The Role of Symmetry in the Development of the Standard Model

Sherwin T. Love

doi:10.1017/9781009238427

Series: Elements in Physics beyond the Standard Model with Atomic and Molecular Systems

The Role of Symmetry in the Development of the Standard Model

Published online by Cambridge University Press: 12 January 2024

Sherwin T. Love

Show author details

Sherwin T. Love: Affiliation:
Purdue University

Summary

Symmetry and its various realizations have played a pivotal role in the development of the extremely well tested Standard Model of the strong, weak and electromagnetic interactions. In this Element, the author traces the development of the model through the interplay of the different symmetries realized in the various components of the model as well as in other sub-fields of physics.

Element contents

Summary
References

Get access

Keywords

symmetry standard model of particle physics Higgs mechanism QED QCD

Type: Element
Information: Series: Elements in Physics beyond the Standard Model with Atomic and Molecular Systems

DOI: https://doi.org/10.1017/9781009238427 [Opens in a new window]

Online ISBN: 9781009238427

Publisher: Cambridge University Press

Print publication: 08 February 2024

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Atlas Collaboration: Aad, G., Abajyan, T., Abbott, B. et al., Phys. Lett. B716 (2012) 1–29. e-Print: 1207.7214 [hep-ex].Google Scholar

CMS Collaboration: Chatrchyan, S., Khachatryan, V., Sirunyan, A. M. et al. Phys. Lett. B716 (2012) 30–61. e-Print: 1207.7235 [hep-ex].Google Scholar

Einstein, A., Preussische Akademie der Wissenschaften, Sitzungsberichte der Preussischen Akademie der Wissenschaften (Berlin), Part 2 (in German) (1915) 844–847.Google Scholar

Einstein, A., Annalen der Physik (in German) 354 (1916) 769.Google Scholar

Peskin, M. E. and Schroeder, D. V., An Introduction to Quantum Field Theory (Westview Press, Nashville, 1995).Google Scholar

Stueckelberg, E. C. G. and Petermann, A., , Helv. Phys. Acta (in French) 26 (1953) 499–520.Google Scholar

Gell-Mann, M. and Low, F. E., Phys. Rev. 95 (1954) 1300–1312.Google Scholar

Wilson, K., Phys. Rev. 179 (1969) 1499.Google Scholar

Wilson, K. and Kogut, J., Phys. Rept. 12 (1974) 75–200.Google Scholar

Wigner, E., Group Theory and Its Application to the Quantum Mechanics of Atomic Spectra (Academic Press, Cambridge, MA, 1959).Google Scholar

Georgi, H., Lie Algebras in Particle Physics (Benjamin/Cummings Publishing Company, San Francisco, 1982).Google Scholar

Noether, E., Mathematisch-Physikalische Klasse (in German) (1918) 236–257.Google Scholar

Wigner, E. P., Proc. Nat. Acad. Sci. 38 (1952) 449.Google Scholar

Weyl, H., , Z. Phys. (in German) 56 (1929) 330.Google Scholar

Lehmann, H., Symanzik, K. and Zimmermann, W., Nuovo Cimento 1 (1955) 1425.Google Scholar

Selected Papers on Quantum Electrodynamics, edited by Schwinger, J. (Dover, Mineola, NY, 1958).Google Scholar

Morel, L., Yao, Z., Cladé, P. and Guellati-Khélifa, S., Nature 588 (2020) 61–65.Google Scholar

Schwinger, J., Phys. Rev. 73 (1948) 416–417.Google Scholar

Laporta, S. and Remiddi, E., Phys. Lett. B 379 (1996) 283–291, e-Print: 9602417 [hep-ph].Google Scholar

Aoyama, T., Kinoshita, T. and Nio, M., Atoms 7 (2019) 28.Google Scholar

Hanneke, D., Fogwell Hoogerheide, S. and Gabrielse, G., Phys. Rev. A83 (2011) 052122, e-Print: 1009.4831 [atom-ph].Google Scholar

