New method of applying conformal group to quantum fields

HAN Lei; WANG Hai-Jun

doi:10.1088/1674-1137/39/9/093102

Chinese Physics C> 2015, Vol. 39> Issue(9) : 093102 DOI: 10.1088/1674-1137/39/9/093102

New method of applying conformal group to quantum fields

HAN Lei ,
WANG Hai-Jun

Abstract
HTML
Reference
Related

PDF

Abstract：
Most of previous work on applying the conformal group to quantum fields has emphasized its invariant aspects, whereas in this paper we find that the conformal group can give us running quantum fields, with some constants, vertex and Green functions running, compatible with the scaling properties of renormalization group method (RGM). We start with the renormalization group equation (RGE), in which the differential operator happens to be a generator of the conformal group, named dilatation operator. In addition we link the operator/spatial representation and unitary/spinor representation of the conformal group by inquiring a conformal-invariant interaction vertex mimicking the similar process of Lorentz transformation applied to Dirac equation. By this kind of application, we find out that quite a few interaction vertices are separately invariant under certain transformations (generators) of the conformal group. The significance of these transformations and vertices is explained. Using a particular generator of the conformal group, we suggest a new equation analogous to RGE which may lead a system to evolve from asymptotic regime to nonperturbative regime, in contrast to the effect of the conventional RGE from nonperturbative regime to asymptotic regime.

References

[1]

Budini P. Czechoslovak Journal of Physics B, 1979, 29: 6[2] LIU Yu-Fen, MA Zhong-Qi, HOU Bo-Yuan. Commun. Theor. Phys., 1999, 31: 481[3] Bateman H. Proc. London Math. Soc., 1910, 8: 223[4] Cunningham E. Proc. London Math. Soc., 1910, 8: 77[5] Polchinski J. Nucl. Phys. B, 1988, 303: 226[6] Nakayama Y. arXiv:1302.0884 [hep-th][7] Gross D J, Wess J. Phys. Rev. D, 1970, 2: 753[8] Kastrup H A. Annalen der Physik, 2008,17: 631; arXiv:0808.2730 [physics.hist-ph][9] Dirac P A M. Annals of Mathematics, 1935, 37: 429[10] Lüscher M, Mack G, Commun. Math. Phys., 1975, 41: 203; Mack G. Commun. math. Phys., 1977, 55: 1[11] Mack G, Salam A. Ann. Phys., 1969, 53: 174[12] Ryder L H. J. Phys. A: Math. Nucl. Gen., 1974, 7: 1817[13] Wheeler J A, Feynman R P. Rev. Mod. Phys., 1945, 17: 157; 1949, 21: 425[14] SU Jun-Chen, YI Xue-Xi, CAO Ying-Hui. J. Phys. G: Nucl. Part. Phys., 1999, 25: 2325[15] SU Jun-Chen, WANG Hai-Jun. Phys. Rev. C, 2004, 70: 044003[16] Curtis G. Callan, Jr. Phys. Rev. D, 1970, 2: 1541[17] Symanzik K. Comm. Math. Phys., 1970, 18: 227[18] Budini P, Furlan P, Raczka R. IL Nuovo Cimento A 52, 191 (21 Luglio 1979).[19] Cartan E. The Theory of Spinors, Dover Publications, Inc. 1981. This is a republication of the first version published by Hermann, Paris. 1966[20] Esteve A, Sona P G. IL Nuovo Cimento XXXII, 1964, 473[21] WANG Hai-Jun. J. Math. Phys., 2008, 49: 053508[22] Feynman R P. Quantum Electrodynamics-A Lecture Note and Preprint Volume, W. A. Benjamin, Inc. 1962. 44, please refer to the Tenth Lecture on Equivalence Transformation[23] Mandl F, Shaw G. Quantum Field Theory, 2nd Edition (Jhon Wiley and Sons Ltd., 2010). page 93, Section 2.4 and Appendix A.7[24] Francesco P, Mathieu P, Senechal D. Conformal Field Theory, Springer-Verlag New York, Inc. 1997[25] Jack I, Osborn H. Nuclear Physics B, 2014, 883: 425C500[26] Kusafuka Y, Terao H. Phys. Rev. D, 2011, 84: 125006[27] Baume F, Keren-Zur B, Rattazzi R et al. JHEP, 2014, 08: 152[28] Osborn H. Nuclear Physics B, 1991, 363: 486

