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

Abstract
HTML
Reference
Related

PDF

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

[1]	F. D. Nobre, M. A. Rego-Monteiro, and C. Tsallis, Phys. Rev. Lett., 106:140601(2011)
[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)

[1]	Xian Gao , Lavinia Heisenberg . Doubly coupled matter fields in massive bigravity. Chinese Physics C, 2018, 42(7): 075101. doi: 10.1088/1674-1137/42/7/075101
[2]	S. A. Alavi , F. S. Kazemian . Photonic dark matter portal and quantum physics. Chinese Physics C, 2016, 40(2): 025101. doi: 10.1088/1674-1137/40/2/025101
[3]	HAN Lei , WANG Hai-Jun . New method of applying conformal group to quantum fields. Chinese Physics C, 2015, 39(9): 093102. doi: 10.1088/1674-1137/39/9/093102
[4]	ZHU Jing-Min . Quantum phase transitions about parity breaking in matrix product systems. Chinese Physics C, 2011, 35(2): 144-148. doi: 10.1088/1674-1137/35/2/007
[5]	Sayipjamal Dulat , LI Kang , . Landau problem in noncommutative quantum mechanics. Chinese Physics C, 2008, 32(2): 92-95. doi: 10.1088/1674-1137/32/2/003
[6]	YUE Peng , SHEN Hong . Antikaon condensation in neutron star matter with strong magnetic fields. Chinese Physics C, 2008, 32(S2): 85-88.
[7]	MO Xiao-Hu . Correlation in Estimation of the Q Value. Chinese Physics C, 2005, 29(9): 831-837.
[8]	Xie Mi , Jin Baiqi , Ma Zhongqi . L^± Operators and Quantum Enveloping Algebras. Chinese Physics C, 1996, 20(S3): 253-260.
[9]	Dai Qirun , Ma Zhanqing , Zhao Shusong , . Fermi-Dirac Correlation and Q^－v)K_v(Q) Distribution. Chinese Physics C, 1996, 20(11): 1014-1020.
[10]	Yu Zhaoxian , Yu Ge , Zhang Dexing , Liu Yehou . Nodvik and Holstein-Primakoff Realizations for Two-ParameterDeformed Quantum Algebra SU(1,1)_(q,s). Chinese Physics C, 1996, 20(12): 1082-1086.
[11]	Yu Zhaoxian , Liu Yehou , Li Qinglin , Liang Bifang . Study of SU(2)_q,s Coherent State by Using (q,s) Deformed Harmonic Oscillators of SU(2)_q,s Quantum Algebra. Chinese Physics C, 1995, 19(3): 258-263.
[12]	Wang Renchuan , Zhu Dongpei . Quantization of Interacting Fields in QED. Chinese Physics C, 1994, 18(S4): 357-366.
[13]	Yu Qingchang . Transport of Charged Particle Beams in Nonlinear Periodic Fields. Chinese Physics C, 1993, 17(S1): 39-43.
[14]	CHEN Yong-Qing . q-Oscillator Representations of the Quantum Superalgebra spl_q(2,1). Chinese Physics C, 1993, 17(7): 631-635.
[15]	FU Hong-Chen , GE Mo-Lin . Verma Module of Quantum Group GL(3)_q Its q-Boson Realization and Cyclic Representations. Chinese Physics C, 1992, 16(10): 912-918.
[16]	Fu Hongchen , Ge Molin . Verma Module of Quantum Group GL(3)_q,and the q-boson Realization and Cyclic Representations. Chinese Physics C, 1992, 16(S4): 431-437.
[17]	HU Zhan-Ning . The q-Deformed KdV Equation. Chinese Physics C, 1991, 15(8): 765-768.
[18]	CHENG Hong-Bo . Gauged Q-stars. Chinese Physics C, 1991, 15(11): 991-996.
[19]	Li Zhuxia , Shi Yijing , Wu Xizhen , Wang Zhongqi , Zhuo Yizhong . Quantum Effect and One-Body Dissipation. Chinese Physics C, 1990, 14(S3): 291-299.
[20]	HUANG CHAO-SHANG , DAI YUAN-BEN . THE PROCESS e⁺+e^-→π+q+q IN QUANTUM CHROMODYNAMICS. Chinese Physics C, 1981, 5(4): 412-416.

Access

Get Citation

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

RIS(for EndNote,Reference Manager,ProCite)

BibTex

Txt

Milestone

Received: 2017-12-16
Revised: 2018-02-21

Article Metric

Article Views(1596)
PDF Downloads(15)
Cited by(0)

Policy on re-use

To reuse of subscription content published by CPC, the users need to request permission from CPC, unless the content was published under an Open Access license which automatically permits that type of reuse.

通讯作者: 陈斌, bchen63@163.com

1.
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.

HTML

Reference (12)

Tsallis' quantum q-fields

Abstract：

References

Access

Article Metrics

Metrics

通讯作者: 陈斌, bchen63@163.com

Email This Article

Tsallis' quantum q-fields

HTML

目录