The tag has no wiki summary.

learn more… | top users | synonyms

2
votes
2answers
407 views

Finding the illuminance from a triangular light source

Since most light sources in games are point-like, it's pretty difficult to approximate area light sources with point sources. As triangles are a universal form to represent 3D models (thus area light ...
1
vote
2answers
29 views

Limits of Integration Trig, Mag Field Infinite Length Wire

I don't understand how the limits of integration should be defined when doing basic integrals of trig functions. It seems like it's an arbitrary decision, I don't understand it. Here's the set up: ...
2
votes
1answer
130 views

Integral over a product of two Green's functions

Need some help here on a frequently encountered integral in Green's function formalism. Forgive me since I am a junior student. I have an integral/summation as a product of a retarded and advanced ...
1
vote
1answer
70 views

Calculating electrodynamic momentum of a dumbbell (consisting of two point charges) in longitudinal motion

I'm working through a paper on momentum in electrodynamics that requires the integration below and would greatly appreciate any help. I'm pretty sure it evaluates to $2/d$ but I can't quite figure ...
0
votes
1answer
48 views

Details of the radial Fourier transform pertaining to certain quantum integrals

Consider the integral $$U(t)=\int\frac{d^3p}{(2\pi)^3}e^{-ip^2t/2m}e^{i\vec p\cdot\Delta\vec x}$$ for the free non-relativistic propagator. I'm not quite sure about the gritty details of radial ...
0
votes
1answer
46 views

What's my $dM$? Gravitational Potential inside a circle of mass

I'm trying to find the gravitational potential for an arbitrary point within a ring of uniform mass density. The point is constrained to be in the same plane as the ring. So we start with: ...
0
votes
1answer
31 views

Buckling of a slender column - total energy

I'm following Goldbart's Mathematics for Physics book, and I ran into a problem with exercise 1.4 (page 43). We have a formula for the energy stored in a slightly bent rod aligned on the $z$ axis: $ ...
0
votes
1answer
30 views

Volume of highdimensional Sphere vs volume of spheres shell

When calculating the phase space volume $\Omega$ in the microcanoncial ensemble with fixed energy $E$, one integrates over a shell that includes all energies in between $E$ and $E+\delta E$: ...
5
votes
0answers
430 views

Gaussian Integrals : Functional determinant expressed as a trace

Be $A_{ij}$ a symmetric matrix. Then I can easily write $$ \int \exp\left(-\frac{1}{2}\sum_{i,j}x_i A_{ij} x_j+\sum_{i} B_i x_i\right)\; d^nx= \sqrt{(2\pi)^n}\exp\left\{-\frac{1}{2}\mathrm{Tr}\log ...
3
votes
0answers
185 views

Propagator in massless scalar field theory

Suppose we have the following Lagrangian: $\mathcal{L} = \frac{1}{2} \phi \Box \phi + V(\phi)$, where $\Box = \partial _ {\mu} \partial ^ {\mu}$ and $V$ is the interaction term. We use the $(-+++)$ ...
3
votes
0answers
60 views

Coordinate Systems in Loop Integrals

Let us consider a two-point two-loop integral $\int \mathrm{d} ^ 4 k _ {2} \int \mathrm{d} ^ 4 k _ {1} \, f(k _ {1}, k _ {2}, p)$, where $k _ {1}$, $k _ {2}$ and $p$ are four-dimensional vectors in ...
3
votes
0answers
55 views

The question about MTW 4-momentum integral expression and lorentz nature

In section 5.8 of Misner, Thorne, and Wheeler's "Gravitation" there is a proof that 4-momentum determined as $$ \tag 1 p^{\mu} = \int T^{\mu 0}\,\mathrm{d}^{3}\mathbf r , \quad \partial^{\mu}T_{\mu ...
2
votes
0answers
94 views

Klein-Gordon propagator integral in the light-like case

In Kerson Huang's Quantum Field Theory From Operators to Path Integrals (Amazon link), pages 28 and 29, he calculates the propagator in the following case: time-like, space-like and light-like. First ...
2
votes
0answers
71 views

Finding the moments of the Boltzmann/Gibbs Distribution

I am trying to compute the moments of the Boltzmann distribution using a moment generating function, by taking the Fourier transform of the distribution and then taking derivatives to find the ...
2
votes
0answers
266 views

Why does this integral come out imaginary?

Im working through Zee and I'm having a little trouble with some integrals. I'm trying to reproduce the analogue of the inverse square law for a 2+1 D universe and I figured I could start with the ...
1
vote
0answers
55 views

Shifting the integration variable in loop integrals

We know that, in four dimensions, shifting the integration variables is valid only for convergent and logarithmically divergent integrals. If we employ a hard cutoff $\Lambda$, is it permissible to ...
1
vote
0answers
46 views

Equivalence of integrals in Classical Electrodynamics

I have a technical question about a section from Jackson's Classical Electrodynamics 3rd ed. In chapter 14, Jackson derives an expression for $ \frac{d^2I}{d\omega d\Omega} $, the frequency spectrum ...
1
vote
0answers
53 views

Partial Integration of outer product of del and position vector

I am trying to understand the solution I have been given to prove the following relation for a current density $\vec{j}(\vec{r})$ that is concentrated around the origin: $$ \int_V dV \, ...
1
vote
0answers
36 views

Normalization constant of the Vacuum polarization

In the article "On gauge invariance and vacuum polarization" by Schwinger, at some point the equation $$\frac{C}{s^2}\int e^{i\frac{x^2}{4s}} \, dx =1$$ is said to have the solution ...
1
vote
0answers
36 views

Why we don't integrate intital velocity in body cast equation?

