Invariant Definition and 406 Threads

How i can see the right lorentz invariance in lqg?

The recent threads makse we want to as a simple question. How many considers the notion of a _fundamental_ "diff invariant observables" as a clear and unquestionable requirement of the future theory of QG? To me this far from clear from the conceptual point of view. It's not even clear...

Homework Statement If \vec{x} is an eigenvector of a Hermitian matrix H, let V be the set of vectors orthogonal to \vec{x} . Show that V is a subspace, and that it is an invariant subspace of H. The Attempt at a Solution The Hermitian H must act on some linear space, call it K and of...

Homework Statement Prove or give a counterexample: If U is a subspace of V that is invariant under every operator on V, then U = {0} or U = V.Homework Equations U is invariant under a linear operator T if u in U implies T(u) is in U.The Attempt at a Solution Assume {0} does not equal U does not...

Homework Statement show that the definition of the invariant divergence divA = 1/√g ∂i (√g Ai) is equivalent to the other invariant definition divA = Ai;i Ai;k = ∂Ai/∂xk + ГiklAl Гkij = gkl/2 (∂gil/∂xj+∂glj/∂xi-∂gij/∂xl) Homework Equations g is the metric tensor...

A subgroup H of a group G is fully invariant if t(H)<=H for every endomorphism t of G. Let G is finite p-group has a fully invariant subgroup of order d for every d dividing |G|. What is the structure of G ?

Is there a general way of proving that the scalar product xuxu = (x0)2 - (x1)2 - (x2)2 - (x3)2 is invariant under a Lorentz transformation that applies no matter the explicit form of the transformation.

I am reading through sidney colemans lectures on QFT and I am stuck on what seem to be a silly question: He talks about the fact that the measure used in a calculation should be invariant in order to prove unitarity and later on that operators transform properly. He uses the example of...

Hey, Is the generalized eigenspace invariant under the operator T? Let T be finite dimensional Linear operator on C(complex numbers). My understanding of the Generalized Eigenspace for the eigenvalue y is: "All v in V such that there exists a j>=1, (T-yIdenitity)^j (v) = 0." plus 0. thanks

invariant "spacetime velocity" This is related to this thread https://www.physicsforums.com/showthread.php?t=207251". To make responding easier, I have marked questions in red. I have tried to address some concerns pre-emptively. These I have marked in silver. If you would like to...

I can appreciate the degeneracy of an infinite cubical well, in which there are three different directions, and hence three different separation constants from Schrodinger's equation which determine three separate n's (for lack of a better word.. principal quantum numbers, i suppose. it really...

Hawking gave the black hole entopy equation: (1) S_{BH} = {k c^3 \over 4G \hbar} A where A is the surface area of the black hole event horizon. All the other factors on the right hand side of the equation are constants. From the point of view of an observer moving relative to the black...

If V is any vector space and S and T are linear operators on V such that ST=TS show that the null space and the range of T are invariant under S. I think I need to begin by taking an element of the range of T and having S act on it and show that it stays in V? Can you help get me started?

Homework Statement Suppose T is in L(V) and U is a subspace of V. Prove that U is invariant under T if and only if Uperp is invariant under T*. Homework Equations V = U \oplus Uperp if v \in V, u \in U, w \in Uperp, then v = u + w. <Tv, w> = <v, T*w> The Attempt at a Solution If U is...

Homework Statement Suppose T is a linear operator on a finite dimensional vector space V, such that every subspace of V with dimension dim V-1 is invariant under T. Prove that T is a scalar multiple of the identity operator. The Attempt at a Solution I'm thinking of starting by letting U...

Rotation Invariant of Sch. Equation and [Lx,H]=0] ?? Here is my first post, How can I prove that the rotation invariability of the Sch. equations? How can I prove that [Lx,H]=0

Hello, I'm working on this problem and I'd like to know how to find the invariant mass using just the lab-frame momentum and rest mass. I've found a lot of equations that deal with E, and I'm not completely sure what that is either. Thanks

Suppose S, T \in L(V) are such that ST=TS. Prove that null(T-\lambdaI) is invariant under S for every \lambda \in F. I can't find anything helpful in my book, I'm not sure where to start...

[SOLVED] rotationally invariant hamiltonian Homework Statement Show that the Hamiltonian H = p^2/2m+V_0r^2 corresponding to a particle of mass m and with V_0 constant is a) rotationally invariant. Homework Equations Rotation operator: U_R(\phi ) = \exp (-i \phi \vec{J} / \hbar...

I was just wondering why what I've done in a spec rel question is wrong. Homework Statement A particle of mass m is traveling at 0.8c with respect to the lab frame towards an identical particle that is stationary with respect to the lab frame. If the particles undergo an inelastic collision...

Homework Statement The Relationship between the input x(n) and the output y(n) for the discrete System A is described by the expression: \frac{x(n) - 2x(n-1) + x(n-2)}{2} What is: (i) The impulse resopnse function h(n)? (ii) The frequency response function H(f)? (iii) The aplitude...

Hello good veiled I have a problem in relativity ,how to show the following relation disintegration is considered one particle a of mass Ma was at rest desintegre in two particles 1 and 2 of mass M1 and M2 convention: Pij: I in index and J in top P2u=Pau-P1u and...

Homework Statement Prove or give a counterexample: If U is a subspace of V that is invariant under every operator on V, then U = {0} or U = V. Assume that V is finite dimensional. The attempt at a solution I really think that I should be able to produce a counterexample, however...

I am working on a homework problem, and because it is a homework problem, I will not tell you the specifics or ask for an answer. My question has very little to do with the problem in particular, I just wanted to make that disclaimer. Oh, and the derivation of the Lorentz transformation was NOT...

