Chinese Physics C > 1989, Vol. 13 > Issue(5): 419-428

ON GEOMETRIC QUANTIZATION FOR THE BOSONIC STRINGS(1)

YU Yue^,,
GUO Han-Ying

Institute of High Energy Physics,Academia Sinica,Beijing2 Institute of Theoretical Physics,Academia Sinica,Beijing

Abstract
HTML
Reference
Related

PDF

Abstract：
The geometric quantization for bosonic strings is discussed in this paper.Relations among different polarizations and representations of operators in different polarizations are given.It is pointed out that the prequantization Hilbert space is the unitary representation of the conformal group where the centre term of Virasoro algebra does not exist but this representation is reducible.By polarization it is reduced into two projective representations with the phase factors with opposite signs.Then the conformal anomaly is obtained.In the viewpoint of geometric quantization,the emergence of the conformal anomaly stems from the fact that polarization is introduced because the quantum states of string must satisfy the uncertainty relation but all generators of conformal transformation don't preserve the same polarization.

References

[1]

J. Scherk, Rev. Mod. Phys., 17(1975), 123;P. Goddard and C. B. Thorn, Phys. Lett., 40B(1972), 235.[2] J. Sniatycki. Geometric Quantization and Quantum Mechanics (Springer-Verlag. New York (1980).[3] N. J. Woodhouse, Geometric Quantization (Clarendon Press, Oxford, UK (1980).[4] M. Bowick and S. G. Rajeev, Nucl. Phys., B293(1987), 348; Phys. Rev. Lett., 58(1987), 353; MIT preprints CTP 1494(1987).D. Harri, D. K. Hong, P. Ramond and V. G. Rodgers, Florida preprints, UFTP-87-10.[5] M. J. Gotay, J. M. Nester and G. Hinds, J. Math. Phys., 19(1978), 2388.M. J. Gotay. J. Math. Phys., 27(1986), 2051.A. Ashtekar and M. Stillerman, J. Math. Phys. 27(1986), 1393.

