Phi Definition and 125 Threads

Hi, Look at \begin{align} & \int d^4 x d^4 x_1 d^4 x_2 d^4 x_3 d^4 x_4 \exp [i(p_1 x_1 + p_2 x_2 -k_1 x_3 -k_2 x_4)] \\ & \times (-i\lambda)D(x_1-x)D(x_2-x)D(x_3-x)D(x_4-x) \end{align} for first order in lambda for 2-2 scattering. In Maggiore I am told to substitute y_i=x_i-x as a...

Consider a light ray emanating from the origin of a FLRW coordinate system in a homogeneous, isotropic universe. The initial velocity of that ray will have only x0 (t) and x1 (r) components. In papers I have seen it is assumed that its velocity will continue to have zero circumferential...

I'm reading University Physics 13e by Young and Freedman and we're given this equation: -L(di/dt)-q/C=0 So we know that i, current, is, i=dq/dt. So the first equation can be read, after some simplification, as q''+(1/LC)q=0 where q prime means the derivative of q (charge) with...

RThe "canonical representation phi" (measure theory) (Royden) Homework Statement I need some help understanding the canonical representation of phi as described on p. 77 of Rodyen's 3rd edition. I've transcribed it below for those of you who don't own the book. Homework Equations The...

I'm working on an online EECS course, and to be frank some of it is going straight over my head - but at the same time parts of it are far below my current knowledge, so I want to work and stick with it. The speaker is working through proving current and voltage - to arrive at Kirchoff's...

A question I have is how is one supposed to calculate phi when simply looking at a sin wave. The equation is of the form x(t) = A*cos(wt + phi). Once again, the only thing i am given is the graph. I appreciate any help you can give!

Homework Statement Find x such that phi(x) = 5,000,000, where phi(x) is Euler's function. Homework Equations I know that if x is prime, then phi(x) = x-1. Also, phi(pk) = pk - pk-1 = pk * (1 - 1/p). The Attempt at a Solution Since 5,000,001 is not a prime number...

In treating the complex scalar field in QFT, \phi and \phi^\dagger are treated as independent variables. I'd like to make sure I understand what this actually means: Is this the same idea as treating \phi and \partial \phi as independent variables in the Lagrangian? Formally, we view the...

Homework Statement Would tau and phi be considered conjugates? Homework Equations \tau = \frac{1-\sqrt{5}}{2} \phi = \frac{1+\sqrt{5}}{2} The Attempt at a Solution I know that a complex number such as 1+2i would have 1-2i as a conjugate. However, for fractions, I can't quite remember if the...

Homework Statement Find the volume bounded rho=5+2cosphi Homework Equations dV=rho squared drho d phi d theta The Attempt at a Solution I am guessing this is some cylindrical shape. Theta should be 0-2pi and phi=0 pi/2

Whyyyyyy??! Whhhhhy?!?

how to define a V-sentence phi such that phi has aebitrarily large finite models and for any finite model G , G is a connected graph. after that to find a connected graph that does not model the sentence phi. please explain it to me.

Prove that the Euler phi equation is always divisible by 2. If n > 2.? I don't understand how this proof works: I think I need to show that the inverse of a and a are both generated by the same group. Therefore, there are at least 2 elements that generate all other elements in the group...

So upon introduction to Euler's phi function, we can see that \phi (1) = 1 and \phi (2) = 1, where it turns out that these are in fact the only numbers in N that map to 1. Now what I'm wondering is if there is some general way to find the inverse image of numbers in the image of phi? Also...

In general, how do I determine the angle phi when you have to use spherical coordinates for integration?

Homework Statement Let p = a prime. Show {x}^{2} ≡ a (mod {p}^{2}[/tex]) has 0 solutions if {x}^{2} ≡ a (mod p) has 0 solutions, or 2 solutions if {x}^{2} ≡ a (mod p) has 2. The Attempt at a Solution OK, my mistake, I don't think this has anything to do with the phi function. But I don't...