Chadwick, J., Nature 129 (1932) 312.Google Scholar

Heisenberg, W., , Z. Physik (in German) 77 (1932) 1–11.Google Scholar

Gell-Mann, M., Phys. Rev. 125 (1962) 1067.Google Scholar

Ne’eman, Y., Nucl. Phys. 26 (1961) 222–229.Google Scholar

Gell-Mann, M., Phys. Rev. 125 (1962) 1067.Google Scholar

Fermi, E., Ric. sci. prog. tec. econ. naz. (in Italian) 2 (1933).Google Scholar

Fermi, E., Il Nuovo Cimento (in Italian) 11 (1934) 1–19.Google Scholar

Fermi, E., , Z. Physik (in German) 88 (1934) 161.Google Scholar

Yang, C. N. and Lee, T. D., Phys. Rev. 104 (1956) 254.Google Scholar

Wu, C. S., Ambler, E., Hayward, R., Hoppes, D. D. and Hudson, R. P., Phys. Rev. 105 (1957) 1413–1415.Google Scholar

Feynman, R. P. and Gell-Mann, M., Phys. Rev. 109 (1958) 193–198.Google Scholar

Marshak, R. and Sudarshan, E. C. G., Phys. Rev. 109 (1958) 1860–1862.Google Scholar

Gershtein, S. S. and Zeldovich, J. B., , Zh. Eksperim. i Teor. Fis. 29 (1955) 698 [English transl.: Soviet Phys.—J. Exp. Theor. Phys. 2 (1955) 576].Google Scholar

Klein, O., Nature 4101 (1948) 897.Google Scholar

Bardeen, J., Cooper, L. N. and Schrieffer, J. R., Phys. Rev. 106 (1957) 162–164.CrossRef Google Scholar

Bardeen, J., Cooper, L. N. and Schrieffer, J. R., Phys. Rev. 108 (1957) 1175–1204.Google Scholar

Nambu, Y., Phys. Rev. 117 (1960) 648–663.Google Scholar

Nambu, Y. and Jona-Lasinio, G., Phys. Rev. 122 (1961) 345–358; Phys. Rev. 124 (1961) 246–254.Google Scholar

Schwinger, J., Ann. Phys. 2 (1957) 407.Google Scholar

Glashow, S. and Baker, M., Phys. Rev. 128 (1962) 2462.Google Scholar

Coleman, S. in Aspects of Symmetry: Selected Erice Lectures, Chapter 5 (Cambridge University Press, Cambridge, 1988).Google Scholar

Ginzburg, V. L. and Landau, L. D., Zh. Eksp. Teor. Fiz. (in Russian) 20 (1950), 1064 [English translation appears in L. D. Landau, Collected Papers (Pergamon Press, Oxford, 1965) p. 546].Google Scholar

Heisenberg, W., Zeitschrift für Physik (in German) 49 (1928) 619–636.Google Scholar

Gell-Mann, M. and Levy, M., Il Nuovo Cimento 16 (1960) 705–726.Google Scholar

Goldstone, J., Nuovo Cimento, 19 (1961) 154–164.Google Scholar

Goldstone, J., Salam, A. and Weinberg, S., Phys. Rev. 127 (1962) 965–970.Google Scholar

Yang, C. N. and Mills, R. L., Phys. Rev. 96 (1954) 191.Google Scholar

Gell-Mann, M., lectures at the 1972 Schladming Winter School, CERN TH.1543 Acta Phys. Austriaca Suppl. (1972).Google Scholar

Fritzsch, H. and Gell-Mann, M. in Proceedings of the XVI International Conference on High Energy Physics, edited by Jackson, J. D. and Roberts, A. (NAL, Batavia, IL, 1972).Google Scholar

Bardeen, W. A., Fritzsch, H. and Gell-Mann, M. in Scale and Conformal Invariance in Hadron Physics, edited by , R. Gatto (Wiley, New York, 1973).Google Scholar

Fritzsch, H., Gell-Mann, M. and Leutwyler, H., Phys. Lett. B47 (1973) 365–368.Google Scholar

