Boost modes for a massive fermion field and the Unruh problem. (English. Russian original) Zbl 1321.83026
Theor. Math. Phys. 182, No. 3, 356-380 (2015); translation from Teor. Mat. Fiz. 182, No. 3, 405-434 (2015).
Summary: We show that the Wightman function of a free quantum field generates any complete set of solutions of the relativistic wave equations. Using this approach, we construct the complete set of solutions of the two-dimensional Dirac equation consisting of eigenfunctions of the generator of Lorentz rotations (boost operator). We show that at the surface of the light cone, the boost modes for a fermion field contain the Gelfand delta function of a complex argument. Because of the presence of such a singularity, excluding even a single mode with an arbitrary value of the boost quantum number makes the set of boost modes incomplete. This results in the nonapplicability of the Unruh quantization scheme to a massive fermion field in the two-dimensional Minkowski space-time. Hence, in full accordance with the boson case, the Unruh procedure for a fermion field cannot be used to prove the existence of the Unruh effect.
MSC:
| 83C47 | Methods of quantum field theory in general relativity and gravitational theory |
| 81T20 | Quantum field theory on curved space or space-time backgrounds |
| 35L05 | Wave equation |
| 83C40 | Gravitational energy and conservation laws; groups of motions |
| 83C60 | Spinor and twistor methods in general relativity and gravitational theory; Newman-Penrose formalism |
| 83C80 | Analogues of general relativity in lower dimensions |
Keywords:
boost symmetry; fermion field; Wightman function; zero mode; Unruh problem; relativistic wave equationReferences:
| [1] | Unruh, W. G., No article title, Phys. Rev. D, 14, 870-892 (1976) · doi:10.1103/PhysRevD.14.870 |
| [2] | Davies, P. C W., No article title, J. Phys. A, 8, 609-616 (1975) · doi:10.1088/0305-4470/8/4/022 |
| [3] | Belinskii, V. A.; Karnakov, B. M.; Mur, V. D.; Narozhnyi, N. B., No article title, JETP Lett., 65, 902-908 (1997) · doi:10.1134/1.567447 |
| [4] | Fedotov, A. M.; Mur, V. D.; Narozhny, N. B.; Belinskii, V. A.; Karnakov, B. M., No article title, Phys. Lett. A, 254, 126-132 (1999) · doi:10.1016/S0375-9601(99)00092-4 |
| [5] | Narozhny, N.; Fedotov, A.; Karnakov, B.; Mur, V.; Belinskii, V., No article title, Ann. Phys. (8), 9, 199-206 (2000) · Zbl 0979.83024 · doi:10.1002/(SICI)1521-3889(200005)9:3/5<199::AID-ANDP199>3.0.CO;2-I |
| [6] | Narozhny, N. B.; Fedotov, A. M.; Karnakov, B. M.; Mur, V. D.; Belinskii, V. A., No article title, Phys. Rev. D, 65, 025004 (2001) · doi:10.1103/PhysRevD.65.025004 |
| [7] | Silaev, P. K.; Khrustalev, O. A., No article title, Theor. Math. Phys., 91, 481-489 (1992) · doi:10.1007/BF01018847 |
| [8] | Arageorgis, A.; Earman, J.; Ruetsche, L., No article title, Philos. Sci., 70, 164-202 (2003) · doi:10.1086/367875 |
| [9] | Nicolini, P.; Rinaldi, M., No article title, Phys. Lett. B, 695, 303 (2011) · doi:10.1016/j.physletb.2010.10.051 |
| [10] | Colosi, D.; Rätzel, D., No article title, SIGMA, 9, 019 (2013) |
| [11] | Chen, P.; Tajima, T., No article title, Phys. Rev. Lett., 83, 256-259 (1999) · doi:10.1103/PhysRevLett.83.256 |
| [12] | Schützhold, R.; Schaller, G.; Habs, D., No article title, Phys. Rev. Lett., 97, 121302 (2006) · doi:10.1103/PhysRevLett.97.121302 |
| [13] | Obadia, N., No article title, Phys. Rev. D, 76, 045013 (2007) · doi:10.1103/PhysRevD.76.045013 |
