Stochastic Description of Supersymmetric Fields with Values in A Manifold

  • Zbigniew Haba
Part of the NATO ASI Series book series (NSSB, volume 144)


The mathematical problem of the (imaginary time) quantum mechanics of a particle moving in a Euclidean space can be considered as a problem from the theory of diffusion processes. The generator of the diffusion process coincides (up to a similarity transformation [1]) with the Hamiltonian of quantum mechanics. The diffusion process can be defined as well by a stochastic equation [2]. The stochastic equation describes the diffusion process as a time evolution of a Brownian particle in a force field. Some forces (like the gravitational one), have a geometrical origin. We wish to suggest in this lecture that the time evolution of some (quantum) Euclidean fields is like a free (geodesic) motion on a curved manifold.


Brownian Particle Stochastic Equation Conformal Supergravi Fermi Field Supersymmetric Quantum Mechanic 
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Copyright information

© Plenum Press, New York 1986

Authors and Affiliations

  • Zbigniew Haba
    • 1
  1. 1.Inst. of Theor. Phys.University of WrocławPoland

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