Abstract
The new approach to quantum mechanical problems is proposed. Quantum states are represented in an algebraic program, by lists of variable length, while operators are well defined functions on these lists. Complete numerical solution of a given system can then be automatically obtained. The method is applied to Wess-Zumino quantum mechanics and D = 2 and D = 4 supersymmetric Yang-Mills quantum mechanics with the SU(2) gauge group. Convergence with increasing size of the basis was observed in various cases. Many old results were confirmed and some new ones, especially for the D = 4 system, are derived. Preliminary results in higher dimensions are also presented. In particular the spectrum of the zero-volume glueballs in 4 < D < 11 is obtained for the first time.
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
Preview
Unable to display preview. Download preview PDF.
References
E. Witten, Nucl. Phys. B185/188 (1981) 513.
F. Cooper, A. Khare and U. Sukhatme, Phys. Rep. 251 (1995) 267, hep-th/9405029.
M. Claudson and M. B. Halpern, Nucl. Phys. B250 (1985) 689; J. Greensite and M. B. Halpem, Nucl. Phys. B242 (1984) 167.
T. Banks, W. Fishier, S. Shenker and L. Susskind, Phys.Rev. D55 (1997) 6189; hep-th/9610043.
B. de Wit, M. Lüscher and H. Nicolai, Nucl. Phys. B320 (1989) 135.
M. Lüscher, Nucl. Phys. B219 (1983) 233.
M. Lüscher and G. Münster, Nucl. Phys. B232 (1984) 445.
P. van Baal, Acta Phys. Polon. B20 (1989) 295; also in At the Frontiers of Particle Physics Handbook of QCD, Boris loffe Festschrift, vol. 2, ed. M. Shifman (World Scientific, Singapore 2001) p.683; hep-ph/0008206.
J. Polchinski, String Theory, Cambridge University Press, Cambridge, 1998.
S. Sethi and M. Stern, Comm. Math. Phys. 194 (1998) 675; P. Yi, Nucl. Phys. B505 (1997) 307; A. V. Smilga, Nucl. Phys. B266 (1986) 45.
G. Moore, N. Nekrasov and S. Shatashvili, Commun. Math. Phys. 209 (2000) 77; M.B. Green and M. Gutperle, JHEP 01 (1998) 005.
W. Krauth and M. Staudacher, Nucl. Phys. B584 (2000) 641, hep-th/0004076.
D. Kabat, G. Lifschytz and D. A. Lowe, Phys. Rev. D64 (2001) 124015, hep-th/0105171.
R. A. Janik and J. Wosiek, Acta Phys. Polon B32 (2001) 2143, hep-th/9903121; P. Bialas and J. Wosiek, Nucl. Phys. B (Proc. Suppl.) 106 (2002) 968, hep-lat/0111034.
H. Aoki et al., Prog. Theor. Phys. Suppl. 134 (1999) 47, hep-th/9908038.
J. Ambjorn, K.N. Anagnostopoulos and A. Krasnitz, JHEP 0106 (2001) 069.
J. Wosiek, hep-th/0203116.
J. Kogut and L. Susskind, Phys. Rev. D11 (1975) 395.
Y. Matsumura, N. Sakai and T. Sakai, Phys. Rev. D52 (1995) 2446.
J. R. Hiller, S. Pinsky and U. Trittmann, hep-th/0112151; hep-th/0106193.
M. A. Shifman, ITEP Lectures on Particle Physics and Field Theory, World Scientific, Singapore, 1999.
M. B. Halpern and C. Schwartz, Int. J. Mod. Phys. A13 (1998) 4367, hep-th/9712133.
C. Itzykson and J.-B. Zuber, Quantum Field Theory, McGraw-Hill, New York, 1980.
P. Jordan and E. P. Wigner, Z. Phys. 47 (1928) 631.
P. van Baal, hep-th/0112072.
J. Trzetrzelewski and J. Wosiek, in preparation.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2002 Springer Science+Business Media Dordrecht
About this chapter
Cite this chapter
Wosiek, J. (2002). Supersymmetric Yang-Mills Quantum Mechanics. In: Greensite, J., Olejník, Š. (eds) Confinement, Topology, and Other Non-Perturbative Aspects of QCD. NATO Science Series, vol 83. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-0502-9_33
Download citation
DOI: https://doi.org/10.1007/978-94-010-0502-9_33
Publisher Name: Springer, Dordrecht
Print ISBN: 978-1-4020-0874-0
Online ISBN: 978-94-010-0502-9
eBook Packages: Springer Book Archive