[1]	LIAO Ling,HUANG Yong-Chang. Faddeev-Jackiw Quantization of the Gauge Invariant Self-Dual Fields Relative to String Theory. Chinese Physics C, 2006, 30(3): 191-195.
[2]	Feng Shengzu,Ruan Tunan. Comments on the Bosonnization Technique of Fermions. Chinese Physics C, 1999, 23(11): 1119-1124.
[3]	Guo Shuohong,Fang Xiyan. Quantization of Lattice Chern-Simons Theory. Chinese Physics C, 1994, 18(8): 706-714.
[4]	Wang Renchuan,Zhu Dongpei. On the Quantization of Interacting Fields in QED. Chinese Physics C, 1994, 18(11): 1012-1019.
[5]	HOU Bo-Yu,YANG Huan-Xiong. The Hamiltonian Formalism and Quantizations of (Generalized) BFOFW Model. Chinese Physics C, 1993, 17(6): 524-533.
[6]	SHEN Qixing,YU Hong. Determination of the Spin-parity of the Boson Resonance X for the Process J/ψ→V₁+X,X→γ+V₂. Chinese Physics C, 1993, 17(11): 988-992.
[7]	CHEN Yong-Qing. q-Oscillator Representations of the Quantum Superalgebra spl_q(2,1). Chinese Physics C, 1993, 17(7): 631-635.
[8]	MIAO Yan-Gang. BFV Quantization of the Bosonized Schwinger Model. Chinese Physics C, 1993, 17(5): 407-411.
[9]	FEI Shao-Ming,YU Yue. THE BKS DERNEL OF BOSONIC STRINGS AND PATH INTEGRAL. Chinese Physics C, 1989, 13(4): 334-338.
[10]	NI Guang-Jiong,WANG Rong-Tai,CHEN Su-Qing. THE NONABELIAN BOSONIZATION OF FERMION FIELDS IN (1+1) DIMENSIONS BY PATH INTEGRAL METHOD. Chinese Physics C, 1989, 13(2): 135-141.
[11]	SUN Yi,JING Si-Cong,RUAN Tu-Nan. QUANTIZATION OF BOSON STRING WITH WEYL ORDERING. Chinese Physics C, 1989, 13(5): 411-418.
[12]	YU Yue. SYMPLECTIC STRUCTURES AND QUANTIZATION FOR BOSONIC STRINGS IN BRST FORMALISM. Chinese Physics C, 1989, 13(1): 92-96.
[13]	YU Yue,GUO Han-Ying. ON GEOMETRIC QUANTIZATION FOR BOSONIC STRING (Ⅱ). Chinese Physics C, 1989, 13(6): 503-511.
[14]	XU Kai-Wen. COVARIANT AND QUANTIZATION OF SPINNING STRING IN M_d×G SPACE-TIME. Chinese Physics C, 1988, 12(3): 315-323.
[15]	CHEN Ren. STOCHASTIC QUANTIZATION WITH SPIN 3/2 FIELD. Chinese Physics C, 1987, 11(2): 157-163.
[16]	HUANG CHAO-SHANG. THE LARGE MOMENTUM BEHAVIOR OF THE ELECTROMAGNETIC TRANSITION FORM FACTOR F_A₁π(q²) IN QCD. Chinese Physics C, 1982, 6(2): 168-175.
[17]	Wu Jing-yuan. QUANTIZATION OF THE PHOTON FIELD AND DIPOLE GHOSTS. Chinese Physics C, 1980, 4(3): 291-301.
[18]	YAN MU-LIN,BAO XI-MING,ZHAO BAO-HENG. CANONICAL QUANTIZATION OF GAUGE FIELDS (Ⅲ)——GRAVITATIONAL FIELD. Chinese Physics C, 1979, 3(5): 582-594.
[19]	ZHAO BAO-HENG,YAN MU-LIN. CANONICAL QUANTIZATION OF GAUGE FIELDS (I)——THE YANG-MILLS FIELD. Chinese Physics C, 1978, 2(6): 501-510.
[20]	GU CHAO-HAO. THEU₁GAUGE FIELD IN ASU_NGAUGE FIELD AND THE QUANTIZED VALUES OF DUAL CHARGES. Chinese Physics C, 1978, 2(4): 295-304.

Access

Get Citation

YU Yue and GUO Han-Ying. ON GEOMETRIC QUANTIZATION FOR THE BOSONIC STRINGS(1)[J]. Chinese Physics C, 1989, 13(5): 419-428.

YU Yue and GUO Han-Ying. ON GEOMETRIC QUANTIZATION FOR THE BOSONIC STRINGS(1)[J]. Chinese Physics C, 1989, 13(5): 419-428. shu

RIS(for EndNote,Reference Manager,ProCite)

BibTex

Txt

Milestone

Received: 1900-01-01
Revised: 1900-01-01

Article Metric

Article Views(3623)
PDF Downloads(470)
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

ON GEOMETRIC QUANTIZATION FOR THE BOSONIC STRINGS(1)

YU Yue^,
GUO Han-Ying

Corresponding author:YU Yue,

Institute of High Energy Physics,Academia Sinica,Beijing2 Institute of Theoretical Physics,Academia Sinica,Beijing

Received Date:1900-01-01
Accepted Date:1900-01-01
Available Online:1989-05-05

Abstract:The geometric quantization for bosonic strings is discussed in this paper.Relations among different polarizations and representations of operators in different polarizations are given.It is pointed out that the prequantization Hilbert space is the unitary representation of the conformal group where the centre term of Virasoro algebra does not exist but this representation is reducible.By polarization it is reduced into two projective representations with the phase factors with opposite signs.Then the conformal anomaly is obtained.In the viewpoint of geometric quantization,the emergence of the conformal anomaly stems from the fact that polarization is introduced because the quantum states of string must satisfy the uncertainty relation but all generators of conformal transformation don't preserve the same polarization.