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Theoretical and Mathematical Physics

Tensor properties of second-quantization operators and analysis of composite physical systems

V. P. Karasev, P. P. Karasev, Leonid A. Shelepin

Published Feb 1, 1978• 1 citation
Publisher
DOI
10.1007/bf01028029

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A practical method is developed to deal with the second quantization of the many-body system containing the composite particles.In our treatment,the modes associated with composite particles are regarded approximately as independent ones compared with those of unbound particles.The field operators of the composite particles thus arise naturally in the second quantization Hamiltonian.To be emphasized,the second quantization Hamiltonian has the regular structures which correspond clearly to different physical processes.
In previous publications a first-principles method was developed for constructing second-quantization representations for systems of composite bound states and their constituents. It is based on the introduction of redundant modes (’’ideal atom variables’’) which are given physical content by carrying out a suitable unitary transformation. A single transformed Hamiltonian explicitly and simultaneously exhibits all kinematically possible scattering and reaction channels. Most of the previous results were limited to the case of two fermion composites. This restriction is removed herein, in order to allow a first-principles approach to the many-particle quantum dynamics and statistics of chemical and nuclear reactions. The kinematical aspects of the relevant transformation are examined.