In this chapter, we exploit ’t Hooft-Polyakov monopole to construct closed algebra of quantum field operators and BRST charge Q. In a first class configuration of Dirac quantization, by including Q-exact gauge fixing term and Faddeev-Popov ghost term, we find the BRST invariant Hamiltonian to investigate de Rham cohomology group structure for the monopole system. Bogomol’nyi bound is also discussed in terms of the first class topological charge defined on the extended internal two-sphere [134].
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
P.A.M. Dirac, Lectures in Quantum Mechanics (Yeshiva University, New York, 1964)
I.A. Batalin, E.S. Fradkin, Phys. Lett. B 180, 157 (1986)
A.J. Niemi, Phys. Lett. B 213, 41 (1988)
T. Fujiwara, Y. Igarashi, J. Kubo, Nucl. Phys. B 341, 695 (1990)
Y.W. Kim, S.K. Kim, W.T. Kim, Y.J. Park, K.Y. Kim, Y. Kim, Phys. Rev. D 46, 4574 (1992)
S.T. Hong, Y.J. Park, K. Kubodera, F. Myhrer, Mod. Phys. Lett. A 16, 1361 (2001)
S.T. Hong, Y.J. Park, Phys. Rep. 358, 143 (2002)
E.S. Fradkin, G.A. Vilkovisky, Phys. Lett. B 55, 224 (1975)
S. Hamamoto, Prog. Theor. Phys. 95, 441 (1996)
G. ’t Hooft, Nucl. Phys. B 79, 276 (1974)
A.M. Polyakov, JETP Lett. 20, 194 (1974)
S.T. Hong, Mod. Phys. Lett. A 25, 2529 (2010)
J.J. Rotman, An Introduction to Algebraic Topology (Springer, Heidelberg, 1988)
T. Frankel, The Geometry of Physics (Cambridge University Press, Cambridge, 1997)
R. Rajaraman, Solitons and Instantons (North-Holland, Amsterdam, 1984)
P.A.M. Dirac, Proc. R. Soc. A 133, 60 (1931)
T.T. Wu, C.N. Yang, Phys. Rev. D 14, 437 (1976)
S.T. Hong, J. Lee, T.H. Lee, P. Oh, Phys. Rev. D 72, 015002 (2005)
S.T. Hong, J. Lee, T.H. Lee, P. Oh, Mod. Phys. Lett. A 22, 1481 (2007)
B. Grossman, Phys. Lett. B 152, 93 (1985)
L. Baulieu, B. Grossman, R. Stora, Phys. Lett. B 180, 95 (1986)
J. Arafune, P.G.O. Freund, C.J. Goebel, J. Math. Phys. 16, 433 (1975)
L.D. Faddeev, V.N. Popov, Phys. Lett. B 25, 29 (1967)
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2015 Springer Science+Business Media Dordrecht
About this chapter
Cite this chapter
Hong, ST. (2015). De Rham Cohomology in Constrained Physical System. In: BRST Symmetry and de Rham Cohomology. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-9750-4_9
Download citation
DOI: https://doi.org/10.1007/978-94-017-9750-4_9
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-017-9749-8
Online ISBN: 978-94-017-9750-4
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)