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    I About Lie group product ([itex]U(1)\times U(1)[/itex] ex.)

    I recently got confused about Lie group products. Say, I have a group U(1)\times U(1)'. Is this group reducible into two U(1)'s, i.e. possible to resepent with a matrix \rho(U(1)\times U(1)')=\rho_{1}(U(1))\oplus\rho_{1}(U(1)')=e^{i\theta_{1}}\oplus e^{i\theta_{2}}=\begin{pmatrix}e^{i\theta_{1}}...
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    What function I'm looking at?

    For some reason your response led me to think that the answer is obvious... :biggrin: So I plotted 1-e^{-x} and it turns out that it's the answer I'm looking for. Never seen an (inverse or whatever it's called) exponential decay plot in log-log scale before .. As for the irrelevant 'where did...
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    What function I'm looking at?

    Hey all What's could the function be on the plot (see the attachment)?
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    Mass dimension of coupling constant -- always an integer?

    Well I was thinking whether it'd be pseudoscalar (that shouldn't be any big problem -- if we really want a parity violating theory). I just thought about gauge transformations, and yup, you were right -- the term wouldn't transform as a (pseudo)scalar but as a spinor. Adding scalar and spinor...
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    Mass dimension of coupling constant -- always an integer?

    Thinking beyond SM, what are the physical consequences if the Lagrangian contains an interaction term with an odd number (i.e. only one) of fermions?
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    Mass dimension of coupling constant -- always an integer?

    Just a simple question -- can the dimension of coupling constant be a rational number or should it always be an integer? The question arose when I was trying to construct a Lagrangian with an interaction term involving two spin-1 particles and a fermion. The dimensions add up to 7/2, which...
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    Momentum space measure -- change of variables

    I'm working through an article called "Cosmic abundances of stable particles -- improved analysis" (link -- viewable only in Firefox afaik), the result of which, equation (3.8), is cited quite a lot. I'm more interested in how they arrived there. Particularly, how come momentum space measure...
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    Feynman rules - where do the imaginary numbers come from?

    I'm trying to learn how to derive Feynman rules (what else to do during xmas, lol). The book I'm using is QFT 2nd ed by Mandl&Shaw. On p 428 they're trying to show how to derive a Feynman rule for W W^\dagger Z^2 interaction term g^2 \cos^2\theta_W\left[W_\alpha W_\beta^\dagger Z^\alpha Z^\beta...
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    Relative velocity of beams

    doh... natural units... thx
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    Relative velocity of beams

    How come relative velocity of the beams can be expressed by v_{12} = \left| \vec{v}_1 - \vec{v}_2 \right| = \left|\frac{\vec{p}_1}{E_1} - \frac{\vec{p}_2}{E_2}\right| where \vec{p}_{1,2} and E_{1,2} is the momenta and energies of incoming particles, respectively? Similar equation is in Peskin &...
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    Plane wave expansion of massive vector boson

    So... I think I'll go with two sets of ladder operators as usual in complex scalar field/fermions. It seems that the thesis uses them implicitly -- in Wick contraction the other operator is neglected because of the normal ordering requirement. About path integral.. thanks but I'll skip it for...
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    Plane wave expansion of massive vector boson

    I'm trying to derive Feynman rules for massive vector boson and its antiparticle. It all boils down to plane wave expansion of the bosons which atm is a little bit confusing. Should I account for two different set of ladder operators (as in the case of complex KG or spinors, cf Peskin&Schröder...
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    UDP multiclient server in C

    Hi all I'm trying to create a server that uses UDP and is capable of handling multiple clients. The server should 'stream' content to the clients only on the initial request (i.e. when starting the client). The general idea is to test how many clients is the server able to 'serve' before the...
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    Dual tensors in Lagrangian

    Yeah, I forgot to mention I'm interested in U(1) theory. Thanks for the link, will read it.
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    Dual tensors in Lagrangian

    Thanks, Bill_K, I didn't know that before. A quick proof for the eager: \begin{align*}\widetilde{F}^{\mu\nu}\widetilde{F}_{\mu\nu} &= \frac{1}{4}\epsilon^{\mu\nu\rho\sigma}\epsilon_{\mu\nu\alpha\beta}F_{ \rho \sigma}F^{\alpha\beta} = \frac{1}{2}\delta_{\alpha...
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    Dual tensors in Lagrangian

    Why is it the case that dual field tensors, e.g. \widetilde{F}^{\mu\nu}=\frac{1}{2}\epsilon^{\mu\nu\rho\sigma}F_{\rho \sigma}, aren't being included in the Lagrangian? For example, one doesn't encounter terms like -\frac{1}{4}\widetilde{F}^{\mu\nu}\widetilde{F}_{\mu\nu} in QED or...
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    Mega quick question: must the Lagrangian (density) be real valued?

    It basically says that the Lagrangian must not be hermitian since it's not observable. But I still have mixed feelings about it. After googling "hermicity of the Lagrangian" this popped up stating that the Lagrangian of the theory invariant under CPT symmetry must be hermitian (don't know...
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    Mega quick question: must the Lagrangian (density) be real valued?

    Mega quick question: must the Lagrangian (density) be hermitian? In other words, must \mathcal{L}=\mathcal{L}^\dagger always be valid?
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    Thermalization of photons

    Thanks, your answers cleared up some of the things. One thing bugs me though, FTA: How is this accomplished? I know that CMB anisotropies are quantitatively obtained by perturbing the metric, but afaik no abundances nor densities don't kick in the derivation. In particular, how does...
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    Thermalization of photons

    Quick question: what is meant by thermalization of photons? And how could this effect distort CMB spectrum (anisotropies)? Any references are also welcome.
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    The origin of baryon number

    Thanks everyone for your input! Got the type of answers I wanted.
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    The origin of baryon number

    I'm doing a little research on quarks on stumbled upon the baryon number. Wikipedia says that the notion predates the quark model. I have no clue why particle physicists were motivated to introduce it before flavour quantum numbers came to the scene. So... What's the (historical) origin of...
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    C/++/# C++ pause and resume while(true) loop

    How to design a class, that executes an infinite loop, but may be paused, resumed and stopped by user input? I'll give you an example class Simulation { public: void start(){ m.init(); while(!m.isFinished()) m.update(); // computationally expensive calculation } void pause(); void...
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    Applicability of Ising model on real materials

    Hi I chose a Monte Carlo simulation of the 2D Ising model as my Computational Physics course project. Unfortunately, I ran intro problems when formulating the exact problem since my professor probably wants me to simulate a real life material and extract magnetization curve M(T,H) out of it...
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    PF Random Thoughts Part 2

    ugh I hate latex for every solution to every problem I have to use new packages ugh
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    What is this ecuation about?

    Looks like the geodesic equation. Einstein summation convention is used in the Wikipedia article.
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    Topics in mathematics

    Maybe some rudimental tensor calculus? Our electrodynamics course was based on Landau&Lifshitz. First google result: link. This is fairly sufficient and not much for an undergraduate level course.
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    What does c.c. in equation represent?

    This one doesn't look like a complex conjugate, since it's an operation not an additive quantity. To OP: You just have to give more context, but the chances are that it's explained in the original text.
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    How To Find The Integral of Sin x dx?

    This is obtained by using's_formula]Euler's[/PLAIN] [Broken] formula and trigonometric identities \sin(-x)=-\sin(x) and \cos(-x)=\cos(x). By knowing that \frac{d}{dx}e^{kx}=ke^{kx}, you can work out the integral by yourself. But memorizing simple derivatives...