Communications in Mathematical Physics

, Volume 177, Issue 1, pp 13–25 | Cite as

Supersymmetry, vacuum statistics, and the fundamental theorem of algebra

  • Donald Spector


I give an interpretation of the fundamental theorem of algebra based on supersymmetry and the Witten index. The argument gives a physical explanation of why a real polynomial of degreen need not haven real zeroes, while a complex polynomial of degreen must haven complex zeroes. This paper also addresses in a general and model-independent way the statistics of the perturbative ground states (the states which correspond to classical vacua) in supersymmetric theories with complex and with real superfields.


Neural Network Statistical Physic Complex System Nonlinear Dynamics Vacuum Statistic 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Ahlfors, Lars V.: Complex Analysis: An Introduction to the Theory of Analytic Functions of One Complex Variable. New York: McGraw-Hill, 1966Google Scholar
  2. 2.
    Alvarez-Gaumé, L.: Supersymmetry and the Atiyah-Singer Index Theorem. Commun. Math. Phys.90, 161–173 (1983)CrossRefGoogle Scholar
  3. 3.
    Spector, D.: Supersymmetry and the Möbius Inversion Function. Commun. Math. Phys.127, 239–252 (1990)Google Scholar
  4. 4.
    Witten, E.: Dynamical Breaking of Supersymmetry. Nucl. Phys.B188, 513–554 (1981)CrossRefGoogle Scholar
  5. 5.
    Witten, E.: Constraints on Supersymmetry Breaking. Nucl. Phys.B202, 253–316 (1982)CrossRefGoogle Scholar
  6. 6.
    Witten, E.: Topological Quantum Field Theory. Commun. Math. Phys.117, 353–386 (1988)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag 1996

Authors and Affiliations

  • Donald Spector
    • 1
  1. 1.Department of Physics, Eaton HallHobart and William Smith CollegesGenevaUSA

Personalised recommendations