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A representation of the Belavkin equation via Feynman path integrals

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Abstract.

 The Belavkin equation, describing the continuous measurement of the position of a quantum particle, is studied. A rigorous representation of its solution by means of an infinite dimensional oscillatory integral (Feynman path integral) defined on the complex Cameron-Martin space is given.

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Received: 7 January 2002 / Revised version: 20 June 2002 / Published online: 19 December 2002

Mathematics Subject Classification (2000): 81, 81S40, 60H15

Key words or phrases: Belavkin equation – Continuous measurement – Quantum theory – Oscillatory integrals – Feynman path integrals

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Albeverio, S., Guatteri, G. & Mazzucchi, S. A representation of the Belavkin equation via Feynman path integrals. Probab Theory Relat Fields 125, 365–380 (2003). https://doi.org/10.1007/s00440-002-0231-5

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Keywords

  • Continuous Measurement
  • Path Integral
  • Quantum Particle
  • Feynman Path
  • Rigorous Representation