Added references

Natalie Stewart

]]>Beginning a page for algebraic patterns, as they are becoming relatively prominent within the work of Barkan-Chu-Haugseng-Steinebrunner, and many equivariant homotopy theorists are beginning to recognize them as a suitable foundation for burgeoning work concerning equivariant operads.

Natalie Stewart

]]>Link to a page on algebraic patterns in the sense of Barkan-Chu-Haugseng-Steinebrunner

Natalie Stewart

]]>Added a cross reference to equivariant symmetric monoidal category

Natalie Stewart

]]>Added a cross-link to PHCTaHA

Natalie Stewart

]]>Factorization homology references

Natalie Stewart

]]>Added many references to papers since the Barwick-et all group mostly stopped

Natalie Stewart

]]>Added reference to the second Spectral Mackey Functors paper

Natalie Stewart

]]>No, quantum gravity is not meant to change the rules of quantum physics. Those $C^\ast$-algebras of quantum observables that you point to are still (embedded into) algebras of linear operators.

]]>definition of $k$-lagrangian submanifold, proposition about the graph of n-plectomorphism, and pointer

- M. de León, S. Vilariño.
*Lagrangian submanifolds in k-symplectic settings*(2012). (arXiv:1202.3964).

mention of integral sections and pointer

- Manuel De León, Modesto Salgado, Silvia Vilarino-Fernández.
*Methods of differential geometry in classical field theories: k-symplectic and k-cosymplectic approaches*. World Scientific, 2015.

Maybe I’m misunderstanding what you are referring to as quantum physics, since what I mentioned is supposed to be an observation of quantum gravity. I guess the question is, doesn’t quantum gravity (understood as a generalization of qft, not as a class of qft’s) take those higher degrees $k$ into account? In the sense you mention an axiom of QM is restricting to order $k=1$, isn’t the point of QG that one of the to-be axioms is the incorporation of those higher degrees?

]]>Not sure what you are after here. Coherent quantum processes are unitary linear operators between Hilbert spaces. That’s essentially one of the axioms of QM.

]]>I added a section on twisting cochains in the topological/geometric sense, which seem to be missing from quite a bit of the literature. Only a brief first draft, but will add more references to O’Brian–Toledo–Tong at some point in the future.

Tim

]]>So what is the more precise statement about linearity here? Would it be “coherent quantum processes *observable to an observer* are linear maps”? This reminds me of the recent series of papers by Witten (e.g. this) where one describes an algebra of observables (hence linear) only in relation to an observer (there described by a timelike curve).

Funny. Fine to present it as a source of bafflement, but the step to simulation seems bizarre.

]]>Mentioned well-pointed endofunctors in the definition.

]]>The degree $k$ in $J^k \mathbf{H}$ refers to Goodwillie polynomials of degree $k$.

By all that is known, coherent quantum processes are linear maps, not more general polynomial maps or worse.

(This reminds me of how Maxim Kontsevich trolled the 2015 Breakthrough Prize ceremony by declaring that the universe must be a simulation because it is “impossible” that quantum physics is really about linear spaces instead of curved manifolds like the rest of physics — around 19:30.)

]]>Ah, OK. So what makes the first degree of linearity stand out as so central to quantum physics?

What would, say, second degree linearity relate to?

]]>Thanks. I was a bit rushed yesterday, so did not get around to adjusting those pages.

]]>The twisting of cohomology seen in an $\infty$-topos just corresponds to dependency of the types in the corresponding internal logic. In this sense plain (L)HoTT is already “twisted”.

In the paragraph you quote it is not the twisting that makes the difference, but the “degree of linearity” of what is being twisted.

]]>have adjusted a little and copied the item also to the author’s pages

]]>have reworked this little entry

]]>