A Treatment of the Non-polynomial Contributions: Application to Calculate Partition Functions of Strings and Membranes
In this chapter we consider a very interesting way of dealing with the additional term of non-polynomial type that shows up in the series commutation relevant to the zeta-function regularization theorem, as described in the preceding chapters. The asymptoticity of the series is proven for the important cases which are useful in Physics (e.g., sums over non-complete lattices, mainly coming from Neumann and Robin BC) and cannot be dealt with using the otherwise very powerful formulas (as Jacobi’s theta function identity) obtained from Poisson’s summation in many dimensions. Later, a first physical application to calculate the partition function corresponding to string, membrane and, in general, p-brane theories is investigated in detail. Such theories are commonly termed as fundamental, in any attempt at a rigorous description of QED from first principles.
KeywordsPartition Function Zeta Function Additional Term Heat Kernel Asymptotic Series
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