I'm pondering, since we've introduced formalism, all operators are either scalars or vector components, does it make sense to define operators like r, theta, phi (as in spherical coordinates) which are neither? In classical mechanics we can easily transform observables fro cartesian to...

Does anyone know the phi factors for overturning, sliding, and soil bearing in a small reinforced footing? If you could site the precise source too, that'd be great. I don't have access to many up to date specs and codes :/

Hi, I'm trying to show that phi^3 theory in d=4 is superrenormalisable (only finite no of terms are power counting divergent). In the following I use, d=#dimensions, I=#internal props, E=external legs, V=#number of vertices (of phi^3 type, i.e. three valent) The Superficial degree of...

I am having trouble with this proof: show that if d|n then phi(d)|phi(n). I know that if d|n, then ad=n and that phi(ad)=(a,d)*phi(a)&phi(d)/phi((a,d)), but I can't seem to get anywhere with this info. Thanks for your help.

"Let m and k be positive integers and φ(m) is the Euler's phi function. Then the number of integers n such that 1≤n≤mk and (n,m)=1 is kφ(m)." I can't figure out why this is true. How can we prove it? Can someone explain this, please? Any help is appreciated!

A 2[\muC] point charge is located at A(4,3,5) in free space. Find E\rho, E\phi, and Ez at P(8,12,2). I know I have to start off in rectangular, convert to cylindrical coordinates. I know how to find the R vector and |R|. Since it says there is a point charge, do I need to integrate...

This is getting on my nerves now. I am stumped on these: Homework Statement Obtain an expression for: phi(p^3) and phi(P^n) Homework Equations phi(p^2)=p(p-1) The Attempt at a Solution The factors of P^n are 1 and P. Any number less than P^n that shares a factor must have p as a...

Generally, I am stumped by the Phi function. I have found out the pattern but I am having difficulty proving it. Homework Statement i) When p is a prime number, obtain an expression in terms of p for:- ϕ(p²)Homework Equations ϕ(p)=p-1 The Attempt at a Solution ϕ(p)=p-1 so ϕ(5)=4 therefore...

What are the dimensions of a scalar field \phi ? The Lagrangian density is: \mathcal L= \partial_\mu \phi \partial^\mu \phi - m^2 \phi \phi So in order to make all the terms have the same units, you can try either: \mathcal L=\frac{\hbar^2}{c^2} \partial_\mu \phi \partial^\mu \phi -...

i have been given a problem for writing s matrix in second order perturbative theory for an interaction hamiltonian with phi 4 and phi 3 contributions. it is also given that our initial state is of 2 particles and final state is of three particles. now in solving that i have to take time...

what does phi mean

Homework Statement The direction of propagation is defined as ex=sin(theta)cos(phi), ey=sin(theta)sin(phi), ez=cos(theta). What are the values of theta and phi characterizing the direction of propagation? Homework Equations We have a point in space with the coordinates...

This is most likely very simple, but I can't figure it out. http://www.sussex.ac.uk/physics/teaching/btv/Lect02_2006.pdf Step 5 they've got an equation for \Phi. They then normalise it to get A = \frac{1}{\sqrt{2\pi}}. Every time I do the integral I get: A^2.^{2\pi}_{0}[...

Moved. Delete please.

I am trying to write the term "Sin^2 theta * Sin 2 phi" in terms of spherical Harmonics (they form a combination of Y(2,-2) and Y(2,2)) but the term I get contains the imaginary number 'i'. Am I doing something wrong.. In fact this term is a part of a Hamiltonian and when I get the eigenvalues I...

phi(20^100) = phi(4^100 * 5^100) = phi(2^200 * 5^100) = (2^200 - 2^199)(5^100 - 5^99) = 2^199(2-1) * 5^99(5-1) = 2^199 * 5^99 * 4 = 2^201 * 5^99. I don't understand line 4-7. Can anyone explain?

