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A mathematician, a programmer, etc. etc.


Apr
20
comment Why the $\zeta$ letter is like this?
foundalis.com/lan/hw/grkhandw.htm
Apr
18
awarded  Civic Duty
Apr
15
comment Solve $\sqrt{1+\sqrt{1-4x^2}}=x\left( 1+\sqrt{1+\sqrt{1+2\sqrt{1-4x^2}}}\right).$
Perhaps set $u=\sqrt{1-4x^{2}}$, so $x = \sqrt{1-u^{2}}/2$ and the problem becomes $2=\sqrt{1-u}(1+\sqrt{1+\sqrt{1+2u}})$...?
Apr
11
revised Evaluate $\int_{0}^{\pi/4}\frac{6 - 6\sin^{2}(x)}{2\cos^2(x)} \mathrm{d}x $
Improved the tex formatting
Apr
11
suggested suggested edit on Evaluate $\int_{0}^{\pi/4}\frac{6 - 6\sin^{2}(x)}{2\cos^2(x)} \mathrm{d}x $
Apr
11
comment Evaluate $\int_{0}^{\pi/4}\frac{6 - 6\sin^{2}(x)}{2\cos^2(x)} \mathrm{d}x $
So...what have you attempted so far?
Mar
31
comment Tensor fields and vector bundles
To be precise, on the level of sections, don't we have an isomorphism $\Gamma(E\otimes F)\cong\Gamma(E)\otimes\Gamma(F)$ and not a strict equality?
Mar
31
comment Divergent Alternating Series
But if $p=1/2$ then $b_{9} = -1/2 < 0$, contradicting one of the premises of the problem ($b_{n}>0$ for all $n$).
Mar
30
comment Tangent space of the tangent bundle
Well...is $dg_{(x,0)}$ surjective?
Mar
10
revised Topological Quantum Field theories
Added some more explanation
Mar
8
comment Topological Quantum Field theories
@SanathDevalapurkar, also, where I'm studying -- I studied at UC Davis as an undergraduate. My current situation is rather strange (not that I'm private about it, I just cannot describe it in 140 characters!). I still study quantum gravity, though :)
Mar
8
comment Topological Quantum Field theories
In, e.g., 1+1 dimensional TQFT, dynamics is done by specifying the number of loops you begin with at time $t=0$, and how many you have at $t=1$, as well as the topology of the world-sheet for $0<t<1$. BUT the partition function (controlling dynamics) then becomes a function of the topological invariants (which invariants depends on the TQFT). This is good for, e.g., BF-theory since computing topological invariants is simpler than, say, solving the Wheeler-DeWitt equation :)
Mar
8
answered Topological Quantum Field theories
Mar
8
comment Topological Quantum Field theories
@SanathDevalapurkar, time reparametrization invariance forces the Hamiltonian to be a constraint; a great review of this can be found in Henneaux and Teitelboim's Quantization of Gauge Systems, viz. chapter 4.
Mar
3
awarded  Revival
Mar
3
answered Superspace as the Hilbert Space for Quantum Gravity
Mar
3
comment Superspace as the Hilbert Space for Quantum Gravity
Well, no, you never do that in -- say -- using geometric quantization for the canonical formalism for electromagnetism (or, a simpler example, a scalar field). You don't do it when geometrically quantizing a mechanical system either. The symplectic manifold $\mathcal{M}$ is a necessary ingredient for constructing the Hilbert space (or Fock space for field theories), but not sufficient to qualify as the Hilbert space (resp. Fock space) for the full quantum theory. NB: you can use phase space path integrals, but this is an irrelevant fun fact rather than pertinent information.
Mar
3
comment Superspace as the Hilbert Space for Quantum Gravity
You might want to read Woodhouse's Geometric Quantization. You don't turn $\mathcal{Riem}$ into a Hilbert space: you use it (well, technically $\mathcal{Riem}/\mathcal{Diff}$) as the configuration space, then construct an infinite-dimensional symplectic manifold $\mathcal{M}$ which you use as the underlying manifold for a complex line bundle. The space of sections on this line bundle then in (insert magical full quantization step here) and you've got a Fock space.
Feb
20
revised Identity $\int_{-\infty}^{\infty}\frac{e^{uz}}{1+e^u} \mathrm{d}u=\frac{\pi}{\sin(\pi z)}$
Modified title, updated some TeX
Feb
20
suggested suggested edit on Identity $\int_{-\infty}^{\infty}\frac{e^{uz}}{1+e^u} \mathrm{d}u=\frac{\pi}{\sin(\pi z)}$