The deviation factor and divergences in quantum electrodynamics, concrete examples. (English) Zbl 1476.81147
Summary: We consider the divergences in quantum electrodynamics. Our approach is based on ideas from the theory of generalized wave operators. In particular, we use the concept of the deviation factor. The deviation factor characterizes the deviations of the initial and final waves from the free waves. The approach is demonstrated on important examples.
MSC:
81V10 | Electromagnetic interaction; quantum electrodynamics |
81T13 | Yang-Mills and other gauge theories in quantum field theory |
81U20 | \(S\)-matrix theory, etc. in quantum theory |
40A05 | Convergence and divergence of series and sequences |
60F05 | Central limit and other weak theorems |
Keywords:
generalized wave operator; generalized scattering operator; deviation factor; divergence problem; power seriesReferences:
[1] | Akhiezer, A. I.; Berestetskii, V. B., Quantum Electrodynamics (1965), Interscience Publishers: Interscience Publishers New York · Zbl 0084.45004 |
[2] | Buslaev, V. S.; Matveev, V. B., Wave operators for the Schrödinger equation with a slowly decreasing potential, Teor. Mat. Fiz., 2, 3, 367-376 (1970) |
[3] | Collins, J. C., Renormalization (1984), Cambridge University Press · Zbl 1094.53505 |
[4] | Dollard, J. D., Asymptotic convergence and the Coulomb interaction, J. Math. Phys., 5, 6, 729-738 (1964) |
[5] | Duhr, C., Scattering amplitudes, Feynman integrals and multiple polylogarithms, Contemp. Math., 648, 109-133 (2015) · Zbl 1346.81046 |
[6] | Dyson, F. J., The S matrix in quantum electrodynamics, Phys. Rev., 75, 11, 1736-1755 (1949) · Zbl 0033.14201 |
[7] | Kubo, R., Relation between the Kulish-Faddeev model and Grammer-Yennie perturbation theory in the infrared problem in quantum electrodynamics, Prog. Theor. Phys., 73, 5, 1235-1244 (1985) |
[8] | Kulish, P. P.; Faddeev, L. D., Asymptotic conditions and infrared divergences in quantum electrodynamics, (Fifty Years of Mathematical Physics. Fifty Years of Mathematical Physics, World Sci. Ser. 21st Century Math., vol. 2 (2016), World Sci. Publ.: World Sci. Publ. Hackensack, NJ). (Fifty Years of Mathematical Physics. Fifty Years of Mathematical Physics, World Sci. Ser. 21st Century Math., vol. 2 (2016), World Sci. Publ.: World Sci. Publ. Hackensack, NJ), Teor. Mat. Fiz., 4, 2, 153-170 (1970), Translation of · Zbl 0197.26201 |
[9] | Levy, M., Wave equations in momentum space, Proc. R. Soc. Lond. Ser. A, 204, 145-169 (1950) · Zbl 0041.12702 |
[10] | Oppenheimer, J. R., (Report for the Solvay Conference on Physics at Brussels, Belgium (1948)), 145-153 |
[11] | Pearson, D. B., Quantum Scattering and Spectral Theory (1988), Academic Press: Academic Press New York · Zbl 0673.47011 |
[12] | Pokorski, S., Gauge Field Theories (1987), Cambridge University Press · Zbl 0637.53103 |
[13] | Reed, M.; Simon, B., Methods of Modern Mathematical Physics, III: Scattering Theory (1979), Academic Press: Academic Press New York · Zbl 0405.47007 |
[14] | Sakhnovich, L. A., Dissipative operators with absolutely continuous spectrum, Tr. Mosk. Mat. O.-va. Tr. Mosk. Mat. O.-va, Trans. Mosc. Math. Soc., 19, 223-297 (1968), Translated in · Zbl 0193.43403 |
[15] | Sakhnovich, L. A., Generalized wave operators, Mat. Sb. (N.S.). Mat. Sb. (N.S.), Math. USSR Sb., 10, 2, 197-216 (1970), Translated in · Zbl 0215.21001 |
[16] | Sakhnovich, L. A., Generalized wave operators and regularization of perturbation series, Teor. Mat. Fiz.. Teor. Mat. Fiz., Theor. Math. Phys., 2, 1, 60-65 (1970), Translated in |
[17] | Sakhnovich, L. A., The invariance principle for generalized wave operators, Funkc. Anal. Prilozh.. Funkc. Anal. Prilozh., Funct. Anal. Appl., 5, 1, 49-55 (1971), Translated in · Zbl 0234.47003 |
[18] | Sakhnovich, L. A., Generalized wave operators, dynamical and stationary cases and divergence problem (2016) |
[19] | Sakhnovich, L. A., Stationary and dynamical scattering problems and ergodic-type theorems, Phys. Lett. A, 381, 36, 3021-3027 (2017) · Zbl 1375.81235 |
[20] | Sakhnovich, L. A., The generalized scattering problems: ergodic type theorems, Complex Anal. Oper. Theory, 12, 3, 767-776 (2018) · Zbl 1390.34238 |
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