5,144 reputation
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bio website thenestofheliopolis.blogspot.…
location Glasgow, United Kingdom
age 27
visits member for 4 years
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]).


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awarded  Self-Learner
1d
awarded  Yearling
Jun
29
revised Uncertainty principle in quantum field theory
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Jun
27
comment Is it possible for two events happen at the exact same time?
Observe that if two events are causally disjoint then there exists a frame of reference where they occur at the exact time. The problem is now how accurately one can choose to be in such a frame of reference.
Jun
24
answered Uncertainty principle in quantum field theory
Jun
21
comment Where do these two equalities for the expectation value come from precisely? Doesn't $\Psi^* x \Psi = x |\Psi|^2$?
They come from the definition of the inner product on the $L^2$ space in the "position representation".
Jun
20
comment Constructing Lagrangian from the Hamiltonian
The Legendre transform is involutive
Jun
19
comment How is quantization related to commutation?
partly related: physics.stackexchange.com/q/155893 and physics.stackexchange.com/q/188330 and physics.stackexchange.com/q/162704
Jun
17
comment How is the Lagrangian defined in GR?
Observe that the second choice gives a zero Hamiltonian
Jun
15
awarded  Nice Answer
Jun
15
comment How to interpret vector operators in quantum mechanics?
that's correct $\ $
Jun
15
comment How to interpret vector operators in quantum mechanics?
think of $|\mathbf v\rangle$ as $|v_1\rangle\otimes\cdots\otimes|v_n\rangle$ for any $\mathbf v\in\mathbb R^n$, assuming that the operators associated to each component generate a commutative algebra. This is certainly the case for ordinary coordinates.
Jun
14
comment Really how can an observable quantity be equal to an operator?
Most of the "magic" of quantum mechanics as presented to physicists can be justified in a mathematically rigorous way. By first principle here I mean the assumption that a physical system is a C*-algebra. This, together with the theory of operator algebras, is enough to justify the mathematical structure of quantum mechanics (in particular I'm referring to the Dirac picture of his infinite dimensional Hilbert spaces and so on and so forth).
Jun
14
answered Really how can an observable quantity be equal to an operator?
Jun
14
comment About the definition of super Hilbert Spaces
Why should $H_0$ and $H_1$ be perpendicular w.r.t. the inner product?
Jun
11
comment Why does knowledge of $\langle 0| x^m p^n |0\rangle$ determine the ground state wave function?
I haven't really attempted at some computations but I'd try to use exponentials here (think of their series expansion).
Jun
10
comment Probability density for momentum in Quantum Mechanics
related: physics.stackexchange.com/q/186112
Jun
9
comment Infinitesimal Rotations
1) I don't see an explicit reference to group theory in my answer; 2) I don't really see the problem with using group theory. IMHO it gives a different perspective on this question. For instance, what is your matrix that you get when you compute that derivative in your answer? Is it an accident that it is skew-symmetric? What happens if one now wants to consider the third dimension as well? How do the formulae generalise? I don't think this quite apparent from your answer...
Jun
9
comment Linearity in Quantum Mechanics that make superposition possible
The OP mentions superposition of states and then wonders about the linearity of quantum mechanical systems. It seemed to me that OP was a bit confused on the uses of the word superposition in the context of quantum mechanics. Hence my answer was an attempt to clarify the possible meanings of this notion.
Jun
9
revised Linearity in Quantum Mechanics that make superposition possible
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