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For simplicity, in what follows we choose the system of units so that 1.
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For simplicity, in what follows we choose the system of units so that 1.
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jbk
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Due to the overcompleteness of the coherent states, there are several ways to perform the semiclassical approximation of the propagator, resulting from different quantization schemes (choices of operator ordering). Each one of these corresponds to a distinct correction term.
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Due to the overcompleteness of the coherent states, there are several ways to perform the semiclassical approximation of the propagator, resulting from different quantization schemes (choices of operator ordering). Each one of these corresponds to a distinct correction term.
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49
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79959687239
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A focal point represents a crossing between trajectories when projected onto a particular subspace of the complete phase space.
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A focal point represents a crossing between trajectories when projected onto a particular subspace of the complete phase space.
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Note that for simplicity of notation, we omit the subindex f for the final condition of the semiclassical propagator. In this way we also emphasize the role of the variables w as coordinates of a classical phase space in which we can represent the quantum states and operators.
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Note that for simplicity of notation, we omit the subindex f for the final condition of the semiclassical propagator. In this way we also emphasize the role of the variables w as coordinates of a classical phase space in which we can represent the quantum states and operators.
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Notice that the action S (except for the boundary term) and the correction term I are real valued when calculated on the principal trajectory. This property makes the removal of the principal trajectory by the heuristic filter a very unlikely event, as can be inferred from the discussion below from inequality.
-
Notice that the action S (except for the boundary term) and the correction term I are real valued when calculated on the principal trajectory. This property makes the removal of the principal trajectory by the heuristic filter a very unlikely event, as can be inferred from the discussion below from inequality.
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