06/05/2021, 12:12 AM
I'm a bit lost tbh. What H* can look like in your opinion? Whatever it is, it is applied to exponentiation so it should be a good news.
Also operators are linear, usually, so Idk how to manage non-linearity inside an ambient, that of vector spaces/Hilbert spaces, where things should be linear.
But I'm curious of what you can carve out of this. Even if you don't get result I believe that what we are doing here is usefull, brushing the dust from the hidden spots, making clear what the mechanisms are.
I went full speed on categories and non-commutative groups just for that reason. Because I wanted a landscape where I couldn't care less about linearity because we don't want to start with a god-given abelian ground (i.e. linearity) by default.
Also operators are linear, usually, so Idk how to manage non-linearity inside an ambient, that of vector spaces/Hilbert spaces, where things should be linear.
But I'm curious of what you can carve out of this. Even if you don't get result I believe that what we are doing here is usefull, brushing the dust from the hidden spots, making clear what the mechanisms are.
I went full speed on categories and non-commutative groups just for that reason. Because I wanted a landscape where I couldn't care less about linearity because we don't want to start with a god-given abelian ground (i.e. linearity) by default.
Mother Law \(\sigma^+\circ 0=\sigma \circ \sigma^+ \)
\({\rm Grp}_{\rm pt} ({\rm RK}J,G)\cong \mathbb N{\rm Set}_{\rm pt} (J, \Sigma^G)\)