Recent content by captain

So I am still confused about how to applying scaling of parameters to a general optimization problem. Let's say I am trying to do maximum likelihood estimation. I understand how to find the scaling matrix (assuming we restrict it to diagonal form) and that the Hessian should be close to the...

Hi all I was wondering if anybody knew any good books (preferably textbooks) on random matrix theory? thanks in advance.Edit: My apologies if this is posted in the wrong section.

I am curious to know the Ising model can be applied to high temperature superconducting materials. If so are there any papers significant papers on this subject that I should know about. Thanks to anyone in advance who can answer this question.

I just want to know when would you use a Fourier transform method to solve a PDE vs. separation of variables or Laplace transform? My guess is that a Fourier transform is for a problem in which the solution exists from negative infinity to positive infinity, whereas a Laplace transform would for...

I was actually talking about partial differential equations like Laplace's equation or other such linear equations

this may seem like a simple question but how does one know that separation of variables for solving linear PDE's will work. What i mean is that it seems to pick out a form of the solution to a given problem (I have heard that linear PDE's have an infinite number of functions of a particular...

I wanted to ask if there is any connection between the SU(2) group for the spin 1/2 and the gauge group of weak interactions. I feel there isn't much of a connection other than the fact that they share the same group properties, but I am not sure. Thanks to anyone in advance that can clarify...

This is a basic question about the scalars, vectors, pseudo-scalars, and pseudo-vectors. I know that scalars and pseudo-vectors don't change sign under parity and vectors and pseudo-scalars do, but does that imply that scalars have to be even function of x, y, z (like for example x^2+y^4+z^2)...

This may be a simple question, but I feel as though I don't clearly understand this fully. How come we can take the photon field to be represented by the four potential instead of the E and B fields? Is it equivalent and more convient to do? Also by using the 4 potential do you atomatically have...

I wanted to ask a quick question about the complex scalar field. My question is that does the scalar field need to be complex in order to include the part for anti-particles or do you regards the scalar field for particles and anti-particles seperate. I saw this specifically when you second...

I have seen that in order to quantize a field there is a need to establish commutation relation (or anti-commutation relations). I am wonder how does that in a sense quantize something. I feel as though I don't have a good grasp of how it works. The only thing that seems apparent is that this is...

A professor told me that in our spacetime we are able to distinguish between different inertial frames because the cosmic microwave background looks different. If this is true then what spacetime do we live in? What would it look like mathematically. Would the det(g) not be negative?

I have seen in a description of QED that it predicts that light can move faster or slower than the speed of light, but on average it moves at the speed of light. I wanted to know if htis was true and if it is, is the reason behind it due to the fact that the phase velocity (since we are dealing...

I have question about the two degrees of polarization of light. I know for a fact that light has only two degrees of polarization for a fact, which just means that light is transverse, but i want to understand what does the longitudinal electric field that you get from a columb field mean...

I wasn't sure where to put this since this is under group theory. I am having a little bit trouble understand when to use direct product vs direct sum. One question I have about this is is that if you have two vector spaces that are orthogonal to each other (and example of this might be two...