Elementary Particle Theory Volume 3: Relativistic Quantum Dynamics


In the first [241] and second [242] volumes of this book, we presented a fairly traditional view on relativistic quantum mechanics and quantum field theory (QFT, QED). This approach proved itself well and achieved remarkable success in many important areas of high-energy physics, in particular in the description of scattering processes. At the same time, both QFT and QED have a number of serious problems. First of all, there is the problem of ultraviolet divergences. The idea of self-acting bare particles governed by a divergent Hamiltonian seems rather dubious. Such a Hamiltonian is not suitable for describing the time evolution of wave functions and observable of interacting particles. Calling itself a fundamental theory of physics, QFT must describe phenomena in the entire spectrum of energies, distances and time intervals, rather than confine itself to a limited set of questions related to energies of stationary states or to the scattering matrix.

In this third volume, we will offer solutions to these problems. Our research will lead us to a new theory of electromagnetic phenomena, which we call relativistic quantum dynamics or RQD and which differs from traditional approaches in two important aspects: (i) the primary role of particles (rather than fields) and (ii) the dynamical character of boosts.

Modern quantum field theories (such as re-normalized QED) encounter serious difficulties when trying to describe the temporal evolution of even the simplest physical systems, such as the vacuum or free elementary particles. A formal application of the QED time evolution operator to such states leads to the spontaneous production of spurious (virtual) particles, which have not been observed in experiments. The problem lies in the fact that bare particles of QED have no relationship to the physically observed electrons, protons, etc. We will solve this problem by using the “dressing” formalism, which is the cornerstone of our RQD. The “dressed” RQD Hamiltonian is obtained by means of a unitary transformation from the traditional QED Hamiltonian. This transformation does not change the S-operator of QED; therefore, its excellent agreement with the experimental data is preserved in our theory.

The RQD Hamiltonian describes electromagnetic phenomena in terms of physical particles (electrons, photons, etc.) interacting with each other directly, i. e., without the mediation of fictitious virtual particles or fields. In this formulation, quantum fields only play an auxiliary, technical role. Our theory will allow us to move beyond the S-matrix and study the time evolution of systems of interacting particles. In addition, this theory can calculate not just energies, but also wave functions of bound states. All RQD calculations are performed according to the rules of standard quantum mechanics without ultraviolet divergences and without resorting to artificial cutoffs, regularization and re-normalization.
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