| [14] | Fuentes-Schuller, I.; Mann, R. B., No article title, Phys. Rev. Lett., 95, 120404 (2005) · doi:10.1103/PhysRevLett.95.120404 |
| [15] | Alsing, P. M.; Fuentes-Schuller, I.; Mann, R. B.; Tessier, T. E., No article title, Phys. Rev. A, 74, 032326 (2006) · doi:10.1103/PhysRevA.74.032326 |
| [16] | Adesso, G.; Fuentes-Schuller, I.; Ericsson, M., No article title, Phys. Rev. A, 76, 062112 (2007) · doi:10.1103/PhysRevA.76.062112 |
| [17] | Brádler, K., No article title, Phys. Rev. A, 75, 022311 (2007) · doi:10.1103/PhysRevA.75.022311 |
| [18] | Han, M.; Olson, S. J.; Dowling, J. P., No article title, Phys. Rev. A, 78, 022302 (2008) · doi:10.1103/PhysRevA.78.022302 |
| [19] | Peña, I.; Sudarsky, D., No article title, Found. Phys., 44, 689-708 (2014) · Zbl 1303.83015 · doi:10.1007/s10701-014-9806-0 |
| [20] | Bièvre, S.; Merkli, M., No article title, Class. Q. Grav., 23, 6525-6541 (2006) · Zbl 1123.83012 · doi:10.1088/0264-9381/23/22/026 |
| [21] | Takagi, S., No article title, Prog. Theoret. Phys., 88, 1-142 (1986) · doi:10.1143/PTPS.88.1 |
| [22] | Rosu, H. C., No article title, Internat. J. Mod. Phys. D, 3, 545-548 (1994) · doi:10.1142/S0218271894000691 |
| [23] | Nikishov, A. I.; Ritus, V. I., No article title, JETP, 67, 1313-1321 (1988) |
| [24] | Mur, V. D.; Karnakov, B. M.; Popov, V. S., No article title, JETP, 87, 433-444 (1998) · doi:10.1134/1.558679 |
| [25] | Marzlin, K-P; Audretsch, J., No article title, Phys. Rev. D, 57, 1045-1051 (1998) · doi:10.1103/PhysRevD.57.1045 |
| [26] | Fedotov, AM; Narozhny, N. B.; Mur, V. D.; Belinskii, V. A., No article title, Phys. Lett. A, 305, 211-217 (2002) · doi:10.1016/S0375-9601(02)01442-1 |
| [27] | N. N. Bogolyubov and D. V. Shirkov, Introduction to the Theory of Quantized Fields [in Russian], Nauka, Moscow (1976); English transl., Wiley, New York (1980). · Zbl 0088.21701 |
| [28] | Hill, E. L., No article title, Rev. Modern Phys., 23, 253-260 (1951) · Zbl 0044.38509 · doi:10.1103/RevModPhys.23.253 |
| [29] | A. I. Akhiezer and V. B. Berestetskii, Quantum Electrodynamics [in Russian], Nauka, Moscow (1981); English transl. prev. ed. (Interscience Monogr. Texts Phys. Astro., Vol. 11), Wiley, New York (1965). · Zbl 0084.45004 |
| [30] | Nikishov, A. I., No article title, Sov. Phys. JETP, 30, 660-662 (1970) |
| [31] | Narozhnyi, N. B.; Nikishov, A. I., No article title, Theor. Math. Phys., 26, 9-20 (1976) · doi:10.1007/BF01038251 |
| [32] | Volkov, D. M., No article title, Z. Phys., 94, 250-260 (1935) · Zbl 0011.18502 · doi:10.1007/BF01331022 |
| [33] | Redmond, P. J., No article title, J. Math. Phys., 6, 1163-1169 (1965) · Zbl 0125.45803 · doi:10.1063/1.1704385 |
| [34] | Grumiller, D.; Kummer, W.; Vassilevich, D. V., No article title, Phys. Rep., 369, 327-430 (2002) · Zbl 0998.83038 · doi:10.1016/S0370-1573(02)00267-3 |
| [35] | Christensen, S. V.; Fulling, S. A., No article title, Phys. Rev. D, 15, 2088-2104 (1977) · doi:10.1103/PhysRevD.15.2088 |
| [36] | Gerlach, U., No article title, Phys. Rev. D, 38, 514-521 (1988) · doi:10.1103/PhysRevD.38.514 |
| [37] | Longhi, P.; Soldati, R., No article title, Phys. Rev. D, 83, 107701 (2011) · doi:10.1103/PhysRevD.83.107701 |
| [38] | Longhi, P.; Soldati, R., No article title, Internat. J. Mod. Phys. A, 28, 1350109 (2013) · Zbl 1277.83064 · doi:10.1142/S0217751X13501091 |
| [39] | Fulling, S. A.; Unruh, W. G., No article title, Phys. Rev. D, 70, 048701 (2004) · doi:10.1103/PhysRevD.70.048701 |