Greenberg, O. W., Phys. Rev. Lett. 13 (1964) 598.Google Scholar

Nambu, Y., in Proceedings of the 2nd Coral Gables Conference on Symmetry Principles at High Energy, 274–285, edited by Kursumoglu, B., Perlmutter, A., and Sanmar, I. (Freeman, New York, 1965).Google Scholar

Nambu, Y., in Preludes in Theoretical Physics in Honor of V. F. Weisskopf, 133–142 edited by De-Shalit, A., Feshbach, H., and Van Hove, L. (North-Holland, Amsterdam, 1965).Google Scholar

Han, Y. and Nambu, Y., Phys. Rev. 139B (1965) 1006.Google Scholar

Gross, D. J. and Wilczek, F., Phys. Rev. Lett. 30 (1973) 1343–1346.Google Scholar

Politzer, H. D., Phys. Rev. Lett. 30 (1973) 1346–1349.Google Scholar

Vanyashin, V. S. and Terent’ev, M. V., J. Exp. Theor. Phys. 21 (1965) 375–380.Google Scholar

Khriplovich, I. B., Sov. J. Nucl. Phys. 10 (1970) 235–242.Google Scholar

, G. ’t Hooft, unpublished talk at the Marseille conference on renormalization of Yang–Mills fields and applications to particle physics (1972).Google Scholar

Zyla, P. A., Barnett, R. M., Beringer, J. et al. (Particle Data Group), Prog. Theor. Exp. Phys. 2020 (2020) 083C01.Google Scholar

Bloom, E. D., Coward, D. H., DeStaebler, H. C. et al., Phys. Rev. Lett. 23 (1969) 930–934.Google Scholar

Breidenbach, M., Friedman, J. I., Kendall, H. W. et al. Phys. Rev. Lett. 23 (1969) 935–939.Google Scholar

Friedman, J. I. and Kendall, H. W., Ann. Rev. Nucl. Par. Sci. 22 (1972) 203–254.Google Scholar

Bjorken, J. D., Phys. Rev. 148 (1966) 1467; 179 (1969) 1547.Google Scholar

Feynman, R. P., Phys. Rev. Lett. 23 (1969) 1415.Google Scholar

Feynman, R. P., Photon-Hadron Interactions (Addison-Wesley, Boston, 1988).Google Scholar

Gell-Mann, M., Phys. Lett. 8 (1964) 214–215.Google Scholar

Zweig, G., CERN Report No.8182/TH.401; CERN Report No.8419/TH.412.Google Scholar

Bjorken, J. D. and Paschos, E. A., Phys. Rev. 185 (1969) 1975.Google Scholar

Chang, C., Chen, K., Fox, D. et al., Phys. Rev. Lett. 35 (1975) 9.Google Scholar

Ellis, R. K., Adv. Ser. Direct. High Energy Phys. 26 (2016) 61–78.Google Scholar

Landau, L. D., Abrikosov, A. A. and Khalatnikov, I. M., Dokl. Akad. Nauk SSSR 95 (1954) 497.Google Scholar

Kolb, E. W. and Turner, M. S., The Early Universe, Frontiers in Physics 69 (Addison-Wesley, Boston, 1990).Google Scholar

Marino, E. C., Quantum Field Theory Approach to Condensed Matter Physics (Cambridge University Press, Cambridge, 2017).Google Scholar

Wilson, K., Phys. Rev. D 10 (1974) 2445.Google Scholar

Gattringer, C. and Lang, C. B., Quantum Chromodynamics on the Lattice (Springer, 2009).Google Scholar

Degrand, T. and DeTar, C., Lattice Methods for Quantum Chromodynamics (World Scientific, 2006).Google Scholar

Montvay, I. and Münster, G., Quantum Fields on a Lattice (Cambridge University Press, 1997).Google Scholar

Kronfeld, A., , Ann. Rev. Nucl. Part. Sci., 62 (2012) 265, e-Print: 1203.1204 [hep-lat].Google Scholar

