Feynman diagrams, 0 electrodynamics

In this section we discuss the nonrelativistic 0(3) b quantum electrodynamics. This discussion covers the basic physics of f/(l) electrodynamics and leads into a discussion of nonrelativistic 0(3)h quantum electrodynamics. This discussion will introduce the quantum picture of the interaction between a fermion and the electromagnetic field with the magnetic field. Here it is demonstrated that the existence of the field implies photon-photon interactions. In nonrelativistic quantum electrodynamics this leads to nonlinear wave equations. Some presentation is given on relativistic quantum electrodynamics and the occurrence of Feynman diagrams that emerge from the B are demonstrated to lead to new subtle corrections. Numerical results with the interaction of a fermion, identical in form to a 2-state atom, with photons in a cavity are discussed. This concludes with a demonstration of the Lamb shift and renormalizability. 

Investigation of the connection between the Many-Body Perturbation Theory (MBPT) approach and the Furry representation of Quantum Electrodynamics (QED) has been shown to allow a precise definition of QED effects.82 Every MBPT diagram has a corresponding Feynman diagram, but there are Feynman diagrams that have no MBPT counterpart. 

Quantum electrodynamics. An example of a Feynman diagram for electron-electron scattering. 

Our principal aim in this chapter is to review briefly the basic ideas of field theory, which we shall illustrate with examples from quantum electrodynamics (QED) and the theory of strong interactions, quantum chromodynamics (QCD). Of necessity, we must assume that the reader has some knowledge of field theory and is conversant with the idea of Feynman diagrams and with the Dirac equation. We shall then give a resume of the theory and phenomenology of the weak interactions as they stood at the time of the inception of the new ideas about quarks and gluons in the early 1970s. The chapter ends with some technical results which will be very useful in later chapters. 

Fermat De Pierre (1601—1665) Fr. math., devised principle of least time (action) and Fermat s small and big (last) theorems, gravity reciprocal attraction, father of modem theory of numbers, probabilities Feynman Richard Phillips (1918-1988) US. phys., quantum electrodynamics, devised Feynman diagrams as means for accounting possible particle transformations ( Theory of Fundamental Processes 1961)... 

In his work, Goldstone70 introduced the graphical techniques into many-body physics making use of Feynman-like diagrams. However, interactions were taken to be instantaneous and the effects of relativity were ignored. In recent years, the growing interest in the treatment of relativistic and quantum electrodynamic effects in atoms and molecules is necessitating the reintroduc-... 

The development of quantum electrodynamics saw the introduction of diagrammatic techniques. In particular, Feynman [28], in a paper entitled Space-Time Approach to Quantum Electrodynamics, introduced diagrams which provide not only a pictorial representation of microscopic processes, but also a precise graphical algebra which is entirely equivalent to other formulations. They have a simplicity and elegance which is not shared by, for example, purely algebraic methods. 

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