Relativistic Quantum Dynamics

by E.V. Stefanovich

Unification of quantum mechanics and the principle of relativity was one of the most desired goals in theoretical physics of the 20th century. This goal is not yet achieved until this day. On this web-site you will find some materials related to a new relativistic quantum theory of charged particles and their interactions. This approach is called "Relativistic quantum dynamics" (or RQD). It is equivalent to renormalized Quantum Electrodynamics in calculations of the S-matrix, i.e., in description of experiments measuring scattering cross-sections and bound states energies. The advantage of RQD is that it allows to perform all calculations (including the time evolution of interacting states) by standard formulas of quantum mechanics without regularization (cutoffs) and renormalization. The relativistic invariance (the Poincare commutation relations) and the cluster separability of RQD are rigorously proven. This theory offers a new perspective on several fundamental physical concepts. In particular, it is established that in interacting systems the transformations of observables to the moving frame of reference cannot be given by universal linear Lorentz transformations. There should be small but important corrections depending on the interaction. So, the 4D Minkowski space-time picture is approximate, and is not used in RQD. RQD is formulated in terms of particles and their direct interactions (action-at-a-distance). The fields play an auxiliary role to facilitate the construction of the interaction terms in the Hamiltonian and the boost operator, The details of this theory are given in six papers and one book listed below.

E.V. Stefanovich, Quantum Effects in Relativistic Decays Int. J. Theor. Phys. 35, 2539-2554 (1996).

E.V. Stefanovich, Quantum Field Theory without Infinities Ann. Phys. 292, 139-156 (2001).

E.V. Stefanovich, Quantum Field Theory without Infinities II. A Simple Model. unpublished (2001)

E.V. Stefanovich, Is Minkowski Space-Time Compatible with Quantum Mechanics? Found. Phys. 32, 673-703 (2002).

E.V. Stefanovich, Renormalization and dressing in quantum field theory hep-th/0503076 (2005)

E.V. Stefanovich, Violations of Einstein's time dilation formula in particle decays physics/0603043 (2006)

E.V. Stefanovich, A Hamiltonian approach to quantum gravity physics/0612019 (2006)

E.V. Stefanovich, Classical electrodynamics without fields and the Aharonov-Bohm effect arXiv:0803.1326 (2008)

Book

E.V. Stefanovich, Relativistic Quantum Dynamics (Mountain View, 2004 - 2006)

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