Translation Definition and 227 Threads

As we face in Poincaré Transformation, there are boost and translational symmetry.What is the difference between these two terms?

Wieland's thesis was posted at tel.archives (the French open-archive website) on 3 March 2014. http://tel.archives-ouvertes.fr/docs/00/95/24/98/PDF/diss.pdf The title of the 160-page dissertation is The Chiral Structure of Loop Quantum Gravity. It is a noteworthy thesis which could be valuable...

How to understand "momentum is the generator of translation" ? "As it is known from classical mechanics, the momentum is the generator of translation", it is from WIKI, (http://en.wikipedia.org/wiki/Momentum_operator) I don't understand its meaning. T(ε) is translation operator, then...

Hello All, I've been searching for days to try and solve this but I'm going round in circles so thought I'd fire it out to into the ether! I'm analysing a gantry system that is essentially cantilevered from one end but the part of the problem I'm struggling with can be simplified thus...

Homework Statement The vectors r1 and r2 below represent atomic positions in a crystal. r1 = (n1 + n3)ax + (n2 + n3)ay + n3az r2 = (n1 + n3 + 1/2)ax + (n2 + n3 1/2)ay + (n3 + 1/2)az Assume first that the two vectors above correspond to two different types of atom. Find a set of...

I'm not sure how they got equation 4.5 Starting from ##\psi'> = U_{(\vec{a})} |\psi>## where ##U_{(\vec{a})} = e^{\frac{-i\vec {a} \cdot \vec {p}}{\hbar}}## Differentiating both sides with respect to ##a_x## and setting ##a = 0##: \frac{\partial |\psi'>}{\partial a_x} = \frac{-ip_x}{\hbar}...

How do I see that when my hamiltonian is translation invariant i.e. H = H(r-r') it means that it is diagonal in the momentum basis? I can see it intuitively but not mathematically.

Hi, In Sidney Coleman's Lectures he talked about space translations such that but when I expanded the exponentials and and used the commutation relation of p and x, I got ρ(x+a) instead of ρ(x-a) Does anyone see where I may of went wrong?

Homework Statement I must show that the equation ##\frac{\partial E}{\partial t}=t\nabla \times E## is invariant under time translations and I must also find its symmetries if it has any. Where E is a function of time and position.Homework Equations Already given. The Attempt at a Solution I...

Inspired by a question in Griffiths' E&M book (1.10), I am wondering why the components of a vector do not change when the coordinate system is translated by a constant vector. I understand that, for instance, the velocity of something moving in a coordinate system won't change if we then...

Homework Statement Hi all. I am having trouble to understand the combination of transformation on a function: h(x)= a*f(b(x-c))+dHomework Equations The problem I am struggling with is the order of transformation; I do see that: f(x-c) is translation in the right since every event happen before...

Srednicki eqn. (2.23) and (2.24) states: We can make this a little fancier by defining the unitary spacetime translation operator T(a) \equiv \exp(-iP^\mu a_\mu/ \hbar) Then we have T(a)^{-1} \phi(x) T(a) = \phi(x-a) How do we get the second equation from the first equation?

I am trying to explain metric spaces and finding it hard to come up with simple to understand, interesting examples of metrics that are not translation invariant. The audience is people who are just now studying general metric spaces.

Dear forumers, I'm looking for the translation in ENGLISH for the following article : On the Dispersion Mechanism in Laminar Flow through Tubes Kunio Arai1), Shozaburo Saito1), Siro Maeda1) 1) Department of Chemical Engineering, Tohoku University Chemical engineering Vol. 31 (1967) No. 1 P...

Maybe someone who knows about FM radio transmission equipment can help me. I'm the pastor of a 200 member church in Berlin Germany. I would like to build a small system to broadcast simultaneous translation. I would think all I need is an FM transmitter, microphone and FM radios or headset...

Homework Statement If the graph of 1/x is reflected in the y-axis, translated 3/4 units to the right and 2 units up, the resulting graph would have the equation... A) 1/(x-2) + 0.75 B) 3/(4x) +2 C) 2 - 1/(3/4x) D) -1/(4x-3) + 2 E) 1/(3-4x) + 2 2. The attempt at a solution So the general...

