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The Hamiltonian \((p^ 2+m^ 2)^{1/2}-\alpha/r\) near the critical value \(\alpha_ c=2/\pi\). (English) Zbl 0883.47084

Spectral properties of the relativistic Hamiltonian \((p^2+m^2)^{1/2}-{\alpha \over r}\) near the critical value of the coupling constant \(\alpha_c={2 \over \pi}\) are investigated. The methods are based on the introducing of special holomorphic family of operators and usage of the Mellin transformation.

MSC:

47N50 Applications of operator theory in the physical sciences
81Q10 Selfadjoint operator theory in quantum theory, including spectral analysis
47A56 Functions whose values are linear operators (operator- and matrix-valued functions, etc., including analytic and meromorphic ones)
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[1] DOI: 10.1103/PhysRevD.50.5443
[2] DOI: 10.1103/PhysRevD.50.5443
[3] DOI: 10.1103/PhysRevD.50.5443
[4] DOI: 10.1007/BF01609852 · Zbl 0375.35047
[5] DOI: 10.1016/0370-2693(94)90831-1
[6] DOI: 10.1103/PhysRevA.31.2020
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