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that lacks electroweak theory and QCD, an unacceptable situation since the real world does include these interactions. One way around this problem is to add charges to the ends of the strings, something we will discuss in Chap. 15, but in this chapter we consider a more successful and elegant approach. The idea of heterotic strings was originally proposed by Gross, Harvey, Martinec, and Rohm. They proposed a theory of closed superstrings with decoupled left- and right-moving modes that preserves the best aspects of both theories, producing a theory which is large enough and sophisticated enough to incorporate the features we know the theory must have to include the standard model. By making the rightmoving modes super-symmetric We are able to include fermions in the theory. We keep tachyons out of the theory, so it has a stable vacuum. We incorporate nonabelian gauge theory in the left-moving modes. This is done by adding Majorana-Weyl fermions A to the left-moving sector, without adding supersymmetry. We must eliminate the extra 16 dimensions from the 26-dimension contribution of the bosonic theory. This can be understood by discarding the view that the extra 16 dimensions are space-time dimensions. First, note that The right-moving modes are supersymmetric. So, there are 10 bosonic elds X among the right-moving modes. We keep 10 bosonic elds X from the left-moving modes to match up with the right-moving modes. Since 26 = 10 + 16, we need to cancel the remaining 16 contributions from the unwanted X present in the left-moving sector. Since the A are spinors, we need 32 of them to enable the desired calculation, hence we take A = 1,..., 32 . The symmetry group for the A is SO(32) when all of the A have the same boundary condition. This is the SO(32) heterotic theory.

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This is the heavy lifting method of this class. This is where you do the real work of taking all your particles and making OpenGL-compatible vertex and UV arrays. You first reset vertexIndex, which is the instance variable that will keep track of where you are in the arrays, so it is pretty important.

We can write down the action as follows: It will include a bosonic contribution for left- and right-moving modes for 10 dimensional space-time. It will include fermionic spinors to add supersymmetry to the 10 dimensional space-time. These will only be rightmovers. It will include a contribution from the left-moving A spinors.

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As a telecom industry analyst and author of numerous books about the business and technology sides of the telecom marketplace, I tend to focus on the words used by the people and companies that comprise the industry, because the careless use of those words often leads to misinterpretation, which in turn leads to inappropriate investment and infrastructure decisions To that end, I realized recently that two important words in our technology lexicon are used synonymously The words mobility and ubiquity are not synonyms However, applications, network designs, investment decisions, strategic planning efforts, and end-user device engineering are being done as if they were one and the same At worst, this will lead to another spate of ill-placed investments and the requisite marketplace blowback; at best it will lead to confusion and the resulting slowdown of effective deployment Hopefully, the former won t occur; the latter already has.

So before this gets too far down a dead-end road, let me clarify the difference between the two, beginning with definitions According to the American Heritage Dictionary, mobility means the quality or state of being mobile, while ubiquity is defined as existence or apparent existence everywhere at the same time From a communications perspective, mobility means being able to move freely while staying connected, as when engaging in the increasingly socially unacceptable practice of using a cell phone while driving Ubiquity, on the other hand, means universal connectivity; that is, the ability to count on the presence of a connection of one kind or another from the bottom of the Grand Canyon to the top of Mount McKinley and everywhere in between From a development point-of-view, these two concepts are being used interchangeably, creating confusion and developmental paralysis Consider, for example, Wi-Fi.

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