# What is Bracket: Definition and 83 Discussions

A bracket is either of two tall fore- or back-facing punctuation marks commonly used to isolate a segment of text or data from its surroundings. Typically deployed in symmetric pairs, an individual bracket may be identified as a left or right bracket or, alternatively, an opening bracket or closing bracket, respectively, depending on the directionality of the context.
Specific forms of the mark include rounded brackets (also called parentheses), square brackets, curly brackets (also called braces), and angle brackets (also called chevrons), as well as various less common pairs of symbols.
As well as signifying the overall class of punctuation, the word bracket is commonly used to refer to a specific form of bracket, which varies from region to region. In most English-speaking countries, an unqualified 'bracket' refers to the round bracket; in the United States, the square bracket.

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1. ### A Problems with the interpretation of the Torsion tensor and the Lie Bracket

Hi, I've been doing a course on Tensor calculus by Eigenchris and I've come across this problem where depending on the way I compute/expand the Lie bracket the Torsion tensor always goes to zero. If you have any suggestions please reply, I've had this problem for months and I'm desperate to...
2. ### A Lie Bracket * Matrix * vector (Need proof)

As an aside, fresh_42 commented and I made an error in my post that is now fixed. His comment, below, is not valid (my fault), in that THIS post is now fixed.Assume s and w are components of vectors, both in the same frame Assume S and W are skew symmetric matrices formed from the vector...

7. ### Lie Bracket and Cross-Product

Prove that for a 2 sphere in R3 the Lie bracket is the same as the cross product using the vector: X = (y,-x,0); Y = (0,z-y) [X,Y] = JYX - JXY where the J's are the Jacobean matrices. I computed JYX - JXY to get (-z,0,x). I computed (y,-x,0) ^ (0,z,-y) and obtained (xy,y2,yz) = (z,0,x)...
8. ### Bracket mounting question

Thanks for taking interest but I studied basic statics about three decades ago and I wasn't quite sure what the definitive answer was...can anybody tell me what the preferred arrangement of this reinforcement bracket should be? Should it be as shown in the picture to achieve maximum stiffness or...
9. ### B L bracket vs reverse L bracket

Hi all, The photo is a reverse L-shaped bracket installed on the wall, L or reverse L is of more supporting force if all things being equal? Why? Thank you very much!
10. ### I Rings, Modules and the Lie Bracket

I have been reading about Rings and Modules. I am trying reconcile my understanding with Lie groups. Let G be a Matrix Lie group. The group acts on itself by left multiplication, i.e, Lgh = gh where g,h ∈ G Which corresponds to a translation by g. Is this an example of a module over a ring...
11. ### Materials selection and manufacture of a bracket

Hi I'm on to the last question for my HNC and having a nightmare trying to work out my best options! Any help would be greatly appreciated! The bracket show in figure 1 is to be used to mount an outboard motor onto the transom of a boat. a. suggest two appropriate materials which will require...
12. ### Lie Bracket for Group Elements of SU(3)

Homework Statement Determine the Lie bracket for 2 elements of SU(3). Homework Equations [X,Y] = JXY - JYX where J are the Jacobean matrices The Attempt at a Solution I exponentiated λ1 and λ2 to get X and Y which are 3 x 3 matrices.. If the group elements are interpreted as vector...
13. ### I Lie bracket on a manifold

Hello! So I have 2 vector fields on a manifold ##X=X^\mu\frac{\partial}{\partial x^\mu}## and ##Y=Y^\mu\frac{\partial}{\partial x^\mu}## and this statement: "Neither XY nor YX is a vector field since they are second-order derivatives, however ##[X, Y]## is a vector field". Intuitively makes...
14. G

### Forces on an L - Bracket

I am installing an L-shaped bracket into a brickwork chimney to support some large pipework. I am trying to work out the forces in each fixing to ensure that I won't be pulling the bracket off the wall once the pipes are filled with water. I've tried drawing the free body diagram and to resolve...
15. ### I Bracket VS wavefunction notation in QM

