Creation operators, 0 electrodynamics

Both A(3> and B(3> are longitudinally directed and are nonzero in the vacuum. Both A(3> and B(3> are phaseless, but propagate with the radiation [47-62] and with their (1) and (2) counterparts. The radiated vector potential A<3 does not give rise to a photon on the low-energy scale, because it has no phase with which to construct annihilation and creation operators. On the high-energy scale, there is a superheavy photon [44] present from electroweak theory with an SU(2)x SU(2) symmetry. The existence of such a superheavy photon has been inferred empirically [44], However, the radiated vector potential A<3) is not zero in 0(3) electrodynamics from first principles, which, as shown in this section, are supported empirically with precision. 

At the end of Section 8.16 we mentioned that the Fock representation avoids the use of multiple integrations of coordinate space when dealing with the many-body problem. We can see here, however, that the new method runs into complications of its own To handle the immense bookkeeping problems involved in the multiple -integrals and the ordered products of creation and annihilation operators, special diagram techniques have been developed. These are discussed in Chapter 11, Quantum Electrodynamics. The reader who wishes to study further the many applications of these techniques to problems of quantum statistics will find an ample list of references in a review article by D. ter Haar, Reports on Progress in Physics, 24,1961, Inst, of Phys. and Phys. Soc. (London). 

The simplest way to show the principal difference between the representations of plane and multipole photons is to compare the number of independent quantum operators (degrees of freedom), describing the monochromatic radiation field. In the case of plane waves of photons with given wavevector k (energy and linear momentum), there are only two independent creation or annihilation operators of photons with different polarization [2,14,15]. It is well known that QED (quantum electrodynamics) interprets the polarization as given spin state of photons [4]. The spin of photon is known to be 1, so that there are three possible spin states. In the case of plane waves, projection of spin on the... 

A further term, which has no analogue in hydrogen, arises in the fine structure of positronium. This comes from the possibility of virtual annihilation and re-creation of the electron-positron pair. A virtual process is one in which energy is not conserved. Real annihilation limits the lifetimes of the bound states and broadens the energy levels (section 12.6). Virtual annihilation and re-creation shift the levels. It is essentially a quantum-electrodynamic interaction. The energy operator for the double process of annihilation and re-creation is different from zero only if the particles coincide, and have their spins parallel. There exists, therefore, in the triplet states, a term proportional to y 2(0). It is important only in 3S1 states, and is of the same order of magnitude as the Fermi spin-spin interaction. Humbach [65] has given an interpretation of this annihi-... 

Moreover, electron-positron pair creation and other proce.s.ses ( radiative corrections ) de.scribed by quantum electrodynamics which has quantized degrees of freedom for both the fermions and the electromagnetic field are usually not included in the theory, although the chaige-conjugated degrees of freedom are still there. Therefore the literature often refers to the no virtual pair or, in short, no pair approximatioa Very few calculations go beyond this approximation. " Nevertheless. the no-pair operator based on the DCB Hamiltonian provides an exellent approximation to the full theory, generally sufficient for the determination of relativistic effects in the electronic structure of neutral atoms and molecules. 

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