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Weinberg argues (Weinberg, QFT, Volume 1) that an expression for the anihilation operator acting on a state vector when all particles are either all bosons or all fermions is $$a(q) \Phi_{q_1 q_2 ... q_N} = \sum_{r=1}^{N} ( \pm 1)^{r+1} \delta (q - q_r) \Phi_{q_1...q_{r-1} q_{r+1}...q_N}$$ I carefully tried to reproduce the scalar product of this state vector with another state vector, but I have not found the above expression to satisfy their inner product, for one thing: the plus sign in the exponent in ##( \pm 1)^{r+1}##. It seems that it only agrees with the expression for the inner product if the sign is "##-##". Am I missing something else or is that sign a typo?

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# I Anihilation operator expression: is there a typo here?

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