Tsallis' quantum q-fields

A. Plastino; M. C. Rocca

doi:10.1088/1674-1137/42/5/053102

Chinese Physics C> 2018, Vol. 42> Issue(5) : 053102 DOI: 10.1088/1674-1137/42/5/053102

Tsallis' quantum q-fields

A. Plastino ^1,3,4 ,
M. C. Rocca ^1,2,3

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

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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.

References

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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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沈阳化工大学材料科学与工程学院沈阳 110142

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

Received Date: 2017-12-16

Accepted Date: 2018-02-21

Available Online: 2018-05-05

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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