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Additional resources for [Article] On the Structure of Finite Continuous Groups with Exceptional Transformations

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The probability of a state, or a configuration, is proportional to ) P{si} = exp [-/3E{si}] (2-23) and the partition function, which is the generating function, is given by the sum o f P over the 2N configurations Z { Hi} = Z exp [-/3 E{si}] (2-24) {Sil We have introduced the notation 0= (kT)-' and Kij = @Ii,, Hi = @hi. The symbol k is Boltzmann's constant, and T is the temperature. In this discrete model Z{Hj} generates all the correlation functions. Namely: is the average magnetization at site i.

They read: for any pair of normdizable states. Two comments are in place here. , on the operators themselves, leads to the result that there is no scattering. Secondly, if one insists that the equal time commutation relation of the a's - the interacting field - be normalized to a 6 function, as in (3-59), then another constant should be multiplying one of the matrix elements in (3-77). We leave this factor out. Furthermore, we will disregard the distinction between strong and weak asymptotic conditions in intermediate steps, and instead we will avoid using it where the weak condition does not suffice.

When H is quadratic in p , the integration over p proceeds as before. Next we consider two times rl tz , such that t < t 2 < t l t 2 . For r l < t2 the right-hand side is equal to the matrix element of the two operators multiplied in the opposite order.

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[Article] On the Structure of Finite Continuous Groups with Exceptional Transformations by Zeldin S. D.


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