publication . Article . Preprint . 2010

SU(N) irreducible Schwinger bosons

Mathur, Manu; Raychowdhury, Indrakshi; Anishetty, Ramesh;
Open Access
  • Published: 29 Mar 2010 Journal: Journal of Mathematical Physics, volume 51, page 93,504 (issn: 0022-2488, eissn: 1089-7658, Copyright policy)
  • Publisher: AIP Publishing
Abstract
We construct SU(N) irreducible Schwinger bosons satisfying certain U(N-1) constraints which implement the symmetries of SU(N) Young tableaues. As a result all SU(N) irreducible representations are simple monomials of $(N-1)$ types of SU(N) irreducible Schwinger bosons. Further, we show that these representations are free of multiplicity problems. Thus all SU(N) representations are made as simple as SU(2).
Subjects
arXiv: High Energy Physics::Phenomenology
free text keywords: Mathematical Physics, Statistical and Nonlinear Physics, Boson, Gauge theory, Quantum field theory, Physics, Representation theory of SU, Lie group, Multiplicity (mathematics), Quantum mechanics, Lattice gauge theory, Irreducible representation
17 references, page 1 of 2

[1] J. Schwinger U.S Atomic Energy Commission Report NYO-3071, 1952 or D. Mattis, The Theory of Magnetism (Harper and Row, 1982).

[2] Marshalek E R, Phys. Rev. C 11, (1975) 1426.

[3] Auerbach A and Arovas D P, Phys. Rev. Lett. 61, 617 (1988). Auerbach A 1994 Interacting Electrons and Quantum Magnetism (Berlin: Springer). Sachdev S and Read N, Nucl. Phys. B 316 609 (1989).

[4] Gunaydin M and Saclioglu C, Commun. Math. Phys. 87, 159 (1982). Gunaydin M and Saclioglu C, Phys. Lett. B 108, 180 (1982).

[5] Manu Mathur, Nucl. Phys. B 779, 32 (2007). Manu Mathur, Phys. Lett. B 640, 292 (2006). Manu Mathur, J. Phys. A 38, 10015 (2005). Chandrasekharan S and Wiese U J, Nucl. Phys. B 492, 455 (1997).

[6] Florian Girelli, Etera R. Livine, Class.Quant.Grav. 22, 3295 (2005). N. D. Hari Dass, Manu Mathur, Class.Quant.Grav. 24, 2179 (2007).

[7] M. Moshinsky, Rev. Mod. Phys. 34, 813 (1962); J. Math. Phys. 4, 1128 (1963).

[8] I.N. Bernstein, I.M. Gelfand, S.I. Gelfand, Funct. Anal. Appl. 9, 322 (1975). I.M. Gelfand and A.V. Zelevinskii, Funct. Anal. Appl. 18, 183 (1984). Bemstein I N, Gelfand I M and Gclfand S I 1976 Proc Pefrovskij Sem. 2 3 Reprinted in Gelfand I 1988 Collecfed Works VoL 1 (Berlin: Springer) p 464.

[9] J. J. De Swart, Rev. Mod. Phys. 35, 916 (1963). J. D. Louck, Am. J. Phys. 38, 3 (1970). C. Itzykson, Rev. Mod. Phys. 38, 95 (1966). Arisaka N, Prog. Theor. Phys. 47, 1758 (1972). N. Mukunda and L. K. Pandit, J. Math. Phys. 6, 746 (1965). M. Resnikoff, J. Math. Phys. 8, 63 (1967). P. Jasselette, Nucl. Phys. B 1, 521 (1967); ibid 529. P. Jasselette, J. Phys. A: Math. Gen., 13, 2261, (1980). Biedenhm L C, J. Math. Phys. 4 436 (1963). R. Anishetty, H. Gopalkrishna Gadiyar, M. Mathur and H. S. Sharatchandra, Phys. Lett. B 271, 391 (1991).

[10] J. S.Prakash and H. S. Sharatchandra, J. Math. Phys. 37, 6530 (1996) and references cited therein.

[11] J. S. Prakash and H. S. Sharatchandra, J. Phys. A 26, 1625 (1993).

[12] Biedenharn, L.C., Flath, D.E., Commun. Math. Phys. 93 , 143 (1984). A. J. Bracken, Commun. Math. Phys. 94, 371 (1984). A J Bracken and J H MacGibbon, J. Phys. A: Math. Gen. 17 2581 (1984) (and references cited therein).

[13] Manu Mathur and Diptiman Sen, J. Math. Phys. 42, 4181 (2001).

[14] S. Chaturvedi and N. Mukunda, J. Math. Phys. 43, 5262 (2002).

[15] Ramesh Anishetty, Manu Mathur, Indrakshi Raychowdhury, J. Math. Phys. 50, 053503 (2009).

17 references, page 1 of 2
Powered by OpenAIRE Open Research Graph
Any information missing or wrong?Report an Issue
publication . Article . Preprint . 2010

SU(N) irreducible Schwinger bosons

Mathur, Manu; Raychowdhury, Indrakshi; Anishetty, Ramesh;