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Local and Covariant Quantization of Linearized Einstein's Equations
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6.The choice of tempered distributions is not strictly necessary. On this point see Ref. 1. Also the spectral condition (d) below is here assumed only for simplicity. The discussion can be carried through without assuming it.
7.Unitarity is intended with respect to the metric operator η of the Hilbert space, on which no hypothesis is made. In this general case U is unitary if .
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12.For example when the indices μ, ν, ρ, σ, are all different Only survives. This implies that must be analytic in Similarly one can see that all the other invariant functions must be analytic in
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14.By vector describing a physical state we mean a vector having a physical meaning. Here and in the following we will call them “physical” states.
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16.Perhaps it is worthwhile noticing that, even if the two‐point function can be calculated simply knowing the definition of the negative frequency part of the definition of the positive frequency part is by no means arbitrary. Indeed the request of locality and Hermiticity for the field uniquely fixes the definition of
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