Schwinger, J., Phys. Rev. Phys. Rev. 128 (1962) 2425–2429.Google Scholar

Anderson, P. W., Phys. Rev. 130 (1963) 439–442.Google Scholar

Meissner, W. and Ochsenfeld, R., Naturwissenschaften (in German) 21 (1933) 787–788.Google Scholar

Stueckelberg, E., Helvetica Physica Acta 11 (1938) 299–312.Google Scholar

Källén, G., Elementary Particle Physics (Addison Wesley, 1964).Google Scholar

Pontecorvo, B., Phys. Rev. 72 (1947) 246.Google Scholar

Puppi, G., Nuovo Cimento 5 (1948) 505.Google Scholar

Glashow, S. L., Nucl. Phys. 2 (1961) 579.Google Scholar

Salam, A. and Ward, J. C., Novo Cim. 11 (1959) 568; 19 (1961) 165.Google Scholar

Glashow, S. L., Iliopoulos, J. and Maiani, L., Physical Review D2 (1970) 1285.Google Scholar

Christenson, J. H., Cronin, J., Fitch, V. L. and Turlay, R., Phys. Rev. Lett. 13 (1964) 138.Google Scholar

Cabibbo, N., Phys. Rev. Lett. 10 (1963) 531–533.Google Scholar

Aubert, J. J. M., Becker, U., Biggs, P. J. et al., Phys. Rev. Lett. 33 (1974) 1404–1406.Google Scholar

Augustin, J.-E., Boyarski, A. M., Breidenbach, M., et al., Phys. Rev. Lett. 33 (1974) 1406–1408.Google Scholar

Kobayashi, M. and Maskawa, T., Progress of Theoretical Physics 49 (1973) 652–657.Google Scholar

Brout, R. and Englert, F., Phys. Rev. Lett., 13 (1964) 321.Google Scholar

Higgs, P., Phys. Lett. 12 (1964) 132; Phys. Rev. Lett. 13 (1964) 508.Google Scholar

Guralnik, G., Hagen, C. R. and Kibble, T., Phys. Rev. Lett. 13 (1964) 585.Google Scholar

Migdal, A. and Polyakov, A., Sov. Phys. J. Exp. Theor. Phys. 24 (1967) 91–98, Zh. Eksp. Teor. Fiz. 51 (1966) 135–146.Google Scholar

Weinberg, S., Phys. Rev. Lett. 19 (1967) 1264.Google Scholar

Salam, A., in Elementary Particle Theory, ed. by Svartholm, N. (Almquist and Wiksell, Stockholm 1968).Google Scholar

Sikivie, P., Susskind, L., Voloshin, M. B. and Zakharov, V. I., Nucl. Phys. B173 (1980) 189.Google Scholar

’t Hooft, G., Nucl. Phys. B33 (1971) 173–177; Nucl. Phys. B35 (1971) 167–188.Google Scholar

Veltman, M. J. G., Nucl. Phys. B 7 (1968), 637–650.Google Scholar

Veltman, M. J. G., Nucl. Phys. B 21 (1970), 288–302.Google Scholar

’t Hooft, G. and Veltman, M., Nucl. Phys. B 44 (1972) 189–219.Google Scholar

’t Hooft, G. and Veltman, M., DIAGRAMMAR, NATO Adv. Study Inst. Ser. B Phys. 4 (1974) 177–322.Google Scholar

Lee, B. W., Phys. Rev. D 6 (1972) 1188; B. W. Lee and J. Zinn Justin, Phys. Rev. D 5 (1972) 3132, 3137, 3155.Google Scholar

Gargamelle Collaboration, F. J. Hasert, Faissner, H., Krenz, W. et al., Phys. Lett. B46 (1973) 121.Google Scholar

Gargamelle Collaboration, F. J. Hasert, Kabe, S., Krenz, W. et al., Nucl. Phys. B73 (1974) 1.Google Scholar

Zel’dovich, Ya. B., Exp, J.. Theor. Phys. 33 (1957) 1531, Ya. B. Zel’dovich, J. Exp. Theor. Phys. 2 (1959) 682.Google Scholar

