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Jun
9
answered Non-associative operators in Physics
May
29
answered Emergence of $SU(2)\times SU(2)$ at the self-dual point in bosonic string theory
May
28
answered Stringy corrections of Einstein's vacuum field equations
May
28
comment Calculation of the spherical harmonic sum in the propagator of the particle on a sphere
@ramanujan_dirac : It means that it is a fractional derivative. One way to understand it is to think about the Fourier transform. The derivative becomes a multiplication by the dual variable $p$ in the Fourier representation. A half-derivative is the multiplication by $p^{\frac{1}{2}}$. Now, a multiplication in the Fourier (momentum) space is a convolution in the position space. This explains the definition 8.14 of the fractional derivative in Comporesi.
May
28
revised Calculation of the spherical harmonic sum in the propagator of the particle on a sphere
edited body
May
27
revised Calculation of the spherical harmonic sum in the propagator of the particle on a sphere
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May
27
answered Calculation of the spherical harmonic sum in the propagator of the particle on a sphere
May
21
comment Coherent $U(N)$ intertwiners in Loop Quantum Gravity (LQG) and a measure on the Grassmannian
@levitopher cont. In fact, the procedure adopted by Qmechanic is a part of the "Faddeev-Popov" procedure for reducing gauge symmetries, and in principle it can be completed to get a BRST invariant integrand.
May
21
comment Coherent $U(N)$ intertwiners in Loop Quantum Gravity (LQG) and a measure on the Grassmannian
@levitopher Yes, the $U(2)$ volume in this case is a component of the integration over $GL(2)$. In fact $Z$, or ( $u_1$ and $u_2$) are redundant for the Grassmannian, even with the constraints because they sum up to $2N-4$ coordinates, while the dimension of the Grassmannian is $2N-8$. Another way to look at it is that the constraints are gauge fixing conditions and $U(2)$ represents the gauge symmetry. This is exactly the meaning of equation 82 in the article.
May
20
revised Coherent $U(N)$ intertwiners in Loop Quantum Gravity (LQG) and a measure on the Grassmannian
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May
20
answered Coherent $U(N)$ intertwiners in Loop Quantum Gravity (LQG) and a measure on the Grassmannian
May
13
revised Parametrization of $U(N)$ non-linear sigma model
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May
13
answered Parametrization of $U(N)$ non-linear sigma model
May
9
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May
7
awarded  Enlightened
May
7
awarded  Nice Answer
Apr
29
revised What does the sum of two qubits tell about their correlations?
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Apr
29
answered What does the sum of two qubits tell about their correlations?
Apr
25
comment What does the sum of two qubits tell about their correlations?
Cont. What is important is that on each manifold type there is an explicit parameterization of the 4-dimensional state vector (in terms of 3, 4, and 5 parameters respectively). (The generic case is not written explicitly in the article but can be easily worked out). Given the state vector, the $S_z$ probability distribution can be explicitly computed for each type of orbit and compared to the experimental distribution
Apr
25
comment What does the sum of two qubits tell about their correlations?
The idea is to use the classification given in arxiv.org/abs/quant-ph/0006068 (Geometry of entangled states) by Marek Kuś Karol Žyczkowski. The manifolds of equal entanglement of the pure two-qubit system fall into three strata parameterized by a single parameter $\theta$. The nongeneric orbits are $\mathbb{R}P^3$ and $S^2 \times S^2 $ correspond to $\theta = \frac{\pi}{2}, 0 $ respectively. The generic orbits correspond to $0 < \theta <\frac{\pi}{2}$ are five dimensional twisted $S^2$ bundles over $\mathbb{R}P^3$.