Radiation field theory

In order to understand the concept of Molecular Photonics, it is crucial for the reader to undertake a study of fundamental principles. Chapter 1 Fundamentals of Molecular Photonics includes four sections dedicated to optics, the molecular field theory, the radiation field theory, and the interactions between the molecular field and the radiation field. Fundamental principles are often treated in an introductory chapter, leading the reader to think that they are of little importance and that they can be understood with ease. This trend of relegating the fundamentals to a brief introduction is getting increasingly common in natural... 

The theories of photo- and opto-related areas can be classified into three categories the fundamentals of optics, the molecular field theory, and the radiation field theory. As we defined molecular photonics by Equation (0.1) which relates the interaction of the radiation field with the molecular field, it may seem sufficient to restrict our discussion to the molecular field theory and the radiation field theory. However we believe that the fundamentals of optics are also very important to understand and appreciate all the photo and opto concepts described in this book. To support this view, consider the following. 

To this point, we have considered only the radiation field. We now turn to the interaction between the matter and the field. According to classical electromagnetic theory, the force on a particle with charge e due to the electric and magnetic fields is... 

In Science, every concept, question, conclusion, experimental result, method, theory or relationship is always open to reexamination. Molecules do exist Nevertheless, there are serious questions about precise definition. Some of these questions lie at the foundations of modem physics, and some involve states of aggregation or extreme conditions such as intense radiation fields or the region of the continuum. There are some molecular properties that are definable only within limits, for example, the geometrical stmcture of non-rigid molecules, properties consistent with the uncertainty principle, or those limited by the negleet of quantum-field, relativistic or other effects. And there are properties which depend specifically on a state of aggregation, such as superconductivity, ferroelectric (and anti), ferromagnetic (and anti), superfluidity, excitons. polarons, etc. Thus, any molecular definition may need to be extended in a more complex situation. 

An extremely interesting question in the photochemistry of interstellar molecules concerns the size at which classes of molecules become resistant to the interstellar radiation field. Up to now, only statistical theories have been brought to bear on the question (see below).83 115... 

A consequent 5-dimensional treatment would require Unified Theory of Quantum Mechanics and General Relativity. This unified theory is not available now, and we know evidences that present QM is incompatible with present GR. The well-known demonstrative examples are generally between QFT and GR (e.g. the notion of Quantum Field Theory vacua is only Lorentz-invariant and hence come ambiguities about the existence of cosmological Hawking radiations [19]). But also, it is a fundamental problem that the lhs of Einstein equation is c-number, while the rhs should be a quantum object. 

Lewis s "decision" between rival theories was published in the paper written with Joseph E. Mayer, "A Disproof of the Radiation Theory of Chemical Activation," Proc.NAS 13 (1927) 623625. A copy of the news release is in the College of Chemistry Papers, 19231936, BL.UCB. Lewis wrote A. F. Joffe in fall 1927 of Mayer s failure to find a chemical reaction when a molecular stream is passed through a radiation field. Letter from G. N. Lewis to A. F. Joffe, 27 October 1927, Lewis Papers, BL.UCL. 

A systematic development of relativistic molecular Hamiltonians and various non-relativistic approximations are presented. Our starting point is the Dirac one-fermion Hamiltonian in the presence of an external electromagnetic field. The problems associated with generalizing Dirac s one-fermion theory smoothly to more than one fermion are discussed. The description of many-fermion systems within the framework of quantum electrodynamics (QED) will lead to Hamiltonians which do not suffer from the problems associated with the direct extension of Dirac s one-fermion theory to many-fermion system. An exhaustive discussion of the recent QED developments in the relevant area is not presented, except for cursory remarks for completeness. The non-relativistic form (NRF) of the many-electron relativistic Hamiltonian is developed as the working Hamiltonian. It is used to extract operators for the observables, which represent the response of a molecule to an external electromagnetic radiation field. In this study, our focus is mainly on the operators which eventually were used to calculate the nuclear magnetic resonance (NMR) chemical shifts and indirect nuclear spin-spin coupling constants. 

Earlier we mentioned briefly that the electron spin is perfectly consistent with the non-relativistic four-component Levy-Leblond theory [44,45]. The EC type interaction does not manifest in Dirac or Levy-Leblond theory. We shall show that on reducing the four-component Levy-Leblond equation into a two-component form the EC contribution arises naturally. A non-relativistic electron in an electromagnetic radiation field is described by the Levy-Leblond equation given by... 

