Tsallis' quantum q-fields

  • We generalize several well known quantum equations to a Tsallis' q-scenario, and provide a quantum version of some classical fields associated with them in the recent literature. We refer to the q-Schrödinger, q-Klein-Gordon, q-Dirac, and q-Proca equations advanced in, respectively, Phys. Rev. Lett. 106, 140601 (2011), EPL 118, 61004 (2017) and references therein. We also introduce here equations corresponding to q-Yang-Mills fields, both in the Abelian and non-Abelian instances. We show how to define the q-quantum field theories corresponding to the above equations, introduce the pertinent actions, and obtain equations of motion via the minimum action principle. These q-fields are meaningful at very high energies (TeV scale) for q=1.15, high energies (GeV scale) for q=1.001, and low energies (MeV scale) for q=1.000001[Nucl. Phys. A 955 (2016) 16 and references therein]. (See the ALICE experiment at the LHC). Surprisingly enough, these q-fields are simultaneously q-exponential functions of the usual linear fields' logarithms.
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    [2] A. Plastino and M. C. Rocca, EPL, 116:41001(2016)
    [3] A. Plastino and M. C. Rocca, EPL, 118:61004(2017)
    [4] A. Plastino and M. C. Rocca, PLA, 370:2690(2015)
    [5] F. D. Nobre and A. R. Plastino, EPJ C, 76:343(2016)
    [6] F. D. Nobre, M. A. Rego-Monteiro, and C. Tsallis, EPL, 97:41001(2012)
    [7] A. Plastino and M. Rocca, Nuc. Phys. A, 948:19(2016)
    [8] A. Plastino, M. C. Rocca, G. L. Ferri, and D. J. Zamora, Nuc. Phys. A, 955:16(2016)
    [9] F. Barile et al (ALICE Collaboration), EPJ Web Conferences, 60:13012(2013); B. Abelev et al (ALICE Collaboration), Phys. Rev. Lett., 111:222301(2013); Yu. V. Kharlov (ALICE Collaboration), Physics of Atomic Nuclei, 76:1497(2013); ALICE Collaboration, Phys. Rev. C, 91:024609(2015); ATLAS Collaboration, New J. Physics, 13:053033(2011); CMS Collaboration, J. High Energy Phys., 05:064(2011); CMS Collaboration, Eur. Phys. J. C, 74:2847(2014)
    [10] C. H. Bennett, D. Leung, G. Smith, and J. A. Smolin, Phys. Rev. Lett., 103:170502(2009)
    [11] A. R. Plastino and C. Zander, in A Century o f Relativity Physics:XXVⅢ Spanish Relativity Meeting, edited by L. Mornas and J. D. Alonso, AIP Conf. Proc. No. 841(AIP, Melville, NY, 2006), pp. 570-573
    [12] L. P. Pitaevskii and S. Stringari, Bose Einstein Condensation (Clarendon Press, Oxford, 2003)
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A. Plastino and M. C. Rocca. Tsallis' quantum q-fields[J]. Chinese Physics C, 2018, 42(5): 053102. doi: 10.1088/1674-1137/42/5/053102
A. Plastino and M. C. Rocca. Tsallis' quantum q-fields[J]. Chinese Physics C, 2018, 42(5): 053102.  doi: 10.1088/1674-1137/42/5/053102 shu
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Received: 2017-12-16
Revised: 2018-02-21
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Tsallis' quantum q-fields

  • 1. Departamento de Fí
  • 2. Consejo Nacional de Investigaciones Cientí
  • 3. SThAR-EPFL, Lausanne, Switzerland
  • 4. Departamento de Matemá
  • 5. Consejo Nacional de Investigaciones Cientí

Abstract: We generalize several well known quantum equations to a Tsallis' q-scenario, and provide a quantum version of some classical fields associated with them in the recent literature. We refer to the q-Schrödinger, q-Klein-Gordon, q-Dirac, and q-Proca equations advanced in, respectively, Phys. Rev. Lett. 106, 140601 (2011), EPL 118, 61004 (2017) and references therein. We also introduce here equations corresponding to q-Yang-Mills fields, both in the Abelian and non-Abelian instances. We show how to define the q-quantum field theories corresponding to the above equations, introduce the pertinent actions, and obtain equations of motion via the minimum action principle. These q-fields are meaningful at very high energies (TeV scale) for q=1.15, high energies (GeV scale) for q=1.001, and low energies (MeV scale) for q=1.000001[Nucl. Phys. A 955 (2016) 16 and references therein]. (See the ALICE experiment at the LHC). Surprisingly enough, these q-fields are simultaneously q-exponential functions of the usual linear fields' logarithms.

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