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Holomorphic gauge theory

Part of the Lecture Notes in Mathematics book series (LNM,volume 775)

Abstract

A new invariant way of obtaining interactions from gauge freedom is explored. No use is made of Lagrangians. Instead, the starting point is a scalar quantity of immediate physical interest: the probability density ρ of the particle in phase space, as defined in references [3–6]. This theory is based not on space-time R4 but on the forward tube T, which is interpreted as an extended classical phase space. The probability density ρ is a positive function on T which can be expressed as the fiberwise inner product 〈f, f〉 of the wave function f with itself. Here f is a holomorphic section of the trivial holomorphic vector bundle T × CS, and the inner product is with respect to a fiber metric h: 〈f, f〉 = f*hf. Conservation of probability, combined with holomorphy, leads to an equation for f which is closely related to the Klein-Gordon equation for a particle minimally coupled to a Yang-Mills field. The Yang-Mills potential is uniquely determined as the canonical connection of type (1,0) defined by h.

Keywords

  • Symplectic Form
  • Holomorphic Section
  • Holomorphic Vector Bundle
  • Canonical Connection
  • Wightman Function

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.

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© 1980 Springer-Verlag

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Kaiser, G. (1980). Holomorphic gauge theory. In: Kaiser, G., Marsden, J.E. (eds) Geometric Methods in Mathematical Physics. Lecture Notes in Mathematics, vol 775. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0092024

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  • DOI: https://doi.org/10.1007/BFb0092024

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-09742-6

  • Online ISBN: 978-3-540-38571-4

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