Duality of two-dimensional field theory and four-dimensional electrodynamics leading to finite value of the bare charge

The holographic duality consisting in the functional coincidence of the spectra of the mean number of photons (or scalar quanta) emitted by a point electric (scalar) charge in 3 + 1-space with the spectra of the mean number of pairs of scalar (spinor) quanta emitted by a point mirror in 1 + 1-space is discussed. Because they are functions of two variables and functionals of the common trajectory of the charge and the mirror, the spectra differ only by a factor $e^{2}/\hbar c$ (Heaviside units). The requirement $e^{2}/\hbar c$ =1 leads to unique values for the magnitude of the point charge and its fine structure constant, $e_{0} = \pm \sqrt {\hbar c}$, $\alpha_{0} = 1/4 \pi$, all their properties being as stated by Gell-Mann and Low for the finite bare charge. This requirement follows from the holographic bare charge quantization principle we propose here, according to which the charge and mirror radiations located correspondingly in four-dimensional space and on its internal two-dimensional surface must have identically coincident spectra. The duality is due to the integral connection of the causal Green functions for 3 + 1- and 1 + 1-spaces and to connections of the current and charge densities in 3 + 1-space with the scalar products of scalar and spinor massless fields in 1 + 1-space. We discuss the close similarity of the values of the point bare charge $e_{0} = \sqrt {\hbar c}$, “charges” $e_\mathrm{B} = 1,077 \sqrt {\hbar c}$ and $e_\mathrm{L} = 1.073 \sqrt {\hbar c}$, characterizing the shifts $e^{2}_\mathrm{B,L} /8\pi a$ of the energy of zero-point electromagnetic oscillations in vacuum by the neutral ideally conducting surfaces of a sphere of radius $a$ and a cube of side 2$a$, and the electron charge $e$ multiplied by $\sqrt {4\pi}$. The near equality $e_\mathrm{L} \approx \sqrt {4 \pi} e$ means that $\alpha_{0} \alpha_\mathrm{L} \approx \alpha$ — the fine structure constant.

PACS: 03.70.+k, 12.20.−m, 41.60.−m (all)
DOI: 10.3367/UFNe.0183.201306c.0591
URL: https://ufn.ru/en/articles/2013/6/b/
Web of Science

000324296600002
Scopus

2-s2.0-84888345421
ADS NASA

2013PhyU...56..565R
Citation: Ritus V I "Duality of two-dimensional field theory and four-dimensional electrodynamics leading to finite value of the bare charge" Phys. Usp. 56 565–589 (2013)

BibTexBibNote ® (generic)BibNote ® (RIS)MedlineRefWorks

Received: 27th, July 2012, revised: 30th, April 2013, accepted: 7th, May 2013

Оригинал: Ритус В И «Дуальность двумерной теории поля и четырёхмерной электродинамики, приводящая к конечному значению затравочного заряда» УФН 183 591–615 (2013); DOI: 10.3367/UFNr.0183.201306c.0591

References (52) ↓ Cited by (3) Similar articles (20)

