Quasi local algebra

The quasi-local algebras are generated by the increasing subalgebras set,, which satisfies a number of stmctural relations which will... 

A quasi-local algebra is a C algebra U and a set t/ of C subalgebras, so that the / indices set has the relation of orthogonality and are satisfied the properties ... 

If ffl is a state over an U quasi local algebra, it can be defined as commutative algebra for the associated representation H through ... 

We recall from the first section that we assumed that there exists, for the description of a physical system S, a C -algebra s, the self-adjoint elements of which are observables on il. In specific problems, our first task will therefore be to determine the proper s/ (see, for instance, the case of the quasi-local algebra defined in Section IV), For the moment, we simply assume that we somehow got js/. 

Let U = be a quasi-loeal algebra, whose generator set is formed by the Neumarm algebras. A state o over U is defined as being local normal if w is normal in the restriction to each algebra M. ... 

In terms of algebraic quantum mechanics, the complete set of observables is divided into two classes microscopic observable and macroscopic observables. The microscopic observables are currently identified with the elements of a C algebra U quasi-local. The macroscopic observables do... 

Note that in most physical applications, si is taken as the algebra of quasi-local observables on S (see, e.g., the next section). In this case, the translation group (and hence the euclidian group) does act in an r -abelian manner on all on as a consequence of locality (i.e, the fact that two observables relative to disjoint regions of space commute). The question of whether the time-evolution acts in the same manner is much more delicate, and on the basis of explicit solutions of known models, we know that this property is by no means guaranteed in general,... 

Under the foregoing assumptions, we now define our C -algebra of quasi-local observables. We first remark that to every finite collection ft... 

Then (see Section IVC) , exists, giving proper time-evolution on the algebra = Uj3/(Q) of quasi-local observables on our system. 

Fig. 15.6(c)]. At the center of each element there is a node. The nodes of adjacent elements are interconnected hy links. Thus, the total flow field is represented by a network of nodes and links. The fluid flows out of each node through the links and into the adjacent nodes of the network. The local gap separation determines the resistance to flow between nodes. Making the quasi-steady state approximation, a mass (or volume) flow rate balance can be made about each node (as done earlier for one-dimensional flow), to give the following set of algebraic equations... 

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