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In this paper about a global theory of supermanifolds, Alice Rogers develops the theory of supermanifolds as they underly supersymetric field theories from a rigorous but physicist-fiedly differential--geometric point of view from their topoligical scratch and also puts some additional structures as vector fields and tangent spaces on them. She also compares the $G^{\infty}$ or deWitt supermanifolds to the algebra-geometric approach of for example Konstant or Leites.

Alice Roger's 2007 textbook explains the supermathematics needed for doing superphysics and contains more applications to different physics topics such as $N=1$ supersymmetry, supergravity, some aspects of string theory, or Brownian motion from the same nice differential-geometric point of view.

Dilaton
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  • 3
  • 16