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Quantum field theories around a large-Z nucleus

Abstract:

We analyze quantum electrodynamics around a hypothetical highly charged (Z137) nucleus by treating it as an external source. In contrast with the foregoing analyses which rely on the one-particle theory we construct a framework which enables us to create the quantum-field-theoretic treatment of the system. To deal with such a nonperturbative question we develop novel truncation and approximation procedures. Keeping only the lowest partial wave of the electron and the photon fields we transcribe the system into the form of two-dimensional fermion theory. We further convert the theory into a two-dimensional boson theory by using a bosonization technique. We then argue that the semiclassical approximation in the resultant boson theory is reasonably good and in particular does take care of the quantum effects of the original fermion theory. We investigate the asymptotic particle state of the theory and find that electrons appear as topological solitons. By analyzing the boson theory with an external source classically we show that the ground state undergoes the phase transition at a certain value of Z (Zf150 for nucleus size f20 fm) from the normal QED vacuum to an anomalous one which is characterized by the occurrence of real pair creation of electrons and positrons. Our result is confronted with the one obtained by the one-particle-theoretic treatment. Some comments are made on the possibility of understanding the peak structure in positron spectrum observed in heavy-ion collisions. © 1986 The American Physical Society.