For potential well problem for well with potential which is zero in the interval ##[0,a]## and infinite outside we get ##\psi_n(x)=\sqrt{\frac{2}{a}}\sin \frac{n\pi x}{a}##. If I want to get this result for well with potential which is zero in the interval ##[-\frac{a}{2},\frac{a}{2}]## and...

hi guys, this is literally my first post here on physicsforums so i apologize in advance that my latex formatting sucks. Homework Statement prove the alternative form of the 2nd translation theorem of the laplace transform: L[f(t)u(t-a)]=e^{-sa}L[f(t+a)] where u(t-a) is the unit step...

e^{\alpha\frac{d}{dx}}=1+\alpha\frac{d}{dx}+\frac{\alpha^2}{2!}\frac{d^2}{dx^2}+...=\sum^{\infty}_{n=0}\frac{\alpha^n}{n!}\frac{d^n}{dx^n} Why this is translational operator? ##e^{\alpha\frac{d}{dx}}f(x)=f(x+\alpha)##

Homework Statement Find the translation vectors of the primitive cell. The figures are provided. Homework EquationsThe Attempt at a Solution I found these are more difficult than what I am learning from Kittel. I did number 1, but not sure if it is correct. Answer or hint for any of the...

It is not hard to show that for QM what takes the wave function from t->t+Δt is the exponential of the hamiltonian. Yet for some mysterious reason my book decides to note the Hamiltonian as the generator of time translation rather than the exponential of it. What is the reason for this?

Homework Statement A perpendicular force F acts on the tip of a thin rod of length L and mass M in the ij-plane which is not fixed. What is the translational and rotational acceleration of the rod about the center of the rod? Homework Equations At first it seems like an easy problem...

I'm trying to understand the construction of the T(ε) operator and why it is equal to I-iεG/hbar. The textbook I'm using (Shankar) talks defines the translation operator with the phase factor: T(ε)\left|x\right\rangle=e^{i \epsilon g(x)/\hbar}\left|x+\epsilon\right\rangle and...

Hi all, I have been trying to solve this problem, I basically have a cam that's pushing up a follower and I was wondering if someone could check my work So from the diagram below I have a force acting on the follower at a 77.6 deg angle. So I did Fy = F x Sin(12.4deg) = 1.012 lbf, Then...

understanding of the word "within" with regards to translation in math I need a clear understanding of the word "within" with regards to translation in math. Like if I say integers of X is within the interval of 5 and 10. Does this mean: [5,10] (5≤ X ≤10)?? The reason I ask this is because in...

I have an equation that I've been trying to solve. I manipulated it until I had a=f(d) and then did by best to put it into a format the computer recognizes. However when I went back to check the results against the unsimplified version of the equation, they didn't work out as they should have...

Hello Forum, if a force is applied to an object along a direction that passes through the center of mass, the object will translate without rotation. If the force acts along a line that does not pass through the CM, will the object both rotate and translate? Where and how does the force...

HI there. Some days ago, whyle studying vector mechanics I came across with a rather dazzling doubt. Why isn't there angular velocity and accelaration in a curvilinear translation? Imagine, a small planet in a perfect circular orbit around a star. Let's say, the planet has no form of...

What happens to mRNA's after translation. Do they get degraded?

Hi, I have some Mathematica code I want to translate in Matlab, does anyone know how to translate the Table [expr,{i,a,b}]to Matlab? I made one with a loop, but loops are very slow and I am going to analyze large datasets with the functions.

Hi! I am trying to translate a paper on inorganic chemistry from Spanish into English but, since I am not an English native speaker and my knowledge of chemistry is limited, I could definitely use some help in order to get everything right. With regard to the title of the paper (NC =...

Hi, I want to calculate the coordinates of an object after a particular translation. I have the 3D coordinates at the origin: x0,y0,z0 and i have the 3x3 rotation matrix: (r11, r12, r13; r21, r22, r23; r31, r32, r33) If I want to move 3 units forward, in the direction i am facing and two...

