Dimensional regularization examples

Any deviation from the ideal three-dimensional regularity of the polymer crystal structure. Note Examples of structural disorder in crystalline polymers are given in Table 2. 

Let us now present an example of simple but striking identity which is valid in dimensionally regularized quantum mechanics but would be wrong in other regularization schemes. Consider the following integral ... 

Returning focus to the more traditional use of the term "polymer", Fox [18] examines what, in common parlance, is referred to as "regularly crosslinked" vs. randomly crosslinked polymers. As an example of a general two dimensional regularly crosslinked polymer, consider the polymer depicted in Figure 12. Although this polymer has fourteen... 

For practical purposes various methods of introducing the regulators are used. The most standard one is the cut-off regularization in 4-momentum space. The other options are the Pauli-Willars regularization [21] or the dimensional regularization (see, for example, [22]). 

EXAMPLE Consider a simple but non-trivial STG consisting of two nodes and three arcs (the reader can check that this regular language actually characterizes the attractors of many one dimensional CA - rules R12, R56 and 162, among others) ... 

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