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>> No.11503780 [View]
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11503780

>>11503723
It's just the [math]G=SU(3)\times SU(2)\times U(1)[/math] Yang-Mills-Higgs functional. Given a [math]G[/math]-equivariant Hermitian vector bundle [math]E\rightarrow M[/math], the action
[math]S[D,\phi]= |D\phi|^2_{L^2(M,E)} + |F_D|_{L^2(M,E)}^2 + \frac{1}{4}|\phi^* \otimes \phi - 1|^2_{L^2(M,E)}[/math] is a functional on the moduli space of holomorphic connections [math]D \in \overline{\mathscr{A}}(M,E)[/math] and the Higgs field [math]\phi \in \Omega^0(M,E)[/math]. Given a choice [math]\rho[/math] of an irrep of [math]G[/math], after a move into the associated vector bundle [math]E\otimes_G V_\rho[/math] it's just a matter of trivial rearrangements and rewriting [math]S[D,\phi][/math].

>> No.11482194 [View]
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11482194

>>11482035
https://arxiv.org/abs/2001.08339

>> No.11401251 [View]
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11401251

>>11396684
Cute.
>>11400839
This is a pretty archaic/naive interpretation. The amount of (quantum) information contained in a state [math]\rho[/math] is given by the von Neuman entropy [math]S = -\operatorname{tr}\rho\ln \rho[/math], which is minimized for pure states, so we [math]do[/math] know how a state collapses: it's when [math]S[/math] achieves a minimum. Schrodinger's cat never was an objection because it never took into account the localization/decoherence of the quantum dot when it couples to the massive classical heat bath (cat), which is described quite well by the thermalization hypothesis.
>>11400914
Let [math]G=(V,E)[/math] be a graph, we know a few things:
1. [math]|V| \geq |E|[/math], since two ,
2. [math]|V| = |\tilde{F}|[/math], where [math]\tilde{F}[/math] are the faces of the dual graph [math]\tilde{G}[/math],
3. Euler characteristic [math]\chi(G) = |V| - |E| + |F| = -2 = \chi(\tilde{G})[/math] for planar graphs [math]G[/math].
What these mean is that a degree sequence [math](d_i)_i[/math] is graphic if [math]\sum_i(2 - d_i)\leq -2 [/math] since [math]|V| = \sum_i[/math] and [math]|E| \leq \sum_i d_i[/math].

>> No.11347084 [View]
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11347084

>>11340981
https://arxiv.org/abs/math/0609210v1

>> No.11305558 [View]
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11305558

>>11303816
Cohomologies with Abelian [math]\mathbb{Z}[/math]-modules as coefficients are completely determined by [math]H^\ast(\bullet,\mathbb{Z})[/math] by the universal coefficient theorem honey. Besides, [math]H^\ast(\bullet,\mathbb{Z})[/math] is in general also a [math]H^0(\bullet,\mathbb{Z})[/math]-module for cohomology theories satisfying the dimensional regularity axiom in addition to the standard EM axioms. Once we know the algebraic structure of [math]H^0[/math], we can pass to any arbitrary [math]R[/math]-module-valued coefficients.
>cases by analogy and classifying spaces
You do know that group cohomologies are just [math]G[/math]-equivariant cohomologies of principal bundles over a point, right? Topology and geometry are fundamental, all other abstract wank isn't.
Especially if the coefficients is a field of characteristic zero; try finding a generalized cohomology theory that isn't isomorphic to the standard singular one, I'll wait.
>>11303956
Try taking the trace of the Heisenberg relation [math][a,a^\dagger] = 1[/math] on a finite dimensional Hilbert space. If [math]\operatorname{dim}\mathcal{H} = N[/math] then [eqn]\operatorname{tr}([a,a^\dagger]) = \operatorname{tr}1 = N,[/eqn] but [math]\operatorname{tr}([a,a^\dagger]) = 0[/math] due to the cyclicity of the trace so [math]\operatorname{dim}\mathcal{H}=0[/math]. There's no QM here, sweetie.

>> No.11287888 [View]
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11287888

>>11287862
If you think an argument is substantial only if an alternative is provided then I've got some bad news for you hun. My problems with string theory [math]\textbf{ as a physical ToE}[/math] is the farthest thing from nitpicking; any theory that fails to reproduce large-scale covariance will be brought into question, stringy or not.
>cared to look at the actual history of the field
Hypocrite that you are, for you never actually look at the actual history of and recent developments in cond mat. Aside from the obvious brane-CFT stuff, people have proposed [math]G[/math]-equivariant, twisted and non-commutative versions of known CFT models, motivated from the cond. mat. perspective, that [math]will[/math] have significant impact on HMS and string theory via holography as a whole.
Remember CFT was first developed with cond. mat. considerations in mind in order to study critical phenomena. Never forget your roots, kid, because the third string revolution will start in cond. mat. and you can quote me on this.

>> No.11265622 [View]
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11265622

>>11265378
Physics.

>> No.11262374 [View]
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11262374

>>11262289
>It's all symbols and hieroglyphs
Stay away from algebra then.

>> No.11107290 [View]
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11107290

>he uses natural units where [math]c = \hbar = 1[/math]
>not supernatural units where [math]k_B = \pi = 1[/math] as well

>> No.11098413 [View]
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11098413

>>11098412
Irreps of [math]SU(2)[/math].

>> No.11063096 [View]
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11063096

>>11062411
Soft matter boys are cute as heck though.

>> No.11042807 [View]
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11042807

>>11042792
Tell him to PURE.
https://www.pureformen.com/
What kind of virginal Amish bottom doesn't know about this?

>> No.11010913 [View]
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11010913

>>11010762
Dear beloved:
I am writing to you in the hope that you will endow me twins within my mental boywomb with your superior intellectual seed. For you see, I have been pleasuring myself recently by inserting combinatorial objects into my cranial rectum and rubbing their properties against my cerebral prostate until completion, whence I begin to spray ejaculates (in the sense of Conan Doyle's Holmes) onto the floor. I would like a strong, mathematically manly third party such as yourself to completely dominate my intellectual being and deformation retract my sphincter of knowledge as a discrete topological space.
Thank you for the considerations.
Yours truly, OP.

>> No.10960933 [View]
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10960933

>>10960203
https://arxiv.org/abs/1105.0805

>> No.10875110 [View]
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10875110

>friend asks me what I'm reading
>tell him it's manifold calculus
>"Oh, Rudin?"
>"Yeah"
>mfw I'm reading Goodwillie-Weiss

>> No.10723761 [View]
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10723761

>>10721606
FPBP

>> No.10325337 [View]
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10325337

>>10324901
>hardest
Fat gymcel detected

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