I am doing some calculation and am now stuck with an integral of the form
\lim_{r \to \infty} \int_{-1}^1 dt f(t) e^{i r (t-1)}
for some function f(t). I don't know what the exact form of f(t) is.
Is there any way to address this integral? Similar to the saddle-point method perhaps...
I am assuming the tilde above an object implies taking a transpose. If that is the case, then M is indeed a symmetric matrix. One can see this by looking at the Lagrangian. Since the Lagrangian is a number, we can take a transpose of L and we'll get back the same number, i.e. L^T=L, this will...
This is confusing me more than it should.
A curve in space is given by x^i(t) and is parameterized by t.
What is the tangent vector along the curve at a point t= t_0 on the curve?
So, in the calculation of D(t,r) = \left[ \phi(x) , \phi(y) \right] , where t= x^0 - y^0,~ \vec{r} = \vec{x} - \vec{y} you need to calculate the following integral
D(t,r) = \frac{1}{2\pi^2 r} \int\limits_0^\infty dp \frac{ p \sin(p r) \sin \left[(p^2 + m^2)^{1/2} t \right]} { (p^2 + m^2...
So I want to calculate the quantum massless photon propagator. To do this, I write
A_\mu(x) = \sum\limits_{i=1}^2 \int \frac{d^3p}{(2\pi)^3} \frac{1}{\sqrt{2\omega_p}} \left( \epsilon_\mu^i (p) a_{p,i} e^{-i p \cdot x} + { \epsilon_\mu^i} ^* (p) a_{p,i}^\dagger e^{i p \cdot x} \right)...
Hi guys,
I figured out the problem with the question. There is not enough information to solve this problem. You can see this by doing the following construction. Draw the line AD first (This can be any length, for this argument atleast). Now draw the two equal angles BAD and DAC on either side...
Hey guys,
This is NOT homework. I remember solving this question many years ago (at least 10 years ago). I am trying to recall the solution again and am just not able to. The question is -
In a triangle ABC, AD is the angle bisector of angle BAC. AB = CD. Prove that angle BAC = 72 degrees...
So I know that the Hodge dual of a p-form A_{\mu_1 \mu_2\cdot \cdot \cdot \mu_p} in d dimensions is given by
(*A)^{\nu_1 \nu_2 \cdot \cdot \cdot \nu_{d-p}} = C\epsilon^{\nu_1 \nu_2 \cdot \cdot \cdot \nu_{d-p}\mu_1 \mu_2 \cdot \cdot \cdot \mu_p}A_{\mu_1 \mu_2\cdot \cdot \cdot \mu_p}
where C...
Is the following the definition of wedge product in tensor notation?
Let A \equiv A_i be a matrix one form. Then
A \wedge A \wedge A \wedge A \wedge A = \epsilon^{abcde}A_a A_b A_c A_d A_e
?
in 5 dimensions. This question is in reference to the winding number of maps.
The first three equations you've written down are correct. The answer is indeed pi/5. Check your calculation again. If you still don't find your mistake, write down your step by step solution, and i'll tell you where you're going wrong.
The equations of motion are of the form
\ddot{x} = -\frac{\partial V}{\partial x}
From this you can read off V. Now that you have the function V(x), what are the conditions for such a function to have a minimum at x=0 ?