4,890 reputation
1416
bio website thenestofheliopolis.blogspot.…
location Glasgow, United Kingdom
age 27
visits member for 3 years, 10 months
seen 17 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]).


May
17
comment Equivalent Resistance
related: en.wikipedia.org/wiki/Y-%CE%94_transform
May
15
answered Is it possible to convert stored fat in the body into electrical energy directly?
May
15
comment Is it possible to convert stored fat in the body into electrical energy directly?
Seems like a valid thermodynamics question to me, although the kind of answers this question would receive might be opinion based. However I don't really feel like this question should be considered too off-topic and closed.
May
15
answered How does one write density as a form?
May
15
comment When can I swap around the order of operators?
Method 2 is an incorrect version of Method 1...
May
9
revised Confused by answer to mechanics question
deleted 4 characters in body
May
9
answered How can I tell if the spectrum of an operator in QM is degenerate?
May
8
comment Meaning of negative density
The idea is that you define charge density whenever you have some charges (like mass density whenever you have some mass spread across a certain region). If you separate positive and negative charges and you just count them you end up with two positive densities whose sum is a positive quantity. So for neutral matter, where there are in general both positive and negative charges cancelling each other, you would have a positive charge density, unless you subtract one density from the other, which means that you can assume one of the two to be negative in the first place.
May
8
comment Meaning of negative density
think of a gas of electrons. How would you define the charge density? Now take neutral matter, which is made of charged particles like electrons and protons? How come that charge density is zero for neutral matter when it actually contains charge distributions?
May
7
comment Commutator of Gauge Covariant derivatives
related: en.wikipedia.org/wiki/Curvature#Generalizations
May
4
comment Why are complex fields in the Lagrangian?
Strictly speaking they are not compulsory. You can still do with real fields by taking multiplets, but sometimes it is more convenient to use complex numbers instead.
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
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 $\{\langle\phi\frac{d}{dq}\}\psi\rangle = \langle\phi\{\frac{d}{dq}\psi\rangle\}$