2,411 reputation
11332
bio website berkeley.academia.edu/…
location Berkeley, CA
age 25
visits member for 3 years, 7 months
seen 2 days ago

Currently a graduate student in mathematics at the University of California - Berkeley.

Previously obtained a MASt. in Applied Mathematics from the University of Cambridge (2013), and a B.S. in Mathematics and a B.A. in Physics from the University of Chicago (2012).


Mar
14
comment The interpretation of mass in quantum field theories
@LubošMotl "What's the problem?" -- The problem is in the details of "...finds that it contains particles whose mass is $m$", namely, that I don't know them and would like to.
Feb
28
comment What made us think that Earth moves around the Sun?
It doesn't; they both happen to rotate (though not necessarily in a circle or constant angular velocity) about their center of the mass (if you ignore the rest of the universe). In practice, however, the rest of the universe is negligible and the sun is so much more massive that the center of mass is actually contained within the sun.
Feb
28
comment Is the quantization of gravity necessary for a quantum theory of gravity?
Perhaps I was unclear about what my professor had said. I don't think he meant that the starting point for string theory is 'promoting' the metric to a quantum field, but rather, at the end of the day, this is how you wind up thinking of the metric. To be quite honest, I'm still in the course, and so quite inexperienced, so I expect my interpretation of his meaning is not so accurate. I would suspect that anything that does not make sense is a result of my ignorance, not his.
Feb
12
comment Charge conjugation in Dirac equation
This can be taken as a definition of $C$ if you like, although it does not uniquely specify a $C$. You have to normalize. Let $\gamma ^\mu$ be an irreducible representation of the Clifford algebra $\mathcal{C}\ell (1,3)$. You can check that the matrices $\gamma '^\mu :=-(\gamma ^\mu )^T$ also define a representation of this algebra. There is a theorem about Clifford algebras that says there is essentially only one (faithful) irreducible representation, and hence these two representations must be equivalent, i.e. there is a unitary $C$ such that $C\gamma ^\mu C^{-1}=-(\gamma ^\mu )^T$.
Jan
26
comment Is the quantization of gravity necessary for a quantum theory of gravity?
I've since added to my original question, and I would be interested if you have anything additional to say.
Jan
26
comment Is the quantization of gravity necessary for a quantum theory of gravity?
I've since added to my original question, and I would be interested if you have anything additional to say.
Jan
26
comment Is the quantization of gravity necessary for a quantum theory of gravity?
I've since added to my original question, and I would be interested if you have anything additional to say.
Dec
7
comment Why quantum mechanics?
@juanrga I completely rewrote one part of my question that I realize was not worded so well. Perhaps it makes more sense now?
Dec
7
comment Why quantum mechanics?
@juanrga I was trying to demonstrate what I meant when I originally said "Make as little use of experiment as possible.". What I really meant was "When you make use of experiment, use it to justify as fundamental results as possible". In principle, you would reduce kinetic theory to even more fundamental physics, and so on, and eventually you would get to the point where you couldn't reduce things theoretically anymore, the only thing you could do is justify your assumptions on the basis of experiment, as opposed to just more theory.
Dec
5
comment Why quantum mechanics?
@dmckee No, that wasn't really what I was thinking of. I already have an abstract formulation in mind: the usual Hilbert space formulation in which states are elements of the space and observables operators on it. If all you were aware of is classical mechanics, no one in their right mind would guess that's how things should work. Are there a couple of fundamental physical principles that we can make use of that could convince a student who had never seen any of this before that this formulation is in fact quite natural.
Dec
5
comment Why quantum mechanics?
In the Weinberg example, he takes a couple of assumptions that we feel are relatively fundamental and in principle verifiable by experiment (Loretnz invariance of the $S$-matrix and Cluster Decomposition Principle), and uses them to show that the concept of a field naturally arises as a result of demanding the interaction be of a particular form (which itself is dictated by the assumptions). I would like to see an argument that utilizes just a few physical principles to justify the usual Hilbert space formulation of quantum mechanics.
Dec
5
comment Why quantum mechanics?
@EmilioPisanty Essentially, yes.
Dec
5
comment Why quantum mechanics?
See edit to question. Obviously, you'e going to have to appeal to experiment somewhere, but I feel as if the less we have to reference experiment, the more eloquent the answer would be.
Dec
5
comment Why quantum mechanics?
As an example of motivation that would satisfy me, the arguments that Weinberg makes in the first part of his first volume to motivate the introduction of quantum fields, while not a proof that nature has to be explained by a field theory, is more than satisfactory if all one seeks is justification to believe that a quantum field theory can be used to describe the universe.
Nov
8
comment What is the role of the vacuum expectation value in symmetry breaking and the generation of mass?
I don't quite see how the requirement that you not have a linear term requires us to make the substitution $\psi :=\phi -|v|$. For example, the trivial substitution $\psi := \phi$ doesn't have a linear term, but this can't be correct, because we don't see a massless particle and antiparticle pair, we see a Goldstone boson and a massive real scalar particle.
Oct
30
comment Is the density operator a mathematical convenience or a 'fundamental' aspect of quantum mechanics?
Perhaps I could rephrase my question as "Does there exist a quantum system that exists in reality which cannot be mathematically described by a pure state?". According to your answer, it seems that the answer is "Yes" and that an example is given by "open quantum systems". What exactly do you mean by this and how are they not described by pure states?
Oct
30
comment Is the density operator a mathematical convenience or a 'fundamental' aspect of quantum mechanics?
@A.O.Tell Can you elaborate on what exactly you mean by "representing states of tensor factor subsystems"?
May
30
comment Yukawa Coupling of a Scalar $SU(2)$ Triplet to a Left-Handed Fermionic $SU(2)$ Doublet
This part of my question can be phrased as: given this statement of the problem, what is the correct form of the Yukawa coupling term? (I realize what I wrote down didn't make sense. The problem is, I don't know how to modify it so that it does make sense).
May
30
comment Yukawa Coupling of a Scalar $SU(2)$ Triplet to a Left-Handed Fermionic $SU(2)$ Doublet
This actually came from a homework problem (there was a five tag limit). The problem reads: "One method of generating neutrino masses that we did not discuss in class involves adding a Higgs field $T$ which is a triplet under $SU(2)_L$ with a Yukawa coupling to the left-handed lepton doublets. If this triplet is a complex field, then it is possible to assign a lepton number to this new scalar field such that the lepton number is conserved.". He doesn't actually write out the Yukawa coupling term, so we are left to figure this out on our own.
May
20
comment The Faddeev-Popov Lagrangian
In the Scholarpedia article, I am looking at the part that begins with "One more improvement was introduced by 't Hooft . . .". It almost seems as if the term I'm wondering about was inserted by hand by allowing a more general gauge fixing condition. With this more general condition, the relevant delta function contributes a nonzero term to the Lagrangian. If I understand this correctly, that's all well and good, but why the need for the more general condition? Is $\partial _\mu A^{\mu k}$ not sufficient? Does this not just complicate things further by introducing an extra term?