Abstract
We present the Dirac propagator constructed as a directed random walk on a sphere, for Chevalley-Crumeyrolle spinors. The resulting Green function is used, in the framework of a supersymmetric (SUSY) algebraic valued field theory, to represent fermionic and bosonic interactions. This algebraic approach is compared with some other formulations of the problem.
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
Brydges, D., Evans, S.N. and Imbrie, J.: 1992, ‘Self-Avoiding Random Walk on a Hierarchical Lattice in Four Dimensions’, Ann. Prob. Vol. no. 20, pp. 82–124.
Crumeyrolle, A.: 1969, ‘Structures Spinorielles’, Ann. Inst. Henri Poincaré Vol. no. XI, pp. 19—55.
Crumeyrolle, A.: 1971, ‘Groupes de Spinorialité’, Ann. Inst. Henri Poincaré Vol. no. XIV, pp. 309–323.
Crumeyrolle, A.: 1989, ‘Isotropic Vector Fields on Spheres, Spinor Structures on Spheres and Projective Spaces’, Rep. Math. Phys. Vol. no. 28, pp. 27–37.
Fernandez, R., Fröhlich, J. and Sokal, A.D.: 1992, ‘Random Walks, Critical Phenomena and Triv¬iality in Quantum Field Theory’, Springer- Verlag, New York.
de Gennes, P. G.: 1979, “Scaling Concepts in Polymer Physics”, Cornell University Press, Ithaca, New York.
Duplantier, B.: 1989, ‘Statistical Mechanics of Polymer Networks of any Topology’, J. Stat. Phys. Vol. no. 54, pp. 581–680, and references therein.
Jaroszewicz, T. and Kurzepa, P.S.: 1991, ‘Spin, Statistics, and Geometry of Random Walks’, Ann. Phys. Vol. no. 210, pp. 255–322.
Jaroszewicz, T. and Kurzepa, P.S.: 1993, ‘Intersection of Fermionic Paths and Four-Fermion Inter¬actions’, Phys. Lett. B Vol. no. 303, pp. 323–326.
McKane, A.J.: 1980, ‘Reformulation of n? 0 Models Using Anticommuting Scalar Fields’, Phys. Lett.A Vol no. 76, pp. 22–24.
Kazakov, D.I.: 1988, ‘Self-Avoiding Random Walk in Superspace’, Phys.Lett. B Vol no. 215, pp. 129–132.
Lawler, G.F.: 1990, ‘The Edwards Model and the Weakly Self-Avoiding Walk’, Journ. of Phys. A Vol no. 23, pp. 1467–1470.
Lawler, G.F.: 1991, ‘Intersection of Random Walks’, Birkhäuser, Boston.
Parisi, G. and Sourlas, N.: 1979, ‘Random Magnetic Fields, Supersymmetry and Negative Dimen¬sion’, J. Phys. Lett. Vol no. 43, pp. 744–745.
Parisi, G. and Sourlas, N.: 1980, ‘Self-Avoiding Walk and Supersymmetry’, J. Phys. Lett. Vol no. 41, pp. L403-L406.
Rodríguez-Romo, S.: 1993, ‘Algebraic Spinors in Dirac Propagators as a Directed Random Walk’, J. Math. Phys. Vol. no. 34, pp. 4590–4600.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1995 Springer Science+Business Media Dordrecht
About this chapter
Cite this chapter
Rodríguez-Romo, S. (1995). Chevalley-Crumeyrolle Spinors in McKane-Parisi-Sourlas Theorem. In: Ablamowicz, R., Lounesto, P. (eds) Clifford Algebras and Spinor Structures. Mathematics and Its Applications, vol 321. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-8422-7_12
Download citation
DOI: https://doi.org/10.1007/978-94-015-8422-7_12
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-4525-6
Online ISBN: 978-94-015-8422-7
eBook Packages: Springer Book Archive