Prescott, C. Y., Atwood, W. B, Cottrell, R. L. A. et al., Phys. Lett. 77B (1978) 347.Google Scholar

Prescott, C. Y., Atwood, W. B, Cottrell, R. L. A. et al., Phys. Lett. 84B (1979) 524.Google Scholar

Khriplovich, I. B., Parity Non-conservation in Atomic Phenomena (Gordon and Breach, New York, 1991).Google Scholar

Bouchiat, M. A. and Bouchiat, C., Phys. Lett. B48 (1974) 111.Google Scholar

Barkov, L. M. and Zolotorev, M. S., Pis’ma Zh. Eksp. Teor. Fiz. 27 (1978) 379 (in Russian), [English trans.: J. Exp. Theor. Phys. Lett. 27 (1978) 357].Google Scholar

Wood, C. S., Bennett, S. C., Cho, D. et al., Science 275 (1997) 1759.Google Scholar

Arnison, G., Aniston, A., Aubert, B. et al. (UA1 Collaboration), Phys. Lett. B122 (1983) 103.Google Scholar

Arnison, G. et al. (UA1 Collaboration), Phys. Lett. B126 (1983) 101.Google Scholar

Banner, M., Battiston, R., Bloch, Ph et al. (UA2 Collaboration), Phys. Lett. B122 (1983) 476.Google Scholar

Bagnaia, P., Banner, M., Battiston, R. et al. (UA2 Collaboration), Phys. Lett. B129 (1983) 130.Google Scholar

Aoyama, T., Asmussen, N., Benayoun, M. et al., Phys. Rept. 887 (2020), e-Print: 2006.04822 [hep-ph].Google Scholar

Abi, B., Albahri, T., Al-Kilani, S. et al., (Muon g-2 Collaboration), Phys. Rev. Lett. 126 (2021) 141801, e-Print: 2104.03281 [hep-ex].Google Scholar

Albahri, T., Anastasi, A., Anisenkov, A. et al., (Muon g-2 Collaboration), Phys. Rev. D 103 (2021) 072002, e-Print: 2104.03247 [hep-ex].Google Scholar

Albahri, T., Anastasi, A., Badgley, K. et al., (Muon g-2 Collaboration), Phys. Rev. A (2021) 103 (2021) 042208, e-Print: 2104.03201 [hep-ex].Google Scholar

Bennett, G. W., Bousquet, B., Brown, H. N. et al., (Muon g-2 Collaboration), Phys. Rev. D 73 (2006) 072003, e-Print: 0602035 [hep-ex].Google Scholar

Sz. Borsanyi, Z. Fodor, Guenther, J. N. et al., Nature 593 (2021) 51, e-Print: 2002:12347 [hep-lat].Google Scholar

ALEPH, DELPHI, L3, OPAL and LEP Electroweak Collaborations, Phys. Rept. 532 (2013) 119–244, e-Print: 1302.3415 [hep-ex].Google Scholar

Denner, A., Dittmaier, S., Roth, M., Wackeroth, D., Nucl. Phys. B560 (1999) 33–65, e-Print: 9904472 [hep-ph].Google Scholar

Jadach, S., Placzek, W., Skrzypek, M., Ward, B. F. L., Was, Z. et al., Comput. Phys. Commun. 140 (2001) 475–512, e-Print: 0104049 [hep-ph].Google Scholar

Bardin, D., Biebel, J., Lehner, D. et al., Comput. Phys. Commun. 104 (1997) 161–187.Google Scholar

ALEPH, DELPHI, L3, OPAL, SLD Collaborations, LEP Electroweak Working Group, SLD Electroweak and Heavy Flavour Groups, Phys. Rep. 427 (2006) 257–454.Google Scholar

Adler, S. L., Phys. Rev. 177 (1969) 2426.Google Scholar

Bell, J. S. and Jackiw, R., Nuovo Cim. 60A (1969) 47.Google Scholar

Adler, S. L. and Bardeen, W., Phys. Rev. 182 (1969) 1517.Google Scholar

Bardeen, W., Phys. Rev. 184 (1969) 1848.Google Scholar

Ross, G. G., Grand Unified Theories (Frontiers in Physics) (Benjamin-Cummings Publishing Co., 1986).Google Scholar