Hi I am doing a course on Program verification and am having trouble with the properties of summation, more specifically the rule of translation: "Suppose function f maps values of type J to values of type K, and suppose g is a function that maps values of type K to values of type J. suppose...

Homework Statement This is the 1st problem in the section 1-5, do Carmo' Differential Geometry of Curves and Surfaces. It is in page 22. We have a parametrized curve \alpha (s)=(a\cos \frac{s}{c}, a\sin \frac{s}{c},b\frac{s}{c}) with c^2=a^2+b^2. The 4th problem is to show...

Hi there, Having a little difficulty. I have to revise Translation and rotation of a rigid body. But I don't know what is meant by translation of a rigid body. Rotation is obvious. I am guessing that it is the movement of a rigid body from one place to another. The best way I can explain...

Homework Statement I am going back and reviewing some elementary material in logic/set theory. Among the problems in the quantifier section is the following english sentence to logic sentence translation: Everyone likes Mary, except Mary herself. Now, my attempt was: (∀x)[(x≠m →...

Hello! This is my first post but I have been a lurker for a long time! I am starting my own business in the U.S. and have run into a bit of lost in translation when it comes to the electrical requirements needed. I am importing a water system from Hong Kong that is based on: Single...

When I was learning translational symmetry I saw that for translation invariance, i.e [T,H]=0 the momentum P needs to be conserved [P,H]=0. This momentum is actually the generator of small translations defined as T:x→x+ε. Now, I was solving some problems and I met one which is...

I am a bit confused about a statement I read in my textbook saying the sum of external forces on a body is equal to the body's mass times the acceleration of it's center of mass. It seems to me if a long rod is suspended in the air by a string at its center of mass, and I tap the rod near one of...

In the concept of translation operator, there's a line said that where and How could they interpret that this parameter ρ is really a momentum operator?

Usually the mean translation speed of the Earth around the sun is calculated (approximating its elliptic orbit with a circular orbit) to be around 29.7 Km/s. This is fine if we consider the sun is still, but we know this is not the case (see for ilustration ), the sun is also moving thru space...

Hi! I don't know if this is the right place to post this topic, if there is a better place, please let me know and I'll move my post. I have to write a resume of my project and I have to write it in English. My mother language is Italian and I'm not so good in writing in English, so can you...

Hi best regard to all This is my first post so forgive me in any mistakes. If some one can explain to me those parts marked in red rectangles? It taught it was more convenient to post picture than typing. It's from a book that is not in English so I cut out parts with words. Many thanks to...

Hello, I am in need of some form of "clamp" or level translation for an input to a uC. How can I prevent a signal from going beyond the VIH of the uC port? (approx 5.5vdc). The signal will be an ADC signal, so ideally the clamping circuit will not alter the adc input in any way. The...

All the texts and sites I can find discuss the rotational dynamics of pure rotation, pure translation, or a combination of an object rolling without slipping. I am trying to resolve some rotational dynamics regarding a spinning object that is moving linearly.. such as a planet in space or a tiny...

Homework Statement Hi, this is not part of a problem but just an equation I'm having a hard time to decipher (for the reference the original one is in "Statistical Mechanics" by Pathria, eq. 3.7.16) We define: r = |r2–r1|, Where bold letters are vectors, and we basically integrate a function...

So assume a vehicle is undergoing translation in the forward direction on a flat surface, and the power is supplied to the rear wheels. Lets say the reaction force on the rear wheel is Nr, and on the front it's Nf U is the coeff. static friction, and there's no slipping. M is the mass G =...

my teacher says that vectors can be translates which is fine... but homework can they be moved paralaly without couple acting on it//??

Hello, Imagine two stars orbiting in circles around their center of mass. Is this movement generally called a translation, a rotation, or both? The concept of "revolution" is bothering me; is this always nothing but a rotation? Is a revolution a certain part of a rotation? A specific case...

Homework Statement Dear All, I have a question regarding RNA translation. Firstly, my book states that Amino-Acids are binded to tRNA through AA-Activation which is possible through ATP->AMP. The AA will then bind to the acceptor stem near 3' end. My question is: a) Each strand of...