angular properties of the two states. In this case, recorded emission spectra show intensities which are determined by the differential cross-section do/dQ. The total cross-section a (which is important when most of the emission in all direction is collected), is... 

Here D(rjtj,r2t2) is the photon propagator jcv, jpv, jfw are the four-dimensional components of the operator of current for the considered particles core, proton, muon x = (vc, Vp, r, t) includes the space coordinates of the three particles plus time (equal for all particles) and y is the adiabatic parameter. For the photon propagator, it is possible to use the exact electrodynamical expression. Below we are limited by the lowest order of QED PT, i.e., the next QED corrections to Im E will not be considered. After some algebraic manipulation we arrive at the following expression for the imaginary part of the excited state energy as a sum of contributions ... 

Another obvious contribution to the Lamb shift of the same leading order is connected with the polarization insertion in the photon propagator (see Fig. 2.2). This correction also induces a correction to the Coulomb potential... 

We have seen above that calculation of the corrections of order a"(Za) m (n > 1) reduces to calculation of higher order corrections to the properties of a free electron and to the photon propagator, namely to calculation of the slope of the electron Dirac form factor and anomalous magnetic moment, and to calculation of the leading term in the low-frequency expansion of the polarization operator. Hence, these contributions to the Lamb shift are independent of any features of the bound state. A nontrivial interplay between radiative corrections and binding effects arises first in calculation of contributions of order a Za) m, and in calculations of higher order terms in the combined expansion over a and Za. 

This situation is radically different from the case of electronic hydrogen where inclusion of the electron loop in the photon propagator generates effectively a (5-function correction to the Coulomb potential (compare discussion in Sect. 2.2). 

In the leading nonrelativistic approximation the denominator of the photon propagator cancels the exchanged momentum squared in the numerator, and we immediately obtain the Hamiltonian for the interaction of two magnetic moments, reproducing the above result of classical electrodynamics. 

Quantum mechanics had exploded between 1923 and 1927. A. H. Compton, in 1923, had discovered the change in frequency of X-rays scattered from the electrons (the Compton effect).25 Compton and, independently, Debye had underlined the importance of this discovery in support of the Einstein conception of light-quanta or photon propagation in space.26... 

The situation with photon propagation in free space is quite diferent. If vacuum is equated to absence of a fluid, what is the support for the waves Of course, particle-like propagation solves the problem, but it (strictly) invalidates Maxwell s equations in vacuum. There is a positive aspect. Since vacuum is nondispersive, all velocities have the same magnitude. 

Let us concentrate on the particle aspect only. The main issue is to identify an space (three- or four-dimensional ) where photons propagate with constant speed c. Einstein s second postulate of the special theory of relativity (STR) requires the speed of light in free space to be the same for all inertial observers. This postulate is conventionally interpreted as implying the non-existence of a preferred frame E. As discussed in section II, the exactly opposite view will be adopted here. 

Let us concentrate here on the photon as a particle only. The main task is to identify the family of frames where the photon propagates with a constant... 

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