5,756 reputation
1520
bio website thenestofheliopolis.blogspot.…
location Glasgow, United Kingdom
age 27
visits member for 4 years, 2 months
seen 21 hours ago

I'm currently involved in a PhD in Mathematics. My research area is that of Functional Analysis. Specifically I'm working on classification of C*-algebras by defining a bivariant version of the Cuntz semigroup, an invariant used to compare positive elements in a C*-algebra and hence infer information about its internal structure.

During my MSc I focused on Algebraic Quantum Field Theory and I have worked on DFR models for Quantum Space-time (arXiv:1211.7050 [gr-qc]).


1d
answered Why do people wear black in the Middle East?
Aug
28
comment Symmetry in quantum mechanics
Assume that $s_2(O)s_1(\psi)=s_1(O\psi)$, with obvious meaning of these symbols. Then preservation of transition probabilities is sufficient. The assumption can be justified by, e.g., Wigner's theorem.
Aug
10
comment If the curl of some vector function = 0, Is it a must that this vector function is the gradient of some other scalar function?
This is true on any 3-manifold with trivial first de Rahm cohomology group, as this would then imply that $\text d\omega = 0$ only if $\omega = \text d\alpha$ for some 0-form $\alpha$. Any vector space falls into this class, and hence the Euclidean 3-space.
Aug
8
comment No two identical fermions can have the same quantum state at once?
If by different you mean different spatial part of the wavefunction, then they can have the same "quantum state", if by this you mean the spin component of the wavefunction. What can't really happen is to have two identical electrons in the same quantum state, in the sense that they cannot have the wavefunction (i.e. spatial and spinor part) as a consequence of the anticommutation relations.
Aug
7
comment Can the inverse operator be expressed as a series?
The theorem in the form discovered by Weierstrass can be proven constructively through Bernstein polynomials (en.wikipedia.org/wiki/Bernstein_polynomial), however this is not the "optimal" way in general, as the convergence is slow.
Aug
7
answered Can the inverse operator be expressed as a series?
Aug
5
comment What is the meaning of $\vec{E}\times\vec{B}$?
they are perpendicular in vacuum.
Aug
5
comment What is the meaning of $\vec{E}\times\vec{B}$?
see en.wikipedia.org/wiki/Poynting_vector
Aug
4
comment Is the Sun dusting my electronics?
what if charge builds up on the sunlit part as a consequence of light stripping off some electrons?
Aug
1
comment Confusion about Fock subspace
What's finite is the number of particle described by each subspace. This doesn't imply that the subspaces are finite dimensional. This happens for the fermionic case, where the single particle Hilbert space is $\mathbb C^2$, but it is infinite dimensional, however separable, for the bosonic case.
Aug
1
comment Confusion about Fock subspace
(1) is the completion of (2) in the metric induced by the inner product on (2). That is the standard way of constructing a Hilbert space out of a countable direct sum of Hilbert spaces.
Jul
31
comment Why does Hamiltonian follow the property $H^*_{ij} = H_{ji} $?
I think he is just arguing that, given that the time evolution is $U(t) = e^{iHt}$, by requiring the probability to be conserved one is requiring $U$ to be unitary, hence $H$ to be self-adjoint.
Jul
30
comment When is the phase space diagram an ellipse?
An ellipse is just a circe. You get an exact circle whenever the system is conservative. When the phase space is two-dimensional (which means that the system has just one degree of freedom), it is enough to exhibit a first integral, which is readily provided by the Hamiltonian. A more general result, which yields the $n$-torus $\mathbb T^n$ as a generalisation of the circle, follows from the angle-action variables for integrable systems.
Jul
28
comment Can the uncertainty principle be redefined for different standard deviations?
You could have a look at Strocchi's "An Introduction to the Mathematical Structure of Quantum Mechanics"
Jul
28
answered Can the uncertainty principle be redefined for different standard deviations?
Jul
28
comment Square root of a matrix appears in massive gravity. How to solve $\sqrt{A+B}$ perturbatively
@EmilioPisanty But so is true for $I+B$. However the OP is explicitly asking for a perturbative solution. Of course, knowing $A$ and $B$ is no problem to compute $\sqrt{A+B}$ exactly in any basis.
Jul
28
comment Square root of a matrix appears in massive gravity. How to solve $\sqrt{A+B}$ perturbatively
$A+B$ is positive definite, so you can diagonalise this matrix and the entries will be perturbations of the eigenvalues of $A$. Hence if these are not all close to 1 (that is, if $A$ is not close to the identity matrix) I don't really see how to apply the perturbative method the OP refers to.
Jul
28
comment Square root of a matrix appears in massive gravity. How to solve $\sqrt{A+B}$ perturbatively
Write $A+B = I + C$, where $C = A + B - I$ and check that $C$ satisfy your criterion of being small.
Jul
28
answered Why are force, momentum, and kinetic energy derivatives of each other
Jul
28
comment Complex scalar theory: annihilation and creation operators give wrong commutators with Hamiltonian
$a^*$ and $b^*$ create orthogonal states, since the single particle Hilbert space is doubled in a complexified theory and $a$ refers to, say, the first direct summand, while $b$ to the other, which are clearly orthogonal as such.