Vol. 2 - The World of Mathematical Equations

April, 2008 PROGRESS IN PHYSICS Volume 2SPECIAL REPORTNew Approach to Quantum ElectrodynamicsSze Kui NgDepartment of Mathematics, Hong Kong Baptist University, Hong Kongand School of Engineering and Information Technology, Deakin University, AustraliaE-mail: szekuing@yahoo.com.hkIt is shown that a photon with a specific frequency can be identified with the Dirac magneticmonopole. When a Dirac-Wilson line forms a Dirac-Wilson loop, it is a photon.This loop model of photon is exactly solvable. From the winding numbers of this loopformof photon, we derive the quantization properties of energy and electric charge. Anew QED theory is presented that is free of ultraviolet divergences. The Dirac-Wilsonline is as the quantum photon propagator of the new QED theory from which we canderive known QED effects such as the anomalous magnetic moment and the Lamb shift.The one-loop computation of these effects is simpler and is more accurate than that inthe conventional QED theory. Furthermore, from the new QED theory, we have deriveda new QED effect. A new formulation of the Bethe-Salpeter (BS) equation solves thedifficulties of the BS equation and gives a modified ground state of the positronium. Bythe mentioned new QED effect and by the new formulation of the BS equation, a termin the orthopositronium decay rate that is missing in the conventional QED is found,resolving the orthopositronium lifetime puzzle completely. It is also shown that thegraviton can be constructed from the photon, yielding a theory of quantum gravity thatunifies gravitation and electromagnetism.1 IntroductionIt is well known that the quantum era of physics began withthe quantization of energy of electromagnetic field, fromwhich Planck derived the radiation formula. Einstein thenintroduced the light-quantum to explain the photoelectric effects.This light-quantum was regarded as a particle calledphoton [1–3]. Quantum mechanics was then developed, usheringin the modern quantum physics era. Subsequently, thequantization of the electromagnetic field and the theory ofQuantum Electrodynamics (QED) were established.In this development of quantum theory of physics, thephoton plays a special role. While it is the beginning of quantumphysics, it is not easy to understand as is the quantummechanics of other particles described by the Schrödingerequation. In fact, Einstein was careful in regarding thelight-quantum as a particle, and the acceptance of the lightquantumas a particle called photon did not come about untilmuch later [1]. The quantum field theory of electromagneticfield was developed for the photon. However, such difficultiesof the quantum field theory as the ultraviolet divergencesare well known. Because of the difficulty of understandingthe photon, Einstein once asked: “What is the photon?” [1].On the other hand, based on the symmetry of the electricand magnetic field described by the Maxwell equation andon the complex wave function of quantum mechanics, Diracderived the concept of the magnetic monopole, which is hypotheticallyconsidered as a particle with magnetic charge, inanalogy to the electron with electric charge. An importantfeature of this magnetic monopole is that it gives the quantizationof electric charge. Thus it is interesting and importantto find such particles. However, in spite of much effort, nosuch particles have been found [4, 5].In this paper we shall establish a mathematical model ofphoton to show that the magnetic monopole can be identifiedas a photon. Before giving the detailed model, let us discusssome thoughts for this identification in the following.First, if the photon and the magnetic monopole are differenttypes of elementary quantum particles in the electromagneticfield, it is odd that one type can be derived from theother. A natural resolution of this oddity is the identificationof the magnetic monopole as a photon.The quantum field theory of the free Maxwell equationis the basic quantum theory of photon [6]. This free fieldtheory is a linear theory and the models of the quantum particlesobtained from this theory are linear. However, a stableparticle should be a soliton, which is of the nonlinear nature.Secondly, the quantum particles of the quantum theoryof Maxwell equation are collective quantum effects in thesame way the phonons which are elementary excitations ina statistical model. These phonons are usually considered asquasi-particles and are not regarded as real particles. Regardingthe Maxwell equation as a statistical wave equation ofelectromagnetic field, we have that the quantum particles inthe quantum theory of Maxwell equation are analogous to thephonons. Thus they should be regarded as quasi-photons andhave properties of photons but not a complete description ofphotons.In this paper, a nonlinear model of photon is established.In the model, we show that the Dirac magnetic monopoleSze Kui Ng. New Approach to Quantum Electrodynamics 15