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Matter-enhanced transition probabilities in quantum field theory. (English) Zbl 1343.81203

Summary: The relativistic quantum field theory is the unique theory that combines the relativity and quantum theory and is invariant under the Poincaré transformation. The ground state, vacuum, is singlet and one particle states are transformed as elements of irreducible representation of the group. The covariant one particles are momentum eigenstates expressed by plane waves and extended in space. Although the \(S\)-matrix defined with initial and final states of these states hold the symmetries and are applied to isolated states, out-going states for the amplitude of the event that they are detected at a finite-time interval T in experiments are expressed by microscopic states that they interact with, and are surrounded by matters in detectors and are not plane waves. These matter-induced effects modify the probabilities observed in realistic situations. The transition amplitudes and probabilities of the events are studied with the \(S\)-matrix, \(S[\mathrm T]\), that satisfies the boundary condition at T. Using \(S[\mathrm T]\), the finite-size corrections of the form of \(1/\mathrm T\) are found. The corrections to Fermi’s golden rule become larger than the original values in some situations for light particles. They break Lorentz invariance even in high energy region of short de Broglie wave lengths.

MSC:

81U20 \(S\)-matrix theory, etc. in quantum theory
81Q05 Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics
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References:

[2] Low, F., Phys. Rev., 97, 1392 (1955)
[3] Ishikawa, K.; Tobita, Y., Prog. Theor. Exp. Phys., 2013, 073B02 (2013)
[4] Goldberger, M. L.; Watson, K. M., Phys. Rev., 136, 1472 (1964)
[5] Ishikawa, K.; Shimomura, T., Progr. Theoret. Phys., 114, 1201 (2005)
[6] Goldberger, M. L.; Watson, K. M., Collision Theory (1965), John Wiley & Sons, Inc.: John Wiley & Sons, Inc. New York · Zbl 1234.81004
[7] Newton, R. G., Scattering Theory of Waves and Particles (1982), Springer-Verlag: Springer-Verlag New York · Zbl 0496.47011
[8] Taylor, J. R., Scattering Theory: The Quantum Theory of non-relativistic Collisions (2006), Dover Publications: Dover Publications New York
[9] Sasakawa, T., Progr. Theoret. Phys. Suppl., 11, 69 (1959)
[10] Srednicki, M., Quantum Field Theory (2007), Cambridge University Press: Cambridge University Press Cambridge, p. 37 · Zbl 1113.81002
[11] Araki, H., Mathematical Theory of Quantum Field (2002), Iwanami: Iwanami Tokyo
[12] Sasaki, S.; Oneda, S.; Ozaki, S., The Science Reports of the Tohoku University First Series (Math., Phys., Chem., Astronomy) XXXIII, 77 (1949)
[13] Steinberger, J., Phys. Rev., 76, 1180 (1949)
[14] Ruderman, M.; Finkelstein, R., Phys. Rev., 76, 1458 (1949)
[15] Anderson, H. L., Phys. Rev., 119, 2050 (1960)
[16] Hosaka, J., Phys. Rev., D74, 032002 (2006)
[17] Fukuda, S., Phys. Lett., B539, 179 (2002)
[18] Ahmed, S. N., Phys. Rev. Lett., 92, 181301 (2004)
[19] Araki, T., Phys. Rev. Lett., 94, 081801 (2005)
[20] Arpesella, C., Phys. Rev. Lett., 101, 091302 (2008)
[21] Aliu, E., Phys. Rev. Lett., 94, 081802 (2005)
[22] Beringer, J., Phys. Rev., D86, 010001 (2012)
[23] Aseev, V. N., Phys. Rev., D84, 112003 (2011), arXiv:1108.5034 [hep-ex]
[24] Komatsu, E., Astrophys. J. Suppl., 192, 18 (2011), arXiv:1001.4538 [astro-ph.CO]
[25] Dollard, J. D., Comm. Math. Phys., 12, 193 (1969)
[26] Gell-Mann, M., The Quark and the Jaguar: Adventures in the Simple and the Complex (1995), St. Martin’s Griffin: St. Martin’s Griffin London · Zbl 0833.00010
[27] Tonomura, A., Amer. J. Phys., 57, 2, 117 (1989)
[28] Tomonaga, S., Progr. Theoret. Phys., 1, 27 (1946)
[29] Schwinger, J., Phys. Rev., 74, 1439 (1948)
[30] Landau, L. D.; Lifshitz, E. M., Quantum Mechanics (2003), Butterworth Heine Mann: Butterworth Heine Mann New York, p. 157 · Zbl 0081.22207
[31] Dirac, P. A.M., The Quantum Theory of the Emission and Absorption of Radiation. Pro. R. Soc. Lond. A, 114, 243 (1927) · JFM 53.0847.01
[32] Schiff, L. I., Quantum Mechanics (1955), McGRAW-Hill Book COMPANY, Inc.: McGRAW-Hill Book COMPANY, Inc. New York, p. 199 · Zbl 0068.40202
[33] Peierls, R., Surprises in Theoretical Physics (1979), Princeton University Press: Princeton University Press New Jersey, p. 121
[36] Ishikawa, K.; Tobita, Y., Progr. Theoret. Phys., 122, 1111 (2009), arXiv:0906.3938 [quant-ph]
[37] Ishikawa, K.; Tobita, Y., AIP Conf. Proc., 1016, 329 (2008)
[38] Kayser, B., Phys. Rev.. Phys. Rev., Nuclear Phys., B19, Proc. Suppl, 177 (1991)
[39] Giunti, C.; Kim, C. W.; Lee, U. W., Phys. Rev., D44, 3635 (1991)
[40] Nussinov, S., Phys. Lett., B63, 201 (1976)
[41] Kiers, K.; Nussinov, S.; Weiss, N., Phys. Rev., D53, 537 (1996)
[42] Stodolsky, L., Phys. Rev., D58, 036006 (1998)
[43] Lipkin, H. J., Phys. Lett., B642, 366 (2006)
[44] Akhmedov, E. K., JHEP, 0709, 116 (2007), arXiv:0706.1216 [hep-ph]
[45] Yabuki, T.; Ishikawa, K., Progr. Theoret. Phys., 108, 347 (2002)
[46] Adamson, P., Phys. Rev., D81, 072002 (2010), arXiv:0910.2201 [hep-ex]
[47] Wu, Q., Phys. Lett., B660, 19 (2008), arXiv:0711.1183 [hep-ex]
[48] Aguilar-Arevalo, A. A., Phys. Rev., D81, 092005 (2010), arXiv:1002.2680 [hep-ex]
[49] Abe, K., Phys. Rev. Lett., 107, 041801 (2001), arXiv:1106:2822 [hep-ex]
[51] Athanassopoulos, C., Phys. Rev. Lett., 75, 2650 (1995), nucl-ex/9504002; 77 (1996) 3082. nucl-ex/9605003; 81, (1998) 1774. nucl-ex/9709006
[52] Danby, G., Phys. Rev. Lett., 9, 36 (1962)
[53] Ahn, M. H., Phys. Rev., D74, 072003 (2006)
[54] Aguilar-Arevalo, A. A., Phys. Rev., D79, 072002 (2009), arXiv:0806.1449 [hep-ex]
[55] Adamson, P., Phys. Rev., D77, 072002 (2008), arXiv:0711.0769 [hep-ex]
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