Let A, M be a commutative ring and a finitely generated A-module respectively. Let \phi be an A-module endomorphism of M such that \phi (M)\subseteq \alpha\ M where \alpha is an ideal of A. Let x_1,\dots,x_n be the generators of M. Then we know that \displaystyle{\phi(x_i)=\sum_{j=1}^{n}...

How do i comput the euler phi function of a large interger? i know that if p is prime then phi(p)=p-1 and I've found a formula for computing non primes but i don't know how to implement in something like Matlab. Does anyone know how?

How do i comput the euler phi function of a large interger? i know that if p is prime then phi(p)=p-1 and I've found a formula for computing non primes but i don't know how to implement in something like Matlab. Does anyone know how?

Phi exists at the center of prime quadruplets, along with its square root, and cube root! http://www.code144.com/zphithrice.png The 'pos' numbers come from the position of the prime numbers in the sequence itself, i.e. 193 is the 44th prime number, and 197 is the 45th prime number...

Hi all, Can anyone point to an explanation of why if ker(phi) = {0}, then phi is injective?

hey there! its my first post, and quite an urgent one. i am into my last year of high school, and i am required to write a 4000 word maths essay. i chose to write on maths, because i like maths! but i am quite stucked at this stage... i decided to writing on the mathematical relationship on...

\foralln\inN\varphi(n)/mid/n

Let [phi](u,v)=(u^2,v). Is phi one-to-one? If not, determine a domain on which phi is one-to-one. Find the image under phi of: - The rectangle R=[-1,1]X[-1,1] The Attempt at a Solution - I'm not sure at all how to determine whether phi is one-to-one or not, so if somebody can...

Iterating Euler's totient function \varphi(n), it eventually arrives at 1. Let h(n) denote the least number of iterations to arrive at 1. For instance, h(18)=3, ie \varphi^{3}(18)=1. There is a conjecture (or is there a proof?) that the largest n for which h(n)=k is 2\times 3^{k-1}. The only...

Guys How do you think our reality would differ if the phi ratio were exactly 3 ? Is infinity a possibility? To me It must be, but in he same breath it can't be! "It is impossible to imagine an impossibility" By the way I am a retired Mechanical Engineer (Electricity power...

The analytical solution for the wavefunction of a hydrogenic electron with quantum numbers n, l and m has a spherical harmonic part that involves theta and phi (in spherical coordinates). I was looking in Griffiths, and the spherical harmonics part only has phi as exp(i m phi) where i is the...

I guess one could use any irrational numbers here, but phi and pi are favorites. I am sure that most people are aware of the infinite monkey theorem. If not use http://en.wikipedia.org/wiki/Infinite_monkey_theorem as a reference. By using this theorem, could one say that the the first...

So I have been invited to join Phi Kappa Phi. I'm short on funds, but that isn't the primary reason why I'm considering not joining. The people part of the honors society tell me that it's worthwhile, which comes to no surprise by me, and poking around the internet makes me think that it might...

Prove that if d divides n then phi(d) divides phi(n). Thanks

Homework Statement Compute the S-operator to first order in the coupling constant lambda. Homework Equations The given Lagrangian density is L = : \frac{1}{2} (\partial_{\mu} \phi)^2 - \frac{1}{2}m^2\phi^2 + \frac{1}{2}\frac{\lambda}{4!}\phi^4 : where phi is a scalar field. The...

Phi is pronounced fi in America, not fee! Bill_Smith is Online: Posts: 0 Fi, not Fee! Okay people, here is the logic behind phi. Yes, in Greece you would pronounce the letter phi as fee. If you lived in Mexico you would pronounce the letter x as eck-ees. In America we pronounce the letter...

Hi, just wondering whether the commutation relation [\phi,L_3]=i\hbar holds and similar uncertainty relation such as involving X and Px can be derived ? thanks

The golden ratio is irrational. Do you know any clever proofs for this fact? I put this here, because it's not homework--only more of a discussion.