In some sources QM is explained using bracket notation. I quite understand algebra of bracket notation, but I do not understand how is this notation related with physically meaningful things? How is bracket notation related to wavefunction notation? Could you tell me whether following is true...
16. ### Stress in bracket distributed eccentric load

Homework Statement I have designed a bracket and am interested in stress at a certain point. I have figured out the load needed to support. The area of interest carries an eccentric load so bending moment and axial load need to be figured out. Not sure which FBD is correct to use. Homework...
17. ### B Bracket notation problem

let say I have a vector |a> and |b> and a transformation matrix A What is the difference between <a|A|b> and <a|Ab>? And also, I don't quite understand why <a|Ab> = <A+a|b>. Where does this identity come from? Thanks!
18. ### I What's the motivation for bracket notation in QM?

I took a semester of QM as an undergrad engineering major, and I don't recall the motivation for replacing traditional vector notation with bracket notation. Can someone enlighten me? Thank you.
19. ### A How to solve the following Poisson bracket

anyone can help me how to solve the following poisson bracket? {U(x,λ), U(y,µ)} = −(1/λµ) {S^{i} (x), S^{j} (y)} σ_{i} ⊗ σ_{j} where U(x, λ) = −(i/λ) S(x)
20. ### Choosing Steel Thickness for a bracket

Just need someone to double check my work. So the bracket is going to be cut out from a steel plate in a weird, rounded out triangular shape, and then a hole will be drilled through it. For simplicity though, let's just say the bracket is a ring with one half of it welded onto a wall. OD of the...
21. ### Calculate Maximum Load of a U Bracket

I have a hydraulic cylinder that can lift up to 3 metric tons and I want to attach it to an arm. The bracket is in a rigid U shape (right angles only, no round corners), with a round pin going through it. At first I thought it'd be a simple bending stress calculation, but there is a giant hole...
22. ### Component forces on angle bracket

Homework Statement See photo attachment Homework EquationsThe Attempt at a Solution Ive begun by defining an x and y axis, followed by find the sum of x-components of the forces, and y-components. Followed by the magnitude of the resultant force. The only method i could think of was to find...
23. ### Lie derivative of tensor field with respect to Lie bracket

I'm trying to show that the lie derivative of a tensor field ##t## along a lie bracket ##[X,Y]## is given by \mathcal{L}_{[X,Y]}t=\mathcal{L}_{X}\mathcal{L}_{Y}t-\mathcal{L}_{Y}\mathcal{L}_{X}t but I'm not having much luck so far. I've tried expanding ##t## on a coordinate basis, such that...
24. ### Fundamental Poisson Bracket - Canonical Transformation

When proofing the poisson brackets algebraically, what is the tool of choice. Can one use the muti dimensionale chain rule or how is it usally done?
25. ### Analyzing Reactions of a Pin and Bracket Supported System

Member ABC is supported by a pin and bracket at C and by an inextensible cable of length L  7.8 m that is attached at A and B and passes over a frictionless pulley at D. Assuming P  450 N and   35 and neglecting the mass of ABC and the radius of the pulley, simplify the problem as much as...
26. ### How do I calculate this Poisson bracket in QED?

Homework Statement To calculate a certain Dirac bracket I need to calculate this Poisson bracket (Weinberg QTF 1 p.349 first eq.) $$[F,\Pi_i(\mathbf{z})]_P$$ where F is any functional of matter fields and their conjugates and pi is the conjugate to the vector potential. It should be zero...
27. ### Lie bracket of derivations in space of r-forms

Hello In textbook by Kobayashi and Nomizu derivation of rank k in space of all differential forms on a manifold is defined to be operator that is linear, Leibnitz and maps r-forms into r+k-forms. By Leinbitz I mean, of course: D(\omega \wedge \eta)=(D \omega) \wedge \eta + \omega \wedge (D...
28. ### Maurer-Cartan form involved in Lie bracket