Hawking S W Nature 248 30 (1974)
Hawking S W Commun. Math. Phys. 43 199 (1975)
Nikishov A I, Ritus V I Zh. Eksp. Teor. Fiz. 108 1121 (1995); Nikishov A I, Ritus V I JETP 81 615 (1995)
Ritus V I Zh. Eksp. Teor. Fiz. 110 526 (1996); Ritus V I JETP 83 282 (1996)
Ritus V I Zh. Eksp. Teor. Fiz. 114 46 (1998); Ritus V I JETP 87 25 (1998); Ritus V I "Popravka" Zh. Eksp. Teor. Fiz. 115 384 (1999); Ritus V I "Erratum" JETP 88 207 (1999)
Ritus V I Zh. Eksp. Teor. Fiz. 116 1523 (1999); Ritus V I JETP 89 821 (1999)
Ritus V I Zh. Eksp. Teor. Fiz. 124 14 (2003); Ritus V I JETP 97 10 (2003)
Ritus V I Zh. Eksp. Teor. Fiz. 129 664 (2006); Ritus V I JETP 102 582 (2006)
Gell-Mann M, Low F E Phys. Rev. 95 1300 (1954)
Bogolyubov N N Zh. Eksp. Teor. Fiz. 34 58 (1958); Bogolyubov N N Sov. Phys. JETP 7 41 (1958)
Schwinger J Particles, Sources, And Fields (Reading, Mass.: Addison-Wesley Publ. Co., 1970); Shvinger Yu Chastitsy, Istochniki, Polya Vol. 1 (M.: Mir, 1973)
Baker M, Johnson K Phys. Rev. 183 1292 (1969)
Landau L D Niels Bohr And The Development Of Physics (Ed. W Pauli) (New York: McGraw-Hill, 1955); Landau L D Nil’s Bor i Razvitie Fiziki (Pod red. V Pauli) (M.: IL, 1958)
Bogolyubov N N, Shirkov D V Vvedenie v Teoriyu Kvantovannykh Polei (M.: Nauka, 1976); Bogoliubov N N, Shirkov D V Introduction To The Theory Of Quantized Fields (New York: John Wiley, 1980)
Itzykson C, Zuber J-B Quantum Field Theory (New York: McGraw-Hill International Book Co., 1980); Itsikson K, Zyuber Zh-B Kvantovaya Teoriya Polya Vol. 2 (M.: Mir, 1984)
Huang K Quarks, Leptons And Gauge Fields (Singapore: World Scientific, 1982); Khuang K Kvarki, Leptony i Kalibrovochnye Polya (M.: Mir, 1985)
Huang K Asymptotic Realms Of Physics. Essays In Honor Of Francis E. Low (Eds A H Guth, K Huang, R L Jaffe) (Cambridge, Mass.: MIT Press, 1983)
Birrell N D, Davies P C W Quantum Fields In Curved Space (Cambridge: Cambridge Univ. Press, 1982); Birrell N, Devis P Kvantovannye Polya v Iskrivlennom Prostranstve-vremeni (M.: Mir, 1984)
DeWitt B S Phys. Rep. 19 295 (1975)
Berestetskii V B, Lifshits E M, Pitaevskii L P Kvantovaya Elektrodinamika (M.: Nauka, 1989); Berestetskii V B, Lifshitz E M, Pitaevskii L P Quantum Electrodynamics (Oxford: Butterworth-Heinemann, 1999)
Lightman A P, Press W H, Price R N, Teukolsky S A Problem Book In Relativity And Gravitation (Princeton, N.J.: Princeton Univ. Press, 1975); Laitman A, Press V, Prais R, Tyukol’ski S Sbornik Zadach Po Teorii Otnositel’nosti i Gravitatsii (M.: Mir, 1979)
Wald R M Commun. Math. Phys. 45 9 (1975)
Titchmarsh E C Introduction To The Theory Of Fourier Integrals (Oxford: The Clarendon Press, 1937); Titchmarsh E Vvedenie v Teoriyu Integralov Fur’e (M. - L.: Gostekhizdat, 1948)
Abbasov I I, Bolotovskii B M, Davydov V A Usp. Fiz. Nauk 149 709 (1986); Abbasov I I, Bolotovskii B M, Davydov V A Sov. Phys. Usp. 29 788 (1986)
Dwight H B Tables Of Integrals And Other Mathematical Data (New York: Macmillan, 1961); Dvait G B Tablitsy Integralov i Drugie Matematicheskie Formuly (M.: Nauka, 1978)
’t Hooft G Salamfestschrift (World Scientific Series In 20th Century Physics, Vol. 4, Eds A Ali, J Ellis, S Randjbar-Daemi) (Singapore: World Scientific, 1993); ’t Hooft G gr-qc/9310026
Susskind L J. Math. Phys. 36 6377 (1995)
Gubser S S, Klebanov I R, Polyakov A M Phys. Lett. B 428 105 (1998)
Maldacena J M Adv. Theor. Math. Phys. 2 231 (1998)
Dirac P A M Proc. R. Soc. Lond. A 114 243 (1927); Dirac P A M Proc. R. Soc. Lond. A 114 710 (1927)
Fock V Z. Phys. 75 622 (1932)
Schrödinger E Naturwissenschaften 14 664 (1926)
von Neumann J Mathematische Grundlagen Der Quantenmechanik (Berlin: J. Springer, 1932); von Neumann J Mathematical Foundations Of Quantum Mechanics (Princeton, N.J.: Princeton Univ. Press, 1955); fon Neiman I Matematicheskie Osnovy Kvantovoi Mekhaniki (M.: Nauka, 1964)
Glauber R J Phys. Rev. 130 2529 (1963); Glauber R J Phys. Rev. 131 2766 (1963)
Akhiezer A I, Berestetskii V B Kvantovaya Elektrodinamika (M.: Nauka, 1969); Akhiezer A I, Berestetskii V B Quantum Electrodynamics (New York: Interscience Publ., 1965)
Landau L D, Lifshits E M Statisticheskaya Fizika Vol. 1 (M.: Nauka, 1976); Landau L D, Lifshitz E M Statistical Physics Vol. 1 (Oxford: Pergamon Press, 1980)
Nikishov A I Zh. Eksp. Teor. Fiz. 57 1210 (1969); Nikishov A I Sov. Phys. JETP 30 660 (1970)
Nikishov A I Tr. FIAN 111 152 (1979)
Landau L D, Lifshits E M Kvantovaya Mekhanika. Nerelyativistskaya Teoriya (M.: Nauka, 1974); Landau L D, Lifshitz E M Quantum Mechanics. Non-Relativistic Theory (Oxford: Pergamon Press, 1977)
Heisenberg W, Euler H Z. Phys. 98 714 (1936)
Schwinger J Phys. Rev. 82 664 (1951)
Ritus V I Dokl. Akad. Nauk SSSR 275 611 (1984); Ritus V I Sov. Phys. Dokl. 29 227 (1984)
Lebedev S L, Ritus V I Zh. Eksp. Teor. Fiz. 86 408 (1984); Lebedev S L, Ritus V I Sov. Phys. JETP 59 237 (1984)
Dirac P A M Directions In Physics (Eds H Hora, J R Shepanski) (New York: Wiley, 1978)
Casimir H B G Physica 19 846 (1953)
Boyer T H Phys. Rev. 174 1764 (1968)
Davies B J. Math. Phys. 13 1324 (1972)
Balian R, Duplantier B Ann. Physics 112 165 (1978)
Milton K A, DeRaad L L (Jr.), Schwinger J Ann. Physics 115 388 (1978)
Schwinger J, DeRaad L L (Jr.), Milton K A Ann. Physics 115 1 (1978)
Lukosz W Physica 56 109 (1971)
Grib A A, Mamaev S G, Mostepanenko V M Vakuumnye Kvantovye Effekty v Sil’nykh Polyakh (M.: Energoatomizdat, 1988)