Work for Camilo to do.

[ndattani]

1. After the sentence "Using the integral representation we could obtain that:the expected value for the displacement operator", there should be some explanation of where this first equation comes from. For example, there is a \pi and an N, whereas before there was not.

[ndattani]

2. "From the definition B10* = <B0+B1->..." seems to start by using B10* rather than deriving the expression using the D operator. Please derive it the way B10 was derive (using the D operator).

[ndattani]

3. Fix H_I section so that it looks nice like H_s section. This is the last section before "free energy minimization".

[ndattani]

4. Change dv to dt^\prime in integrals.

[ndattani]

5. After: "As the combined system and environment is closed, within the interaction picture the system-environment density operator evolves according to", all \rho should be \rho_T

[ndattani]

\tilde{B_i}(t) is defined using H_B instead of U, which is defined in terms of H_s. This needs to be explained.

[ndattani]

It appears that all the Lambda(tau) expressions should be in terms of B_i rather than B ?

[ndattani]

It seems we have define the Lambda(tau) in two separate parts. Once seems to be correlation functions of B_i, B_j, while the other seems to involve B_i,z and B_j,z