Abel, C., Afach, S., Ayres, N. J. et al., Phys. Rev. Lett. 124 (2020) 081803, e-Print: 2001.11966 [hep-ex].Google Scholar

Bardeen, W. A., Nucl. Phys. B75 (1974) 246.Google Scholar

Peccei, R. D. and Quinn, H. R., Phys. Rev. Lett. 38 1440–1443.Google Scholar

Peccei, R. D. and Quinn, H. R., Phys. Rev. D 16 (1977) 1791–1797.Google Scholar

Weinberg, S., Phys. Rev. Lett. 40 (1978) 223–226.Google Scholar

Wilczek, F., Phys. Rev. Lett. 40 (1978) 279–282.Google Scholar

Super-Kamiokande Collaboration: Fukuda, Y., Hayakawa, T., Ichihara, E. et al., Phys. Rev. Lett. 81 (1998) 1562–1567, e-Print: 9807003 [hep-ex].Google Scholar

Nakamura, K., Hagiwara, K., Hikasa, K. et al. (Particle Data Group), J. Phys. G 37 (2010) 075021.Google Scholar

Raffelt, G. G., Lect. Notes Phys. 741 (2008) 51–71 (2008), e-Print: 0611350 [hep-ph].Google Scholar

Anastassopoulos, V., Aune, S., Barth, K. et al., Nature Physics 13 (2017) 584.Google Scholar

Chang, J. H., Essig, R., and McDermott, S. D., J. High Energy Phys. 1218 (2018) 1.Google Scholar

Pontecorvo, B., Zh. Eksp. Teor. Fiz. 33 (1957) 549–551; reproduced and translated in Sov. Phys. J. Exp. Theor. Phys. 6 (1957) 429–431.Google Scholar

Majorana, E., Nuovo Cimento (in Italian) 14 (1937) 171–184.Google Scholar

Weinberg, S., Phys. Rev. Lett. 43 (1979) 1566–1570.Google Scholar

Maki, Z., Nakagawa, M. and Sakata, S., 28 (1962) 870.Google Scholar

Minkowski, P., Phys. Lett. B. 67 (1977) 421.Google Scholar

Yanagida, T., , Prog. Theor. Phys. 64 (1980) 1103–1105.Google Scholar

de Swart, J. G., Bertone, G. and van Dongen, J., Nat. Astron. 1 (2017) 0059.Google Scholar

Zwicky, F., , Helv. Phys. Acta 6 (1933) 110–127; Astrophys. J. 86 (1937) 217–246.Google Scholar

Oort, J. H., Astrophys. J. 91 (1940) 273–306.Google Scholar

Rubin, V. C. and Kent, W. Ford, Jr., Astrophys. J. 159 (1970) 379–403.Google Scholar

Rubin, V., Science 220 (1983).Google Scholar

Collaboration, WMAP, Spergel, D. N., Verde, L., Peiris, H. V. et al., Astrophys. J. Suppl. 148 (2003) 175–194, e-Print: 0302209 [astro-ph].Google Scholar

Bertone, G., Hooper, D. and Silk, J., Phys. Rept. 405 (2005) 279–390, e-Print: 0404175 [hep-ph].Google Scholar

Trimble, V., , Annu. Rev. of Astr. and Astro. 25 (1987) 425–472.Google Scholar

Clowe, D., Gonzalez, A. and Markevich, M., Astrophys, J. 604 (2004) 596–603, e-Print 0312273 [astro-ph].Google Scholar

Markevitch, M., Gonzalez, A. H., Clowe, D. et al., Astrophys. J. 606 (2004) 819–824, e-Print 0309303 [astro-ph].Google Scholar

Sloan Digital Sky Survey, D. J. Eisenstein et al., Astron. J. 142 (2011) 72, e-Print 1101.1529 [astro-ph].Google Scholar

