Field operators photon

Quantization of the Electromagnetic Field.—Instead of proceeding as in the previous discussion of spin 0 and spin particles, we shall here adopt essentially the opposite point of view. Namely, instead of formulating the quantum theory of a system of many photons in terms of operators and showing the equivalence of this formalism to the imposition of quantum rules on classical electrodynamics, we shall take as our point of departure certain commutation rules which we assume the field operators to satisfy. We shall then show that a... 

Thus the current operator indeed transforms like a vector. This must be the case in order that the equation Qdu(x) = ju(x) transform properly, assuming the transformation property (11-267) for Au(x). We now inquire briefly into tike question of the uniqueness of the U(ia) operator, in particular into the question of the phase associated with the fermion field operator. Note that the phase of the photon field operator is uniquely determined (Eq. (11-267)) by the fact that An is a hermitian field which commutes with the total charge operator Q. The negaton-positon field operator on the other hand does not commute with the total charge operator, in fact... 

Electromagnetic interactions are thought to operate by the same mechanism, but mediated by photons. Because photons are massless they have an infinite range that defines the electromagnetic field. Unlike photons, electrons are massive particles and the covalent interaction is of shorter range, of the order 100 pm. 

Due to the fact that the Lagrangian incorporates the creation and destruction of field quanta, not even the time-development of a single particle is a simple matter. The time development can be expressed in terms of the electron (fermion) and photon propagators, which are defined as the vacuum expectation values of the time-ordered product of field operators. For the fermions one has... 

Since for the photon-number states the expectation values of the field operators vanish, all the information about the state of the system is contained in the intensities of the corresponding fields... 

Employing the preceding field operator expansions enables the radiation Hamiltonian (2) to be recast in a form that more readily identifies its own quantum properties, explicitly featuring the photon creation and annihilation operators ... 

The nature of media effects relates to the fact that, since the microscopic displacement field is the net field to which molecules of the medium are exposed, it corresponds to a fundamental electric field dynamically dressed by interaction with the surroundings. The quantized radiation is in consequence described in terms of dressed photons or polaritons. A full and rigorous theory of dressed optical interactions using noncovariant molecular quantum electrodynamics is now available [25-27], and its application to energy transfer processes has been delineated in detail [10]. In the present context its deployment leads to a modification of the quantum operators for the auxiliary fields d and h, which fully account for the influence of the medium—the fundamental fields of course remain unchanged. Expressions for the local displacement electric and the auxiliary magnetic field operators [27], correct for all microscopic interactions, are then as follows... 

Details of the derivation of general expressions for energy shifts at a given order can be found in Mohr et al. (1998). Contractions between pairs of fermion or boson field operators AM lead to electron and photon propagator functions. The exact electron propagator in a static external field is homogeneous in time and appears as... 

This Green function is analytic in the complex energy plane except for the bound-state poles at En, with branch points at = 1 and cuts along the real axis for E > 1. Bound states occur only at energies E > 0. The firee-photon propagator appears as a time-ordered product of firee-photon field operators (in Feynman gauge)... 

The field operators that do not enter any contraction act on the right and left state vectors in the 5-matrix elements and produce the wave functions for the electrons (positrons) and photons in the initial and final states of the system under consideration. 

The present derivation of the scattering cross-section is based on a non-relativistic quantum electrodynamic approach. In this picture, the modes of the radiation field are quantized and the electric field is treated as a quantum-mechanical operator that annihilates or creates photons populating the various modes. The field operator is given by... 

Multiphoton processes are also undoubtedly involved in the photodegradation of polymers in intense laser fields, eg, using excimer lasers (13). Moreover, multiphoton excitation during pumping can become a significant loss factor in operation of dye lasers (26,27). The photochemically reactive species may or may not be capable of absorption of the individual photons which cooperate to produce multiphoton excitation, but must be capable of utilising a quantum of energy equal to that of the combined photons. Multiphoton excitation thus may be viewed as an exception to the Bunsen-Roscoe law. 

Fig. 4.7. A semiconductor detector operated as a pin diode with a reverse voltage or bias. An incident X-ray photon ultimately produces a series of electron-hole pairs. They are "swept out" by the bias field of-500 V- electrons in the direction ofthe n-layer holes in the direction ofthe p-layer. Thus, a small charge pulse is produced after [4.21],...

The new delightful book by Greenstein and Zajonc(9) contains several examples where the outcome of experiments was not what physicists expected. Careful analysis of the Schrddinger equation revealed what the intuitive argument had overlooked and showed that QM is correct. In Chapter 2, Photons , they tell the story that Einstein got the Nobel Prize in 1922 for the explaining the photoelectric effect with the concept of particle-like photons. In 1969 Crisp and Jaynes(IO) and Lamb and Scullyfl I) showed that the quantum nature of the photoelectric effect can be explained with a classical radiation field and a quantum description for the atom. Photons do exist, but they only show up when the EM field is in a state that is an eigenstate of the number operator, and they do not reveal themselves in the photoelectric effect. 

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