That is exactly what I have thought. Physics studies space, time, matter, energy, and the forces; geometry studies just space. Therefore, geometry is part of physics and physics is an extension of geometry. Euclid's theory was the first theory of physics, as it was the physics of space...
It takes at least three steps
I don't see it immediately.
-\frac{1}{(2\pi)^2} \int d^3x d^3y \frac{(\nabla\times\vec{a}(\vec{x}))\cdot(\nabla\times\vec{a}(\vec{y}))}{|\vec{x}-\vec{y}|^2}
=...
The field equation is
i \frac{\partial\varphi}{\partial t} = -\frac{\partial^2\varphi}{\partial x^2} + 2c|\varphi|^2\varphi (2.84)
which is the ordinary Shroedinger equation plus self-interaction term.
The field Hamiltonian is
H = \int^L_0 dx...
Apology accepted. I appreciate the importance of presentation, however, typing in all the latex code is a lot of work, so I decided I would present as much information as I believed was necessary at first, and give clarifications as needed.
Anyway, the answer to your question about the theta...
NLS is a second-quantized theory. Its field equation is nonlinear. However, solving for the eigenvalues for finite-particle states leads to (2.87). I don't know why the book has a section on this. It hardly seems relevant to the subsequent development of the book and I've been able to move...
The book's preface claims that calculations are presented "in step-to-step detail". Yet when I encounter problems like this, I suspect that I'm missing something. I've put a lot of hours into reading the book already. So help me out or don't help me, but don't get mad at me.
The ground state wave functional for the photon theory is given as
\Psi_0[\tilde{a}] = \eta \exp \left(-\frac{1}{2} \int \frac{d^3k}{(2\pi)^3} \frac{(\vec{k}\times\tilde{a}(\vec{k}))\cdot(\vec{k}\times\tilde{a}(-\vec{k}))}{|\vec{k}|}\right)(10.81)
where \tilde{a} is given as the Fourier...
Relevant to the NLS is the differential equation,
\left( -\sum^N_{i=1} \frac{\partial^2}{\partial x^2_i} +c \sum_{i\neq j} \delta(x_i-x_j)\right)f_N = E_Nf_N(2.87)
How does one show that
\left(\prod_{i<j}(\theta(x_i - x_j) +...
Very interesting. The integral \int^\infty_{-\infty}e^{2\pi ikx} dx does in some ways behave like a delta function. And the delta function is an ideal function. However it's own Fourier transform is an exponential, which is a real funtion. The Fourier transform as an operator on Hilbert...
Why is it that the Fourier transform of e^{2\pi ikx} is equal to \delta(k) ? The delta function is supposed to be zero except at one point. But the integral doesn't converge for k \ne 0 . Yet I see a lot of books on QFT use this identity.
You know you are using one if...
1. You are using Emacs, even though you hate it!
2. You are thinking of getting a Linux box, but aren't sure of it.
3. You've never had more trouble with any other application program.
4. You have downloaded a lot of new programs and have deleted them...
Russell's type theory has some philosophical embellishments, such as the axiom of reducibility, which asserts that every formula is equivalent to another formula that is predicable. This does two things: it makes the restriction redundant, and it is actually not a very plausible axiom. If you...
Latex -- how to do Dirac slash notation
How do you do Dirac slash notation using LaTeX?
For instance, I want to be able to type
/\partial = \gamma_i \partial^i
/p = \gamma_i p^i
/A = \gamma _i A^i
with the slashes running through the symbols \partial , p, and A.