Weinberg, D. H., Dave, R., Katz, N. and Kollmeier, J. A. in The Emergence of Cosmic Structure: Thirteenth Astrophysics Conference, Holt, S. H. and Reynolds, C. S. eds. (AIP Conference Series) 666 (2003) 157–169, e-Print 0301186 [astro-ph].Google Scholar

Battaglieri, M., Belloni, A., Chou, A. et al., contribution to US Cosmic Visions: New Ideas in Dark Matter (2017), e-Print: 1707.04591 [hep-ph].Google Scholar

Peebles, P. J. E., Astron. J. 263 (1982) L1.Google Scholar

Blumenthal, G. R., Pagels, H. and Primack, J. R., Nature. 299 (1982) 37–38.Google Scholar

Peebles, P. J. E. and Ratra, B., Rev. Mod. Phys. 75 (2003) 559–606, e-Print: 0207347 [astro-ph].Google Scholar

Frieman, J., Turner, M. and Hutere, D., Ann. Rev. Astron. Astrophys. 46 (2008) 385–432, e-Print: 0803.0982 [astro-ph] (The term “dark energy” may first have appeared in the title of this paper.)Google Scholar

Riess, A. G., Filippenko, A. V., Challis, P. et al., Astron. J. 116 (1998) 1009–1038.Google Scholar

Supernova Cosmology Project Collaboration: Perlmutter, S., Aldering, G, Goldhaber, G. et al., Astrophys. J. 517 (1999) 565–586, e-Print: 9812133 [astro-ph].Google Scholar

Supernova Search Team: Riess, A. G., Strolger, L.-G., Tonry, J. et al., Astrophys. J. 607 (2004) 665–687, e-Print: 0402512 [astro-ph].Google Scholar

Paál, G., Horváth, I. and Lukács Astrophys, B.. Space Sci. 191 (1992) 107–124.Google Scholar

Planck Collaboration: Aghanim, N., Akrami, Y., Arroja, F. et al., Astron. and Astrophys. 641 (2020) A6, e-Print: 1807.06205 [astro-ph.CO].Google Scholar

Planck Collaboration: Aghanim, N., Akrami, Y., Ashdown, M. et al., Astron. and Astrophys. 641 (2020) A6, e-Print: 1807.06209 [astro-ph.CO].Google Scholar

Einstein, A., Sitzungsber. Preuss. Akad. Wiss. (in German), 142 (1931) 235–237.Google Scholar

Weinberg, S., Rev. Mod. Phys. 61 (1989) 1–23.Google Scholar

Dine, M. and Kusenko, A., Rev. Mod. Phys. 76 (2003) 1, e-Print: 0303065 [hep-ph].Google Scholar

Sakharov, A. D., J. Exp. Theor. Phys. Lett. 5 (1967) 32–35.Google Scholar

t’Hooft, G., Phys. Rev. Lett. 37 (1976) 8; Phys. Rev. D 14 (1976) 3432.Google Scholar

Kuzmin, V. A., Rubakov, V. A. and Shaposhnikov, M. E., Phys. Lett., B155 (1985) 36.Google Scholar

Rubakov, V. A. and Shaposhnikov, M. E., Usp. Fiz. Nauk, 166 (1996) 493–537.Google Scholar

Fukugita, M. and Yanagida, T., Phys.Lett.B 174 (1986) 45–47.Google Scholar

Buchmuller, W., Di Bari, P. and Plumacher, M., Ann. Phys. 315 (2005) 305–351, e-Print: hep-ph/0401240 [hep-ph].Google Scholar

Davidson, S., Nardi, E. and Nir, Y., Phys.Rept. 466 (2008) 105–177, e-Print: 0802.2962 [hep-ph].Google Scholar

Andreassen, A., Frost, W. and Schwartz, M. D., Phys. Rev. D97 (2018) 056006.Google Scholar

Chigusa, S., Moroi, T. and Shoji, Y., Phys. Rev. Lett. 119 (2017) 211801.Google Scholar