On this site I've found a formula for calculating the $x, y$ coordinates for a body throwed by an angle to a horizon. It looks like this: $$x(t) = V_0 t \cos(\alpha); $$ $$y(t) = V_0 t ...
1
vote
0answers
53 views

Changing Coordinate Systems in Two-Loop Integrals

Suppose we have the two-loop integral $\int \mathrm{d} ^ 4 k _ {2} \int \mathrm{d} ^ 4 k _ {1} \, f(k _ {1}, k _ {2})$, where $k _ {1}$ and $k _ {2}$ are four-dimensional vectors in Euclidean space. ...
1
vote
0answers
33 views

Hemisphere irradiance

How do I calculate sky irradiance from radiance (L) from a hemisphere above a surface which is tilted relative to the normal (x=0,y=0,z=1). I have L as a function of zenith (0 to 180deg) and azimuth ...
1
vote
0answers
128 views

How to integrate twice of this viscous term?

I am reading a paper, and I do not understand why the author said the following term when integrated twice will become, $\int\limits_\Omega {{\rm{d}}\Omega {{\bf{\psi }}^{\bf{u}}}\cdot\nabla ...
1
vote
0answers
309 views

How to find the electric field at a point based on a uniformly charged surface

What is the general solution to finding the electric field at a point based on some (or multiple) charged surfaces. I know that we can perform a line/surface integral if a charge is close to a wire or ...
0
votes
0answers
19 views

Integration for quantum amplitude of the coupling between two molecules

I am trying to solve following expression for quantum amplitude of coupling between two molecules, (arriving from the second order perubation) $$\frac{1}{p}\nabla_{j}\int e^{ipR\cos(\theta)} dT=i\int ...
0
votes
0answers
15 views

Integrating Charged Bodies

Why is it possible to integrate charged bodies by first taking a small charge and adding more small charges around it? Wouldn't the similarly charged particles exert an immense amount of force on ...
0
votes
0answers
39 views

Fourier Transforming a $n$-dimensional ket (QM)

I would like to evaluate the Fourier Transform of $n$ functions. I am aware from the derivation of the convolution how this is done for the case of $n=2$. How could this be generalised for $n=3$? ...
0
votes
0answers
33 views

How can one approximate integral def. of Z by the max value of the integrand?

I am taking a course in statistical physics, and while reviewing my notes from the lectures I came across something that I cannot get my head around. We arrive at an integral expression for the ...
0
votes
0answers
77 views

Magnitude of Electric field vector on the axis of a conducting half sphere

I need to calculate the electric field of a conducting half-sphere shell ( just the outer shell, it has no base ) of a radius $a$ and surface charge density $\sigma$ on the arbitrary point on axis ...
0
votes
0answers
45 views

simplification of Green's intergral for diffusion

\begin{eqnarray} I_1 = \int^{\infty}_{0} \frac{1}{\tau}d\tau \int^{+\infty}_{-\infty} \exp\left[-\frac{p}{2\tau}(x-x')^2 + (z-z' + \tau)^2\right]dx' \end{eqnarray} where, $p$, $x$ $z$ and $\tau$ are ...
0
votes
0answers
62 views

Compute energy from displacement via time integration (using ODE)

How to compute energy from displacement given by solving an ODE via, e.g., ODE45. Say one has: $$ \ddot{z}+\zeta \dot{z}+z=\kappa\cos\left(\Omega t\right),\quad z=z\left(t\right) $$ and wishes to ...
0
votes
0answers
26 views

Verlet timestep

I am using velocity Verlet in molecular dynamics. Is just a simple question, if a simulation using time-step femtosecond, in velocity Verlet is just necessary $dt = 10^{-15}$ to use femtosecond?
0
votes
0answers
41 views

Geometric Interpretation of these equations of motion?

I was reading my Engineering Mechanics book, and it derived some strange looking integrals I'll have to apply. I could memorize them, but I'd rather understand them - then I won't have to memorize. ...
0
votes
0answers
130 views

Langreth rules and Keldysh formalism

I am trying to confirm the proof of Langreth's theorem / rules as seen in http://www.iue.tuwien.ac.at/phd/pourfath/node52.html . My problem is equation 3.55. I would do it like this: $\int_{C_{1}} ...
0
votes
0answers
289 views

Making a 3D physics engine, realistic? If so, where do I begin my research?

As a programming (technology), physics and math project in school, I'm considering programming my own 3D physics engine as a learning exercise. The physics engine should then be able to be used in a ...
0
votes
0answers
122 views

Nicholas Kollerstrom article on the history of Calculus

Today, Newton´s birthday, I read an article posted in the arXiv by Nicholas Kollerstrom http://www.arxiv.org/abs/1212.2666 That basically claims that Newton did not invent Calculus. The article does ...