/sci/ - Science & Math

>>11383175
Yeah, if you start out with an interacting Hubbard Hamiltonian then its symmetries [math]G[/math] will tell you what kinds of Cooper pairs can form. Mean-field amounts to the replacement [math](c^\dagger,B c^\dagger) \rightarrow B\cdot \Delta = \langle (c^\dagger,B c^\dagger)\rangle[/math] for some fermion bilinear form [math]B[/math], which breaks the model's symmetry.
This question would've fit better in the physics general but I really don't have much hope for it in its current state.

>>11378550
Nope. Gravity is am emergent property from the entanglement of non-commutative string states, or equivalently flux-twisted FQHE states
https://arxiv.org/abs/1903.11066
https://arxiv.org/abs/1802.09421
"Cosmology is a subset of condensed matter" t. Volovik
>b-but muh non-thermodynamic surfaces
Shut

>>11300882

>>11245231
Every local relativistic field theories have [math]CPT[/math] symmetry. If it's broken then it's either non-relativistic or non-local.

>>11158998
You forgot physics sweetie.
>>11158866
That's a pretty wide dichotomy thee. Which do you like best? Inequality chasing or invariant chasing?

>>11109180
Check out https://www.springer.com/gp/book/9783319897998..
Haven't read it but it's got Brezis in the name so it can't be bad.

>>10955029
Mathologer is absolutely based. He's the only math youtuber I watch (aside from Sloane's numberphile vids which I use for ASMR).

If gay people are real, why does evolution exist?

>>10722799
Special autism theory or general autism theory?

>>9916597
>making observations and noticing patterns is anti-scientific
Hmm

>>9471259
Let [math]\iota: U \hookrightarrow V[/math] be the canonical inclusion, and let [math]M,N[/math] be [math]3[/math]-manifolds such that [math]T(M)
= U[/math] and [math]T(N) = V[/math] by the TQFT functor [math]T: (\mathscr{B},\mathscr{A})
\rightarrow \mathscr{M}[/math]. Suppose [math](W,f:M \rightarrow N)[/math] is the cobordism between [math]M[/math] and [math]N[/math] such that [math]T(W) = \iota[/math]. Denote by [math](v_X, X \rightarrow \emptyset) [/math] the cobordism such that [math]T(v_X)[/math] is the inner product by the vector [math]v_X \in T(X)[/math], and let [math]v_X^*[/math] be its dual.
By composition the cobordism [math](v_M^* W v_N, \emptyset \rightarrow \emptyset)[/math] is sent to the map of multiplication by the scalar [math]\langle v_M, \iota(v_N)\rangle \in R[/math]. Suppose [math]\operatorname{dim}V = \operatorname{dim}U[/math], then the multiplication [math]\langle v_M, \iota(v_N)\rangle: E \rightarrow E[/math] has non-zero rank for any vector space [math]E[/math]. However this is only possible if [math]\langle v_M,\iota (v_N)\rangle = 1[/math], hence the cobordism [math](v_M^* W v_N, \emptyset \rightarrow \emptyset)[/math] is the identity and hence by the functoriality of [math]T[/math], [math]\iota = \operatorname{id}[/math].