The extension to the (noncommutative) Standard Model and beyond-Standard Model physics is conceptually straightforward, and will be discussed as well. Such physics merits a more elaborate investigation which we reserve for later work.

This paper is organised as follows. In Section 2, we will review twisted quantization on noncommutative spaces and gauge theories based on this formalism. Section 3 will elaborate the LSZ formalism for twisted quantisation and discuss in detail the Gell-Mann-Low formula and its modifications on the GM plane. In Section 4, we will summarise our rules for twisted quantum field theories followed by application of the same to spontaneously broken theories and Higgs mechanism on the GM plane in Sec.5. Our conclusions and future outlook are in Section 6.

Twisted Quantization
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The algebra of functions ${\cal A}_\theta({\mathbb R}^N)$ on the GM plane consists of smooth functions on ${\mathbb R}^N$, with the multiplication map $$\begin{aligned}
m_\theta: {\cal A}_\theta ({\mathbb R}^N) \otimes {\cal A}_\theta
({\mathbb R}^N) &\rightarrow& {\cal A}_\theta ({\mathbb R}^N)\,,
\nonumber \\
\alpha \otimes \beta &\rightarrow& \alpha \;e^{\frac{i}{2}
  \overleftarrow{\partial}_\mu \theta^{\mu \nu}
  \overrightarrow{\partial}_\nu} \ \beta := \alpha \ast \beta
\label{starmult}\end{aligned}$$ where $\theta^{\mu \nu}$ is a constant antisymmetric tensor.

Let $$F_\theta = e^{\frac{i}{2} \partial_\mu \otimes \theta^{\mu \nu}
  \partial_\nu} = 