In anglo-american literature -a physical quantity is invariant if it has the same magnitude in all inertial reference frame, -an expression relating more physical quantities is covariant if it has the same algebraic structure in all inertial reference frames (rr-cctt) ? Thanks in advance

An photon has mass zero by virtue of its momentum canceling its energy in m^2c^4 = E^2-p^2c^2 But in electromagnetism a field configution only has momentum when both a magnetic field and an electric field are present, e.g. in an electromagnetic wave. Now when there is only an electric or...

Homework Statement Let U be a unitary operator on an inner product space V, and let W be a finite-dimensional U-invariant subspace of V. Prove that (a) U(W) = W (b) the orthogonal complement of W is U-invariant (for ease of writing let the orthogonal complement of W be represented by...

Ok, when you use positrons to shoot at stationary electrons in a collider with enough energy so that you make a pair of proton and antiproton. The total energy of the pair would be E = T + MC^2, where M is the total invariance mass of the pair, namely 2*938Mev, or I can use E^2 = (pc)^2 +...

I understand that the quantities E^2 - B^2 \vec{E} \cdot \vec{B} (the dot is vector inner product). where E and B are the electric and magnetic components of an EM wave, are invariant under Lorentz/Poincare transformations. Can someone explain the physical significance of this ? Is...

Hey guys, I know this subject is a bit of an old chesnut but i thought id ask it anyway. What logical steps did the various physicists take to realize that c was constant in all reference frames? I've sort of found some weird ways to justify that fact in my head, but its more reverse...

Comment: My question is more of a conceptual 'why do we do this' rather than a technical 'how do we do this.' Homework Statement Given a lie group G parameterized by x_1, ... x_n, give a basis of left-invariant vector fields. Homework Equations We have a basis for the vector fields...

I'm not sure whether this has been discussed before. If one just looks at Heisenberg's uncertainty relation (energy-time), one easily sees that this is not Lorentz invariant. Even very simple results, such as the energy of a particle in a potential well seems not to transform according to the...

Are there any other phenomena (optical or not) whose speed is constant and does not depend on whether the source is moving or not?

In some cases, inertial mass does not equal invariant mass? What is the relation between the two? So the photon can have non zero inertial mass but always 0 invariant mass?

Why is charge an invariant quantity? My professor once said that that is an experimental fact. I believe him. But is there an "intuitive" reason for why a charge should be an invariant quanity?

Since antiparticles have reversed proper time, can I conclude that all invariants are reversed for antiparticles?

Hi, All, First time post, and this is quite possibly a very basic question: Is there a way to describe a particle's momentum such that the momentum itself is Lorentz invariant? The reason I am asking is this: As I understand it, if for example an electron and a positron were to collide and...

In many textbooks on relativity, one finds at some point a statement that the vacuum stress energy tensor should be Lorentz invariant, from which it then follows that the vacuum pressure is minus the vacuum energy density. However, the vacuum energy density (or stress tensor) is not an...

First, I need to be able to do equations in my post but it has been a long time since I posted here. Someone please point me to a resource that gives the how-to. If you make a infinitesimal rotation of the free-field Lagrangian for the Dirac equation, you get an extra term because the Dirac...

Introducing particle width via the Breit-Wigner propagator can break gauge invariance. Anyone know of some "nice" way to incorporate widths while still retaining gauge invariance?

From the Lorentz-invariant Faraday tensor F(H,E) two scalar invariants can be constructed: Inv1 = H²-E² and Inv2 = E.H Thinking at waves, electrostatic fields, magnetostatic fields, I see examples where Inv2 = 0. It is however easy to arrange an electrostatic field...

I'm reading a book on quontum mechanics in japanese (Quontum Mechanics by Shinichiro Tomonaga) and am stuck in proving the action variable "J" is constant in a one dimensional cyclic movement. i.e. The action variable "J" created by the trajectory of H(p(t),q(t),a(t/T)) = E(t) doesn't...

I am an MPhys graduate currently reading Joseph Polchinski’s, String Theory, Vol. 1. Unsurprisingly I’m stuck on the first real bit of maths… :p I quote from page 10, heh: “The simplest Poincaré invariant action that does not depend on the parametrization would be proportional to the proper...

I am an MPhys graduate currently reading Joseph Polchinski’s, String Theory, Vol. 1. Unsurprisingly I’m stuck on the first real bit of maths… :p I quote from page 10, heh: “The simplest Poincaré invariant action that does not depend on the parametrization would be proportional to the proper...

what is the reason that the lagrangian remains invariant under addition of an arbtrary function of time?

What makes an equation lorentz-covariant? When is an equation lorentz-invariant?

I'm wondering what happens if the scale factor of cosmological expansion increases without limit? Will you always calculate the same quantum foam and virtual particle production rates no matter what the scale is of the universe's expansion? If particles are extended objects, then of course...

please help me, i was stuck in here 2 days! algorithm to prove lcm: a:=m b:=n while a != b if a < b a:= a + m else b:= b + n //postcondition: a is the lcm(m,n) what's the loop invariant?I thought it is(not sure): lcm(ak, bk) = lcm(ak/m, bk/n) *lcm(m,n) I am...

title says it all. I've heard these two phrases. Lorentz invariant: Equation (Lagrangian, or ...?) takes same form under lorentz transforms. Lorentz covariant: Equation is in covariant form. I'm don't think I know what I mean when I say the latter. Can someone elucidate the...

Does every linear operator have a nontrivial invariant subspace? My professor mentioned this question in class, but never actually answered it. I am curious if this is true or not and why.