Elias-Miro, J., Espinosa, J. R., Giudice, G. F., Lee, H. M. and Strumia, A. J. High Energy Phys. 06 (2012) 031 e-Print: 1203.0237 [hep-ph].Google Scholar

Starobinskii, A. A., J. Exp. Theor. Phys. 30 (1979) 682.Google Scholar

Linde, A., Phys. Lett. B 108 (1982) 389–393.Google Scholar

Linde, A., , Lect. Notes Phys. 738 (2008) 1; Mukhanov, V., Physical Foundation of Cosmology (Cambridge University Press, 2005) 421.Google Scholar

Spergel, WMAP Collaboration D. N., Bean, R., Doré, O. et al., Astrophys. J. Suppl. 170 (2007) 377–408, e-Print: 0603449 [astro-ph].Google Scholar

’tHooft, G., NATO Sci. Ser. B 59 (1980) 135–157; Cargese Summer Inst. (1979) 135.Google Scholar

Wess, J. and Bagger, H., Supersymmetry and Supergravity (second edition). Princeton Series in Physics (Princeton University Press, 1992).Google Scholar

Bardeen, W. A., in Ontake Summer Institute on Particle Physics (1995) 8, FERMILAB-CONF-95-391-T.Google Scholar

Lidsey, J. E., Liddle, A. R., Kolb, E. W. et al., Rev. Mod. Phys. 69 (1997) 373–410, e-Print: 9508078 [astro-ph].Google Scholar

Bezrukov, F. L. and Shaposhnikov, M., Phys. Lett. B 659 (2008) 703, e-Print: 0710.3755 [hep-th].Google Scholar

De Simone, A., Hertzberg, M. P. and Wilczek, F., Phys. Lett. B 678 (2009) 1–8, e-Print: 0812.4946 [hep-ph].Google Scholar

Bezrukov, F., Magnin, A., Shaposhnikov, M. and Sibiryakov, S., J. High Energy Phys. 01 (2011) 016, e-Print: 1008.5157 [hep-ph].Google Scholar

Barbon, J. L. F. and Espinosa, J. R., Phys. Rev. D 79 (2009) 081302, e-Print: 0903.0355 [hep-ph].Google Scholar

Hilbert, D., Nachrichten von der Gesellschaft der Wissenschaften zu Gö ttingen – Mathematisch-Physikalische Klasse (in German) 3 (1915) 395–407.Google Scholar

DeWitt, B., Phys. Rev. 160 (1967) 1113–1148.Google Scholar

DeWitt, B., 162 (1967) 1195–1239.Google Scholar

DeWitt, B., 162 (1967) 1239–1256.Google Scholar

Feynman, R. P., Acta. Phys. Pol. 24 (1963) 697.Google Scholar

Donoghue, J. F., Phys. Rev. D50 (1994) 3874–3888, e-Print: 9405057 [gr-qc].Google Scholar

Carlip, S., Rep. Prog. Phys. 64 (2001) 885–942.Google Scholar

Blau, M. and Theisen, S., Gen. Relativ. Gravit. 41 (2009)743–755.Google Scholar

Mangano, M. and Parke, S., Phys. Rept. 200 (1991) 301–367, e-Print: 0509223 [hep-th].Google Scholar

Dixon, L. J. in Proceedings of the Theoretical Advanced Study Institute in Elementary Particle Physics (TASI 95) 539–584 (World Scientific, 1996, ed. D. E. Soper, ), e-Print: 9601359 [hep-ph].Google Scholar

Faddeev, L. D. and Popov, V., Phys. Lett. 25 (1967) 29.Google Scholar

Becchi, C., Rouet, A. and Stora, R., Phys. Lett. B52 (1974) 344–346; Comm. in Math. Phys., 42 (1975) 127–162; Annals of Physics 98 (1976) 287–321.Google Scholar

Tyutin, I. V., Lebedev Physics Institute preprint 39 (1975), e-Print: 0812.0580 [hep-th].Google Scholar

Element contents

The Role of Symmetry in the Development of the Standard Model

Summary

Keywords

Access options

References

Save element to Kindle

Save element to Dropbox

Save element to Google Drive