The Maurer-Cartan one-form ##\Theta = g^{-1} dg## is though of as a lie algebra valued form. It arises in connection with Yang-Mill's theory where the gauge potential transforms as $$A \mapsto g Ag^{-1} - g^{-1} dg.$$ However, one also defines for lie-algebra valued differential forms...
29. ### What is a Poisson bracket

Definition/Summary In the Hamiltonian formulation of classical mechanics, equations of motion can be expressed very conveniently using Poisson brackets. They are also useful for expressing constraints on changed canonical variables. They are also related to commutators of operators in...
30. ### MHB Solving equation with fraction & bracket help required please

Hi, I am having awful trouble working this out and have been going round in circles. Can you help me please? Its: x/x+1 - 4/x - 2 = 2
31. ### Hamiltons equations of motion in terms of poisson bracket

In Hamiltonian formulation there is an expression df / dt = { f , H } + ∂f / ∂t where f is function of q, p and t. While expressing Hamiltons equations of motion in terms of Poisson Bracket, i.e if the function f = q of p then its partial time derivative ∂f / ∂t becomes zero.. Please explain why?
32. ### Design of dowels in a bracket

Hi all, I just started learning engineering mechanics this semester,so what I'm about ask may be a basic question in the subject.I came across a bracket that is used in a industrial equipment (i have attached a sketch as image).The bracket is used to mount a hydraulic cylinder.The cylinder has...

43. ### Poincare Algebra from Poisson Bracket with KG Action

Homework Statement Consider the Klein-Gordan action. Show that the Noether charges of the Poincare Group generate the Poincare Algebra in the Poisson brackets. There will be 10 generators.Homework Equations \{ A,B \}=\frac{\delta A}{\delta \phi}\frac{\delta B}{\delta \pi}-\frac{\delta...
44. ### Cantilever Bracket Calculations

I have a cantilever bracket, fixed at one end, free at the other. One vertical element AB, 330mm long with a fixing at either end to a wall. One horizontal element CD, 375mm long. CD is fixed at 90deg to AB, 130mm from the top. A constant, downward load W=30kg, is applied to the end of CD...
45. ### Solving a Force Problem with Three Cables and a Bracket

Hi everyone, i came across this forum a while ago and have been lurking here for a while. Any ways, i have a simple problem but can't seem to find a solution to it the photo of the problem is the link just here http://i1053.photobucket.com/albums/s463/Popa911/1cc85138.jpg Homework...
46. ### Poisson Bracket - Constrained system

Hi friends I am trying to drive constraints of a Lagrangian density by Dirac Hamiltonian method. But I encountered a problem with calculating one type of Poisson Bracket: {\varphi,\partial_x\pi}=? where \pi is conjugate momentum of \varphi. I do not know for this type Poisson Bracket I can...
47. ### Poisson Bracket Porperties

Hello, If you have two observables f and g both of which start off as: f =0 and g =0 and you evaluate their possion bracket: {f,g}, will it necessarily be equal to zero? Also, if just f=0 and g wasn't zero, would {f,g} =0? Thanks!
48. ### Transition from Poisson bracket into Canonical Commutation Relations

In book http://www.phy.uct.ac.za/people/horowitz/Teaching/lecturenotes.pdf in section 2 it is described transition from Poisson bracket into Canonical Commutation Relations. But it is written The experimentally observed phenomenon of incompatible measurements suggests that position and...
49. ### Design a Mounting Bracket for 100kg Steel to Aluminum Plate

Homework Statement I have to create a design to mount a steel (yield=250MPa) weight 100kg and thickness of 15 mm to aluminum plate (Yield = 100MPa) with a tap hole of 15mm in vertical direction with 6 of M6 screws. Homework Equations σ (bearing load) =F/A τ (shear load) = F/A The...
50. ### This question may not come in the bracket of quantum mechanics but

This question may not come in the bracket of quantum mechanics but here's the question- If most of the atom is empty space what gives the illusion of solidity?