| [40] | Narozhny, N. B.; Fedotov, A. M.; Karnakov, B. M.; Mur, V. D.; Belinskii, V. A., No article title, Phys. Rev. D, 70, 048702 (2004) · doi:10.1103/PhysRevD.70.048702 |
| [41] | Fedotov, A. M.; Narozhnyi, N. B.; Mur, V. D.; Gelfer, E. G., No article title, JETP Lett., 89, 385-389 (2009) · doi:10.1134/S0021364009080025 |
| [42] | Soffel, M.; Müller, B.; Greiner, W., No article title, Phys. Rev. D, 22, 1935-1937 (1980) · doi:10.1103/PhysRevD.22.1935 |
| [43] | W. Greiner, B. Müller, and J. Rafelski, Quantum Electrodynamics of Strong Fields, Springer, Heidelberg (1985). · doi:10.1007/978-3-642-82272-8 |
| [44] | D. McMahon, P. M. Alsing, and P. Embid, “The Dirac equation in Rindler space: A pedagogical introduction,” arXiv:gr-qc/0601010v2 (2006). |
| [45] | R. Jost, The General Theory of Quantized Fields, Amer. Math. Soc., Providence, R. I. (1965). · Zbl 0127.19105 |
| [46] | R. F. Streater and A. S. Wightman, PCT, Spin, and Statistics, and All That, Benjamin, New York (1964). · Zbl 0135.44305 |
| [47] | N. N. Bogolyubov, A. A. Logunov, and I. T. Todorov, Fundamentals of the Axiomatic Approach to Quantum Field Theory [in Russian], Nauka, Moscow (1969); English transl.: Introduction to Axiomatic Quantum Field Theory, Benjamin, Reading, Mass. (1975). · Zbl 0195.28402 |
| [48] | Wightman, A. S.; Levy, M. (ed.), Introduction to some aspects of the relativistic dynamics of quantized fields, 171-291 (1967), New York |
| [49] | Crispino, L. C B.; Higuchi, A.; Matsas, G. E A., No article title, Rev. Modern Phys., 80, 787-838 (2008) · Zbl 1205.83030 · doi:10.1103/RevModPhys.80.787 |
| [50] | I. S. Gradshteyn and I. M. Ryzhik, Tables of Integrals, Series, and Products, Acad. Press, New York (1980). · Zbl 0521.33001 |
| [51] | G. M. Gelfand and G. E. Shilov, Generalized Functions [in Russian], Vol. 1, Generalized Functions and Operations on Them, Fizmatlit, Moscow (1959); English transl.: Vol. 1, Properties and Operations, Acad. Press, New York (1968). · Zbl 0091.11102 |
| [52] | Fock, V. A., No article title, Z. Phys., 57, 261-277 (1929) · JFM 55.0513.06 · doi:10.1007/BF01339714 |
| [53] | R. Paley and N. Wiener, Fourier Transforms in the Complex Domain, Amer. Math. Soc., Providence, R. I. (1934). · Zbl 0011.01601 |
| [54] | Krasnikov, N. V.; Matveev, V. A.; Rubakov, V. A.; Tavkhelidze, A. N.; Tokarev, V. F., No article title, Theor. Math. Phys., 45, 1048-1058 (1980) · doi:10.1007/BF01016704 |
| [55] | Gabriel, C.; Spindel, P., No article title, Ann. Phys., 284, 263-335 (2000) · Zbl 0983.81066 · doi:10.1006/aphy.2000.6071 |
| [56] | Narozhny, N. B.; Mur, V. D.; Fedotov, A. M., No article title, Phys. Lett. A, 315, 169-174 (2003) · Zbl 1057.81572 · doi:10.1016/S0375-9601(03)01007-7 |
| [57] | Gelfer, E. G.; Mur, V. D.; Narozhny, N. B.; Fedotov, A. M., No article title, JETP, 113, 934-948 (2011) · doi:10.1134/S1063776111150040 |
| [58] | L’vov, D. V.; Shelepin, A. L.; Shelepin, L. A., No article title, Phys. Atomic Nucl., 57, 1083-1088 (1994) |
| [59] | R. Haag, Local Quantum Physics: Fields, Particles, Algebras, Springer, New York (1992). · Zbl 0777.46037 · doi:10.1007/978-3-642-97306-2 |
| [60] | N.D. Birrell and P. C. W. Davies, Quantum Fields in Curved Space, Cambridge Univ. Press, Cambridge (1982). · Zbl 0476.53017 · doi:10.1017/CBO9780511622632 |
| [61] | A. S. Eddington, The Nature of the Physical World, Cambridge Univ. Press, Cambridge (1928). · Zbl 1258.01016 |
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