Is the Polyakov path integral prescription too restrictive?

Details Is the Polyakov path integral prescription too restrictive? Is the Polyakov path integral prescription too restrictive?

1993-06-18

arxiv.org/abs/hep-th/9306090v1

Physics

High Energy Physics

High Energy Physics - Theory

37 pages, harvmac

Scientific paper

In the first quantised description of strings, we integrate over target space co-ordinates $X^\mu$ and world sheet metrics $g_{\alpha\beta}$. Such path integrals give scattering amplitudes between the `in' and `out' vacuua for a time-dependent target space geometry. For a complete description of `particle creation' and the corresponding backreaction, we need instead the causal amplitudes obtained from an `initial value formulation'. We argue, using the analogy of a scalar particle in curved space, that in the first quantised path integral one should integrate over $X^\mu$ and world sheet {\it zweibiens}. This extended formalism can be made to yield causal amplitudes; it also naturally allows incorporation of density matrices in a covariant manner. (This paper is an expanded version of hep-th 9301044)

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