5,656 reputation
1520
bio website thenestofheliopolis.blogspot.…
location Glasgow, United Kingdom
age 27
visits member for 4 years, 1 month
seen 38 mins 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
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"
1d
answered Can the uncertainty principle be redefined for different standard deviations?
1d
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.
1d
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.
1d
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.
1d
answered Why are force, momentum, and kinetic energy derivatives of each other
1d
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.
2d
comment Is it possible to generalize the Maxwell equations to higher dimensions?
WetSavannaAnimalakaRodVance has indicated Penrose's book "Road to reality". I have a copy of that book however not with me at the moment, but I'm sure it contains some really nice ideas worth having a look at.
2d
answered $[A_1, H] =[A_2, H] = 0$ but $[A_1, A_2] \neq 0$?
2d
awarded  Nice Answer
2d
comment Is it possible to generalize the Maxwell equations to higher dimensions?
It is an interesting question, but I don't know the answer on top of my head. As the dimension increases I would expect the gauge freedom to increase, but this'd need to be checked.
2d
answered Physical Meaning of Phase Ambiguity
2d
answered Is it possible to generalize the Maxwell equations to higher dimensions?
Jul
22
answered Noether's theorem: meaning of transformation of coordinates
Jul
22
answered How to express a convex function of a Hermitian operator in terms of its eigenvalues and eigenvectors?
Jul
22
awarded  Nice Answer
Jul
20
comment Why electron can not be found at some node locations in the infinite potential well?
related en.wikipedia.org/wiki/Standing_wave
Jul
20
comment Postulates of Relativistic Quantum Mechanics
No I mean a system like countably many independent QHOs. For a system like this there is no unique irreducible representation, up to equivalence (see e.g. Gårding-Wightman, 1954).
Jul
20
answered Postulates of Relativistic Quantum Mechanics
Jul
17
comment Prove: $A$ and $B$ commute, therefore functions $f(A)$ and $g(B)$ will always commute with one another
Yes. More generally every element of a C*-algebra has finite norm and every $*$-homomorphism (like a representation) is always contractive.