The application of microdosimetry to medical physics derives from biological models of radiation action (primarily, the Theory of Dual Radiation Action [14]) that explicitly utilize for their predictions a microdosimetric description of the radiation field. Specifically, they concern the following two problems ... 

The Maxwell-Heaviside theory seen as a U(l) symmetry gauge field theory has no explanation for the photoelectric effect, which is the emission of electrons from metals on ultraviolet irradiation [39]. Above a threshold frequency, the emission is instantaneous and independent of radiation intensity. Below the threshold, there is no emission, however intense the radiation. In U(l), electrodynamics energy is proportional to intensity and there is, consequently, no possible explanation for the photoelectric effect, which is conventionally regarded as an archetypical quantum effect. In classical 0(3) electrodynamics, the effect is simply... 

Various theories have been proposed for horizontal transfer at the isoenergetic point. Gouterman considered a condensed system and tried to explain it in the same way as the radiative mechanism. In the radiative transfer, the two energy states are coupled by the photon or the radiation field. In the nonradiative transfer, the coupling is brought about by the phonon field of the crystalline matrix. But this theory is inconsistent with the observation that internal conversion occurs also in individual polyatomic molecules such as benzene. In such cases the medium does not actively participate except as a heat sink. This was taken into consideration in theories proposed by Robinson and Frosch, and Siebrand and has been further improved by Bixon and Jortner for isolated molecules, but the subject is still imperfectly understood. 

The first attempt to formulate a theory of optical rotation in terms of the general equations of wave motion was made by MacCullagh17). His theory was extensively developed on the basis of Maxwell s electromagnetic theory. Kuhn 18) showed that the molecular parameters of optical rotation were elucidated in terms of molecular polarizability (J connecting the electric moment p of the molecule, the time-derivative of the magnetic radiation field //, and the magnetic moment m with the time-derivative of the electric radiation field E as follows ... 

In a model in which a random phase approximation would be valid, all pv would vanish. It is therefore appropriate to consider pv as expressing the correlations in the system while p0 refers to the vacuum of correlations, We shall illustrate the theory with the example of an atom in interaction with a radiation field. (For more details, see Henin.12) Then the quantum-mechanical version of Eq. (7) is ... 

The dipole moment is the total dipole of the sample, p = Y.i Pi The correlation function describes the response of the system to the weakly coupled radiation field. The effects of the field are modeled by the response of the individual atoms or molecules unaffected by the weak coupling. The Hamiltonian describes the interaction of the field and matter (first-order perturbatiuon theory). The correlation function describes how the perturbed system approaches equilibrium. 

Specifically, the collision-induced absorption and emission coefficients for electric-dipole forbidden atomic transitions were calculated for weak radiation fields and photon energies Ha> near the atomic transition frequencies, utilizing the concepts and methods of the traditional theory of line shapes for dipole-allowed transitions. The example of the S-D transition induced by a spherically symmetric perturber (e.g., a rare gas atom) is treated in detail and compared with measurements. The case of the radiative collision, i.e., a collision in which both colliding atoms change their state, was also considered. 

We now consider the effect of exposing a system to electromagnetic radiation. Our treatment will involve approximations beyond that of replacing (3.13) with (3.16). A proper treatment of the interaction of radiation with matter must treat both the atom and the radiation field quantum-mechanically this gives what is called quantum field theory (or quantum electrodynamics). However, the quantum theory of radiation is beyond the scope of this book. We will treat the atom quantum-mechanically, but will treat the radiation field as a classical wave, ignoring its photon aspect. Thus our treatment is semiclassical. 

The semiclassical treatment just given has the defect of not predicting spontaneous emission. According to (3.13), if there is no outside perturbation, that is, if // (0 = 0, then dcm/dt = 0 for all m if the atom is in the nth stationary state at / = 0, it will persist in that state forever. However, experimentally we find that unperturbed atoms in excited states spontaneously radiate energy and drop to lower states. Quantum field theory does predict spontaneous emission. Since quantum field theory is beyond us, we shall use an argument given by Einstein in 1917 to find the spontaneous-emission probability. 

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