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--- advanced_tools:group_theory:representation_theory:dean_proffesor_reza_sanaye [2020/06/24 19:38]
178.62.43.135 created
+++ advanced_tools:group_theory:representation_theory:dean_proffesor_reza_sanaye [2023/03/19 21:45] (current)
edi [Concrete]
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-====== dean proffesor reza sanaye ======
+====== Trivial Representation ======
+<tabbox Intuitive>
-Persistent interaction with other functionalities of molecular topography can still take place for those electrons that are diffracted. The localization of sub-cellular proteins is in need of decrypting those areas of a Macromolecule's neighborhoods in which surface residues are themselves significations of features to carry out extremely peculiar functional roles. Sub-cellular morphology of light-interacting particles is the science that can pave the way for going even below the level of Angstrom in highly precision drug delivery. Any expansion of ability to regard the above mentioned sub-cellular sub-manifolds as NOT overlapping, depends on how we define our non-light microscopy. One of the areas where topography of Macromolecules would be best fruitful, is the study of the self-co-localization of homomultimers. Their binding partner concentrations are generally so high as to give us the opportunity to –at least theoretically –divide the whole neighboring zones into as many sub-manifoldic neighborhoods as possible. It is only then that we might well arrive at decoding mereotopological features in favor of a number of induced genetic mutations by which the resultant protein topological changes give us the knowledge as to how pass through barriers of energetics. Critics could as well raise issues regarding the highly trial-and-error nature of such a protocol. Trials and errors, yes indeed, have to be carried out and repeated so many times that we become capable of basing our sub-nano microscopy of drug delivery not on particularly chemical characteristics, but on post translational changes in the topology of protein amino acid sequences  [as locally as is imaginable]. Such methodology would enable variations both inside and beyond confines of even a single gene or the smallest ever studied amino acid sequences. In point of fact, the most remarkable effect of post-translational topological modifications is the way electron streaming continues to excite and get excited over a wide range of "developed'' spectra. They are thus synthesized, made, made up, artifacted, manipulated, only for their energetics variations which in itself is ALMOST only dependent upon the mereology and topology of the electron stream vs the functionally regulated factors.
+The trivial representation maps all group elements to the identity element. This representation exists for any group.
-Figure 3 Backward transformation of energetically temporal timescale as encoded in the neighboring sub-manifolds
+Spin-$0$ particles transform under the trivial representation of $SU(2)$. That is, their spin value does not change under rotation.
-<tabbox Intuitive>
+The action (and often the Lagrangian) transforms under the trivial representation of the Lorentz group and the relevant gauge  groups. That is, the action is not affected by these symmetry transformations.
-<note tip>
-Explanations in this section should contain no formulas, but instead colloquial things like you would hear them during a coffee break or at a cocktail party.
-</note>
 <tabbox Concrete>
+**Example**
+The diagram below shows the defining representation of $SU(2)$ in its upper branch and the trivial (1-dimensional) representation in its lower branch.
+[{{ :advanced_tools:group_theory:representation_theory:su2_1d_rep.jpg?nolink }}]
-<note tip>
+For a more detailed explanation of this diagram see [[https://esackinger.wordpress.com/blog/lie-groups-and-their-representations/#su2_1d_rep|Fun with Symmetry]].
-In this section things should be explained by analogy and with pictures and, if necessary, some formulas.
-</note>
 <tabbox Abstract>

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