[1]	Jing-Bo Wang , Chao-Guang Huang . Conformal field theory on the horizon of a BTZ black hole. Chinese Physics C, 2018, 42(12): 123110. doi: 10.1088/1674-1137/42/12/123110
[2]	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
[3]	Yunlong Zheng , Yicen Mou , Haomin Rao , Mingzhe Li . Conformal invariant cosmological perturbations via the covariant approach: multicomponent universe. Chinese Physics C, 2018, 42(3): 035102. doi: 10.1088/1674-1137/42/3/035102
[4]	A. Plastino , M. C. Rocca . Tsallis' quantum q-fields. Chinese Physics C, 2018, 42(5): 053102. doi: 10.1088/1674-1137/42/5/053102
[5]	Jia-ju Zhang . Note on non-vacuum conformal family contributions to Rényi entropy in two-dimensional CFT. Chinese Physics C, 2017, 41(6): 063103. doi: 10.1088/1674-1137/41/6/063103
[6]	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
[7]	LIU Lang . No-core Monte Carlo shell model calculations with unitary correlation operator method and similarity renormalization group. Chinese Physics C, 2015, 39(5): 054103. doi: 10.1088/1674-1137/39/5/054103
[8]	ZENG Zhuo-Quan , SHEN Peng-Nian , DING Yi-Bing . An improved variational method. Chinese Physics C, 2009, 33(3): 191-196. doi: 10.1088/1674-1137/33/3/006
[9]	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
[10]	YUE Peng , SHEN Hong . Antikaon condensation in neutron star matter with strong magnetic fields. Chinese Physics C, 2008, 32(S2): 85-88.
[11]	XU Ye , HOU Jian , ZHU Kai-En . Applying Bayesian neural networks to identify pion, kaon and proton in BESⅡ. Chinese Physics C, 2008, 32(3): 201-204. doi: 10.1088/1674-1137/32/3/008
[12]	Zhang Weigang . Particle-group Correlations and Collectivity for 2.1A GeV Ne+NaF Collision. Chinese Physics C, 1997, 21(S4): 65-72.
[13]	Yang Kongqing , Luo Yan . Conformal Transformation and Symplectic Structure of Self-Dual Fields. Chinese Physics C, 1996, 20(9): 789-793.
[14]	Wang Renchuan , Zhu Dongpei . Quantization of Interacting Fields in QED. Chinese Physics C, 1994, 18(S4): 357-366.
[15]	Yu Qingchang . Transport of Charged Particle Beams in Nonlinear Periodic Fields. Chinese Physics C, 1993, 17(S1): 39-43.
[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]	Li Zhuxia , Shi Yijing , Wu Xizhen , Wang Zhongqi , Zhuo Yizhong . Quantum Effect and One-Body Dissipation. Chinese Physics C, 1990, 14(S3): 291-299.
[18]	Long Guilu , Sun Hongzhou . A Group-Chain Check on the Proton-Neutron Interacting Boson Model Computer Code NPBOS. Chinese Physics C, 1989, 13(S3): 313-320.
[19]	Chen Wei . Alternative Regularization Scheme and Conformal Anomaly Strings. Chinese Physics C, 1988, 12(S4): 379-386.
[20]	Jing Sicong , and Ruan Tunan . Quantization of Pure Gauge Fields on Coset Space of Abelian Chiral Group. Chinese Physics C, 1988, 12(S4): 347-358.

Access

Get Citation

HAN Lei and WANG Hai-Jun. New method of applying conformal group to quantum fields[J]. Chinese Physics C, 2015, 39(9): 093102. doi: 10.1088/1674-1137/39/9/093102

HAN Lei and WANG Hai-Jun. New method of applying conformal group to quantum fields[J]. Chinese Physics C, 2015, 39(9): 093102. doi: 10.1088/1674-1137/39/9/093102 shu

RIS(for EndNote,Reference Manager,ProCite)

BibTex

Txt

Milestone

Received: 2014-12-04
Revised: 2015-04-22

Article Metric

Article Views(1911)
PDF Downloads(119)
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

New method of applying conformal group to quantum fields

Received Date: 2014-12-04

Accepted Date: 2015-04-22

Available Online: 2015-09-05

Abstract: Most of previous work on applying the conformal group to quantum fields has emphasized its invariant aspects, whereas in this paper we find that the conformal group can give us running quantum fields, with some constants, vertex and Green functions running, compatible with the scaling properties of renormalization group method (RGM). We start with the renormalization group equation (RGE), in which the differential operator happens to be a generator of the conformal group, named dilatation operator. In addition we link the operator/spatial representation and unitary/spinor representation of the conformal group by inquiring a conformal-invariant interaction vertex mimicking the similar process of Lorentz transformation applied to Dirac equation. By this kind of application, we find out that quite a few interaction vertices are separately invariant under certain transformations (generators) of the conformal group. The significance of these transformations and vertices is explained. Using a particular generator of the conformal group, we suggest a new equation analogous to RGE which may lead a system to evolve from asymptotic regime to nonperturbative regime, in contrast to the effect of the conventional RGE from nonperturbative regime to asymptotic regime.

HTML

Reference (1)

New method of applying conformal group to quantum fields

Abstract：

References

Access

Article Metrics

Metrics

通讯作者: 陈斌, bchen63@163.com

Email This Article

New method of applying conformal group to quantum fields

HTML

目录