Tangleoids with quantum field theories in biosystems

Abstract

Abstract The open question whether quantum field theories can be used in biological systems will be addressed in this study. Quantum effects were reported for certain biological systems like the magnetic orientation sense in migratory birds. In quantum field theories it is possible to derive effective quantum field theories with welded tangleoids including braid relations that describe composite particles based on the dynamics of microscopic particle where these composite particles are made of. We observe that the generators of the tangleoid category that will depict the Feynman graphs are X X for a scattering vertex. This arises after carrying out the integral over bosonic fields A μ {A}_{\mu } in the partition function (D) that will lead to an four-valent interaction vertex generated by a quartic term in the fermionic fields. With X + {X}_{+} and X − {X}_{-} we will depict order changes like that regarding time orderings. Ordinary propagators are depicted by ∪ \cup and ∩ \cap . Finally, the generators ! \! and ¡ \hspace{0.1em}\text{¡}\hspace{0.1em} come into play if other foreign fields are picked up.