Jonathan Gleason

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bio	website	cambridge.academia.edu/…
	location	Cambridge, United Kingdom
	age	23
visits	member for	2 years
	seen	7 hours ago
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Currently undertaking Part III of the Mathematical Tripos at the University of Cambridge.

Previously obtained a B.S. in Mathematics and a B.A. in Physics from the University of Chicago (2012).

	1,306 reputation	bio	website	cambridge.academia.edu/…	visits	member for	2 years
421 badges		location	Cambridge, United Kingdom		seen	7 hours ago

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Oct 19	comment	Confusion between Electric field and Magnetic field of a charged particle. @claws This is a great question. You are hitting upon something that eventually led to the idea that there is no electric field, nor is there the magnetic field, but only the electromagnetic field. That is to say, whether you observe an electric field, a magnetic field, or a "mixture" of the two is dependent on your frame of reference, i.e., the electric and magnetic fields are really just two sides of the same coin. Regardless of whether you see the electric field or the magnetic doing the job, i.e. regardles of your frame of reference, you will still observe the same physical results.
Oct 19	comment	Non-unitarity of wave function collapse @lurscher This is kind of off topic, but for what it's worth, you can define the square of the delta function. In fact, you can define the product of any two tempered distributions as the Fourier transform of their convolution (which can be defined directly). I have a feeling that you can also make precise sense out of the square-root of a nonnegative tempered distribution, but I'd have to think about how to do that.
Oct 19	comment	Confusion between Electric field and Magnetic field of a charged particle. I believe your response to (i) is not quite correct. This argument would apply to the field inside an ideal conductor, but the electrons inside the conductor don't care about the field outside because the field outside does not affect their equilibrium.
Oct 18	comment	Graduate School for Theoretical Physics @Phira I don't think he means "assumptions" in the sense of axioms. More likely he means something along the lines of just assuming things work out, converge, can be made percise, etc., instead of "wasting" hours worrying about how to make precise sense of a particular integral, for example.
Oct 18	comment	Graduate School for Theoretical Physics That is true. Well, honestly, I love the fact that it is a physics book with a great amount of rigor, but do not like so much that it is not formatted like a mathematics book. I am probably biased, but I think it could have been organized/formatted in a much clearer way had it been written closer to the "math book" standard. In particular, I found that a lot of important content that could have stood out as 'Theorem' or 'Definition' "boxes" was hidden away in paragraphs of text.
Oct 18	comment	Graduate School for Theoretical Physics Yes, I would be very interested in talking with him about this. Feel free to send me an e-mail if you would like.
Oct 18	comment	Graduate School for Theoretical Physics @Domenic Could you please elaborate? It seems as if you are not the only one who thinks I have a misguided notion of what "rigor" is, means, and what it's role in theoretical physics is. Could you please explain?
Oct 18	comment	Graduate School for Theoretical Physics Nope, can't say I've heard the term "concentration" since I've been here. Thanks for the input!
Oct 18	comment	Graduate School for Theoretical Physics @BenjaminHorowitz You seem to be implying that Wald does not conform to a typical mathematician's level of rigor. I personally have only read the first half of the book or so, but as far as I remember, in terms of rigor, it might as well have been written by a mathematician. Do you have a specific example where it does not hold up to these standards?
Oct 18	comment	Graduate School for Theoretical Physics For what it's worth, I would say that I am more interested in placing QFT on a firm foundation than "generating new knowledge". That is to say, I am interested in taking the knowledge that we currently have, and placing it on a rigorous mathematical footing.
Oct 18	comment	Graduate School for Theoretical Physics @Moshe I don't understand. What is not an efficient way of making life decisions? I have spoken to as many people at Chicago as I can, and while must of their advice has been useful, I am still without a clear idea of good schools for theoretical physics are. I am excited about Cambrdige and the Perimeter Institute, but besides these places, I am afraid of going to grad school in math and not able to work on the problems I want to, or conversely, going to grad school in physics and not being able to work on the problems I want to in the way I want to. I just want the best of both worlds :)
Oct 18	comment	Graduate School for Theoretical Physics Perhaps I should also mention that I am more interested in placing QFT on a mathematically rigorous foundation, so that, in my research at least, I probably would not be working "on top" of things like renormalization.
Oct 18	comment	Graduate School for Theoretical Physics Unfortunately, the department I'm in has given me the impression that this attitude is more or less typical of theoretical physicists.
Oct 18	comment	Graduate School for Theoretical Physics Perhaps we have differing views of what it means to be rigorous? I have only skimmed serious TP research papers before, so I can only speak to the level of rigor I have experienced in taught classes. From that experience, however, perhaps all except for one or two (theoretical) professors I've had could even define a Hilbert space, Lie group, manifold, etc. For example, my current QFT professor openly denounces questions pertaining to how to make arguments precise (he says to stop being like a mathematician).
Oct 18	comment	Graduate School for Theoretical Physics The best example I can think of a good level of rigor would be Wald's General Relativity book. An example of a bad level of rigor would be defining a Lie group to be a group whose elements can be "continuously" labeled by a finite set of parameters. If more specific examples would help, please feel free to ask.
Oct 10	comment	Quantum Field Theory from a mathematical point of view Before studying QFT itself, I would recommend at the very least getting comfortable with special relativity and quantum mechanics. Being a student of mathematics myself, I understand how frustrating it can be to learn physics from a physicist, but at the end of the day, it will make learning QFT (or any subject of physics for that matter) much easier if you understand the physical meaning of the subject and why you are doing what you are doing. In any case, it will certainly improve your appreciation of the subject.
Oct 10	comment	Quantum Field Theory from a mathematical point of view I second the recommendation of Folland's QFT.
Sep 29	comment	How do you find the uncertainty of an weighted average? Yes, but doing this, I arrive at $\sqrt{5}/2$. According to the practice test, this is incorrect.
Sep 10	comment	Equation of Motion in a Non-Inertial (Rotating) Frame \widehat{}. \hat{} should also work.
Sep 8	comment	K3 gravitational instanton How are you supposed to have a basic knowledge of general relativity with no knowledge of differential geometry? How would you even talk about the metric tensor?