Understand Logic of Wald & Zoupas' Expression on Conserved Quantities

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Wald and Zoupas explore the concept of conserved quantities in diffeomorphism invariant theories, presenting a specific expression in their work. The discussion centers on the clarity and understanding of this expression, particularly its logical foundations. Participants seek clarification on the intricacies of the expression and its implications. The need for specific questions regarding the expression's components and their meanings is emphasized. Overall, the conversation aims to demystify the logic behind Wald and Zoupas' formulation.
qinglong.1397
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Wald and Zoupas discussed the general definition of ``conserved quantities" in a diffeomorphism invariant theory in this work. In Section IV, they gave one expression (33) in the linked article. I cannot really understand the logic of this expression. Would you please help me with this?
 
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qinglong.1397 said:
I cannot really understand the logic of this expression

You're going to have to be more specific. What about the expression don't you understand?
 
In an inertial frame of reference (IFR), there are two fixed points, A and B, which share an entangled state $$ \frac{1}{\sqrt{2}}(|0>_A|1>_B+|1>_A|0>_B) $$ At point A, a measurement is made. The state then collapses to $$ |a>_A|b>_B, \{a,b\}=\{0,1\} $$ We assume that A has the state ##|a>_A## and B has ##|b>_B## simultaneously, i.e., when their synchronized clocks both read time T However, in other inertial frames, due to the relativity of simultaneity, the moment when B has ##|b>_B##...

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