are some situations in which the entire correlation function is needed in order to properly formulate the sum rule. For example, some terms in the correlation function may be singular at the branch point. This occurs in Chapter 3, for instance. In this case, the integrand in Eq. (1.95) is singular at the lower limit of integration. However, this difficulty can be overcome by noting that contribution to the inverse Laplace transform from the integration contour I$_{η}$ in Eq. (1.93) is singular as the radius of the contour is taken to zero. This compensates for the integration divergence in Eq. (1.95). In this way a limiting procedure can be developed such that the integration in Eq. (1.95) is well-defined. In order to do so the entire correlation function Π ( Q $^{2}$) must be known, however. In QSR analyses we typically wish to study a hadronic state | h 〉 with certain J PC quantum numbers. To do so, we define a current J with the same quantum numbers that couples to the hadronic state where Λ is a dimensionful constant and f$_{h}$ is a dimensionless factor that measures how strongly the hadronic state | h 〉 couples to the current J . The current is a local composite operator composed of quark and gluon fields that approximate the valence quark and gluon content of the hadronic state | h 〉 . However, it is important to note that more than one current J may couple to a single hadronic state. Chapter 6 explores such a scenario. Once the current J has been constructed, we form the correlation function which can be calculated using the perturbative expansion (1.19). However, as mentioned previously the QCD coupling becomes large at hadronic energy scales and hence a purely perturbative approach cannot adequately describe low energy phenomena. In QSR, confinement is assumed to exist, and its effects are parametrized through the 41 Π $^{(}$Q 2 ) = i$^{∫}$ d $^{4}$x e iq · $^{x}$〈 Ω | T $^{[}$J ( x ) J $^{†}$(0) ] | Ω 〉 , Q 2 = − q $^{2}$, (1.97) 〈 Ω | J | h 〉 = Λ f$_{h}$ (1.96) 1.4.3 Operator Product Expansion