4,685 reputation
1416
bio website thenestofheliopolis.blogspot.…
location Glasgow, United Kingdom
age 27
visits member for 3 years, 10 months
seen 10 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]).


Apr
16
answered Constants of motion in quantum mechanics
Apr
15
comment What is the physical interpretation of the Poisson bracket
I would try Dirac's Lectures on Quantum Mechanics perhaps, although the description is in a sense "advanced". However I think it gives a good feeling of what the PB are when you have constraints, and how they then relate to quantum systems.
Apr
15
comment What is the physical interpretation of the Poisson bracket
Classical mechanics has a commutative structure. In terms of operator algebras it is described by the algebra of smooth functions on the phase space, and the real value functions are the observables. The fact that Heisenberg relations are linked to the canonical brackets is just a quantisation procedure. Poisson brackets have a precise definition and the canonical brackets follow from it.
Apr
14
answered What is the physical interpretation of the Poisson bracket
Apr
12
comment Identity operator in terms of the energy eigenstates in case of continuous spectrum
I suppose $w(E)=1$? With $w(E)=E$ you would have the (formal) spectral decomposition of the energy operator...
Apr
12
revised About the orthogonality of the Hamiltonian eigenstates for the the continuous energy spectrum
added 1 character in body
Apr
12
comment How to convert $V \otimes W^*$ to a matrix space?
en.wikipedia.org/wiki/Kronecker_product
Apr
8
answered Use of Imaginary Angles in Physics
Apr
7
comment How does Dirac define the representative of $\{\langle\phi\frac{d}{dq}\}\psi\rangle = \langle\phi\{\frac{d}{dq}\psi\rangle\}$
Well this is what Dirac does, except that I have tried to use a more mathematically correct notation. On your second equation you should think of the LHS as a formal expression that defines the kernel of the functional $\langle\eta|T$, with the RHS giving you the way this formal functional acts on $\psi$.
Apr
7
answered How does Dirac define the representative of $\{\langle\phi\frac{d}{dq}\}\psi\rangle = \langle\phi\{\frac{d}{dq}\psi\rangle\}$
Apr
6
comment Ballentine's proof of (one half of) Stone's theorem
@Harald, yes. You can verify that from the definition of derivative.
Apr
6
answered Ballentine's proof of (one half of) Stone's theorem
Apr
3
awarded  Fanatic
Apr
1
answered Metric and the Lagrangian
Apr
1
revised The equivalence between Heisenberg and Schroedinger pictures
added 895 characters in body
Apr
1
comment The equivalence between Heisenberg and Schroedinger pictures
It may be that my answer actually tackles another kind of equivalence, namely that between matrix mechanics and the wavefunction picture. However the two things are not too far apart, as in the Heisenberg pictures you can identify the matrices with the operators and the you look at the time evolution of these matrices. Anyway I'll a few more details in the answer
Mar
31
comment What's up with my whipped cream?
they look like they are stuck to the cup.
Mar
31
awarded  quantum-mechanics
Mar
30
answered The equivalence between Heisenberg and Schroedinger pictures
Mar
30
comment Is the interference quantum mechanical superposition the same as entanglement?
For entangled states you can choose a vector state which factorises in the tensor product, so with this choice there is no superposition. Of course you can take an arbitrary base for the tensor product Hilbert space and decompose the entangled state in a superposition of other states, so as you can see from this there is no direct link between entanglement and superposition.