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Prog. Theor. Phys. Vol. 26 No. 1 (1961) pp. 99-122

Some Converging Examples of the Perturbation Series in the Quantum Field Theory

Yusuke Kato

Department of Physics, Kobe University, Kobe

(Received March 23, 1961)

Abstract:

Properties of the Hamiltonian operator of the quantized field is studied in the framework of the theory of Hilbert space. The fixed source theory and the boson-fermion interaction are mainly investigated in the cases of both discrete and continuous spectra. The total Hamiltonian operator is defined first in a domain dense in the Hilbert space, under the condition that the interaction form factor in the momentum space is “square integrable”. Then it is shown that the total Hamiltonian as a self-adjoint operator can be determined in terms of the perturbation series for every finite value of the coupling constant if the boson mass is not zero and that it is the unique self-adjoint extension of the symmetric operator defined initially. For the boson-fermion interaction with continuous spectrum, some additional condition on the interaction form factor is needed. Further the perturbation series of the S-matrix element for scattering is discussed in the framework of the wave packet formulation.

URL : http://ptp.ipap.jp/link?PTP/26/99/
DOI : 10.1143/PTP.26.99

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Citing Article(s) :

1. Progress of Theoretical Physics Vol. 30 No. 1 (1963) pp. 103-133 :

   Regular Perturbation and Asymptotic Limits of Operators in Quantum Field Theory

   Yusuke Kato and Nobumichi Mugibayashi

2. Progress of Theoretical Physics Vol. 30 No. 3 (1963) pp. 409-411 :

   On the Definition of the Total Hamiltonian in the Fixed-Source Theory

   Yusuke Kato and Nobumichi Mugibayashi

3. Progress of Theoretical Physics Vol. 30 No. 4 (1963) pp. 545-549 :

   A Note on the Van Hove-Miyatake Catastrophe

   Hiroshi Ezawa

4. Progress of Theoretical Physics Vol. 31 No. 2 (1964) pp. 300-310 :

   Regular Perturbation and Asymptotic Limits of Operators in Fixed-Source Theory

   Nobumichi Mugibayashi and Yusuke Kato

5. Progress of Theoretical Physics Vol. 34 No. 5 (1965) pp. 734-753 :

   Spectrum of the BCS Reduced Hamiltonian in the Theory of Superconductivity

   Yusuke Kato

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