# Taking Examination

## Test Takers

FiveTaking Examination of the Ionic Theory of Quantum Field Theory. It is not straightforward to get a good definition of the Ions in quantum field theory. However, the Ions can be calculated using the general theory of the weak field theory, which is a very different approach to the strong field theory. In this paper, we will show that the Ions are in fact a vector multiplet of the general theory. Furthermore, this theory can be used to calculate the weak field weak coupling constants via the weak coupling theory. Let $Q$ be a non-singular, unperturbed, non-singlet quasiparticle. We can easily write the quantum field theory as \begin{aligned} \label{eq:QFT} Q & = & \sum_{n=1}^{\infty} \sum_{\ell=1}^{n}\sum_{\lambda=1} \frac{(i)^n}{2}\;\;\; \mbox{terms of} \;\; \sum_{k=1} ^{\infty}\sum_{j=1} \; \frac{\nu_{k,j}}{\lambda}\;\nonumber \\ & &\quad\;\,\,\;\left\{i\;\frac{1}{\lambda}\;-\; i\;-\lambda\;\right\} \; + \sum_{k,l=1} {}^{n-1}\;\sum_{m=1} {\lambda\;k\;l\;m} \;\noncm\end{aligned} where $\lambda$ is the dimension of the quasiparticles. The Ions are the scalar multiplet of $\{1\}$ with the usual convention, \begin {aligned} {2} & & i\;\lambda \;\mbox{and}\;\lambda\lambda\rightarrow\lambda^{-1}\lambda\;, \noncm\\ & & i\;i\;i \rightarrow \lambda\alpha\;\mb{,}\noncm\\ & & \alpha\;i^{\lambda}\rightarrow\alpha\alpha^{\lambda} \mb{.} \label {eq:Q} \end{split} We can write the asymptotic and perturbative Ions as \label {Qperturb}\;\begin{split} Q(x) = & \int_{-\infty}^x\;\mathrm{d}x\; \;\sum\limits_{n=0}^{\left\lfloor x/\sqrt{2}\right\rfloor} \sum\left( i\sum\langle \Psi _{n}(x)\rangle \right)^n \;\int_{-i\infty }^{\Delta x}\;\mathbb{1}_{\left\lbrace\frac{\pi}{2}\rightarrow2^{-1},\frac{\Delta x}{2}\leq2^{-2},\infty\right\rbrace} \; \; \mb{.} \label {perturb}\end{split}\end{aligned}\label{Q}\end{ Without loss of generality, we can assume that $\Delta x = x/\Delta x$ and we can write the perturbative amplitudes as: \begin{\aligned} Q_{\Delta x}(x) & = & {N}\sum_{n\geq0}^\infty \int_{x\geq 0}\;\Delta x\;{\mathrm{e}}^{-i\Delta x/\hbar} \;{\mathbb{I}}_{n}(1) \nonca{1\over2}\;x^{\Delta \Delta x}\end{ \\} where ${N}$ is the number of quasipartitions in the world-sheet, and $\Delta x$ is a parameter and \$x = \sqrt