Quantum electrodynamics radiation

Quantum Electrodynamics in the Heisenberg Picture.— With the present section we begin our discussion of the quantum theoretical description of the interaction between the negaton-positon field and the radiation field i.e., of quantum electrodynamics proper. 

Quantization of radiation field in terms of field intensity operators, 562 Quantum electrodynamics, 642 asymptotic condition, 698 gauge invariance in relation to operators inducing inhomogeneous Lorentz transformations, 678 invariance properties, 664 invariance under discrete transformations, 679... 

Craig, D. P. and Thirunamachandran, T. (1984). Molecular Quantum Electrodynamics. An Introduction to Radiation Molecule Interactions. Dover Publications, Inc., Mineola. 

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. 

Abstract. There is presented a consistent energy approach to the quantum electrodynamics (QED) theory of the discharge of a nucleus with emission of a y radiation and further muon conversion, which initiates this discharge. A numer-... 

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. 

There exists another more consistent way of obtaining the electron transition operators. We can start with the quantum-electrodynamical description of the interaction of the electromagnetic field with an atom. In this case we find the relativistic operators of electronic transitions with respect to the relativistic wave functions. After that they may be transformed to the well-known non-relativistic ones, accounting for the relativistic effects, if necessary, as corrections to the usual non-relativistic operators. Here we shall consider the latter in more detail. It gives us a closed system of universal expressions for the operators of electronic transitions, suitable to describe practically the radiation in any atom or ion, including very highly ionized atoms as well as the transitions of any multipolarity and any type of radiation (electric or magnetic). 

This is due to the comparative weakness of the electromagnetic interaction, the theory of which contains a small dimensionless parameter (fine structure constant), by the powers of which the corresponding quantities can be expanded. The electron transition probability of the radiation of one photon, characterized by a definite value of angular momentum, in the first order of quantum-electrodynamical perturbation theory mdy be described as follows [53] (a.u.) ... 

The data of atomic spectroscopy are of extreme importance in revealing the nature of quantum-electrodynamical effects. For the investigation of many-electron atoms and ions, it is of great importance to combine theoretical and experimental methods. Therefore, the methods used must be universal and accurate. A number of physical characteristics of the many-electron atom (e.g., a complete set of quantum numbers) may be found only on the basis of theoretical considerations. In many cases the mathematical modelling of physical objects and processes using modern computers may successfully replace the corresponding experiments. In this book we shall describe the contemporary state of the theory of many-electron atoms and ions, the peculiarities of their structure and spectra as well as the processes of their interaction with radiation, and some applications. 

Now we will introduce quantum electrodynamics. Just as we quantized the atoms and molecules, we must also quantize the electromagnetic radiation field, to deal with field-molecule interactions properly [14,34],... 

The following picture emerges The radiation field, represented classically by a vector potential—that is, by a superposition of plane waves, as before, with transverse electrical and magnetic fields—is now, in quantum electrodynamics, a system with quantized energies. The general eigenfunction is then a product eigenfunction of the type... 

So far as the classification of the type of spectroscopy performed is concerned, the characterisation of the dynamical motions of the nuclei and electrons within a molecule is more important than the region of the electromagnetic spectrum in which the corresponding transitions occur. However, before we come to this in more detail, a brief discussion of the nature of electromagnetic radiation is necessary. This is actually a huge subject which, if tackled properly, takes us deeply into the details of classical and semiclassical electromagnetism, and even further into quantum electrodynamics. The basic foundations of the subject are Maxwell s equations, which we describe in appendix 1.1. We will make use of the results of these equations in the next section, referring the reader to the appendix if more detail is required. 

The problems for quantum chemists in the mid-forties were how to improve the methods of describing the electronic structure of molecules, valence theory, properties of the low excited states of small molecules, particularly aromatic hydrocarbons, and the theory of reactions. It seemed that the physics needed was by then all to hand. Quantum mechanics had been applied by Heitler, London, Slater and Pauling, and by Hund, Mulliken and Hiickei and others to the electronic structure of molecules, and there was a good basis in statistical mechanics. Although quantum electrodynamics had not yet been developed in a form convenient for treating the interaction of radiation with slow moving electrons in molecules, there were semi-classical methods that were adequate in many cases. 

Dirac s 1929 comment [227] The underlying physical laws necessary for the mathematical theory for a large part of physics and the whole of chemistry are thus completely known, and the difficulty is only that the exact application of these laws leads to equations much too difficult to be soluble has become a part of the Delphic wisdom of our subject. To this confident statement Richard Feynman [228] added in 1985 a codicil But there was still the problem of the interaction of light and matter , and . .. the theory behind chemistry is quantum electrodynamics . He goes on to say that he is writing of non-covariant quantum electrodynamics, for the interaction of the radiation field with the slow-moving particles in atoms and molecules. 

Book MOLECULAR QUANTUM ELECTRODYNAMICS. An Introduction to 164a. Radiation-Molecule Interactions. 

Radiation-Molecule and Molecule-Molecule Interactions. A Unified Viewpoint from Quantum Electrodynamics. 

Theoretical studies in photophysics tend to be diverse and no particular themes are evident at the present time. A somewhat refined paper deals with radiation-molecule interactions from the viewpoint of quantum electrodynamics and a more conventional... 

AN OVERVIEW OF QUANTUM ELECTRODYNAMICS AND MATTER-RADIATION FIELD INTERACTION... 

Molecular Quantum Electrodynamics of Radiation-Induced Intermolecular Forces... 

---