Invariance Definition and 454 Threads

Suppose I have a field \hat{X}... What kind of operator should it be in order to develop a vev which doesn't break the Poincare invariance? I am sure that a scalar field doesn't break the poincare invariance, because it doesn't transform. However I don't know how to write it down mathematically...

If gauge symmetries are really just redundancies in our description accounting for nonphysical degrees of freedom, then how does one explain the deep and powerful fact that if one begins with, say, just fermions and no gauge field in one's theory (and no interactions & essentially no dynamics)...

This is a very basic question, but I cannot get my head around the following: Any physical system should be invariant under changes of coordinates, because these are just a way of parametrizing the manifold/space in which my physical system is embedded. Now, let us consider a system that...

Hi, I’m a bit confused. I am familiar with the chain rule: if y=f(g(t,x),h(t,x)) then dy/dt=dy/dg*dg/dt+dy/dh*dh/dt To show that an equation is invariant under a galiliean transform, it’s partially necessary to show that the equation takes the same form both for x and for x’=x-v(T). So if you...

Surely I am missing something, can you explain what? If we shoot a gun while traveling on a train, the speed of the bullet is its usual speed plus the speed of the train vt, because the bullet inside is already traveling at vt. If we produce an EMR on the train (or on the Earth in the case...

Hi, so I'm trying to derive the charge conservation law for a general SU(N) gauge field theory by using gauge invariance. For U(1) this is trivial, but for the more general SU(N) I seem to be stuck... So if anyone sees any flaws in my logic below please help! Starting with the Lagrangian...

I suspect this is somewhat off the beaten track here, but there may be some few that could give it a go. Einstein called his concept of coordinate independent physical theory General Covariant. The mathematicians call coordinate independent differential topology, diffeomorphism invariant...

Homework Statement y(n)=x(4n+1). Is this system T.I or NOT T.I The professor marked this question wrong for my homework. He says it's NOT time invariant. I proved it is time invariant. Homework Equations System is time invariant if a shift in time in input results in the same shift in time...

Einstein's field equations are time invariant. So is it conceivable that a reverse black hole can exist i.e a "white hole"? Or would the second law of thermodynamics prevent such a thing?

Homework Statement Show that [\hat{\phi}(x_1),\hat{\phi}^\dagger(x_2)] = 0 for (x_1 - x_2)^2 < 0 where \phi is a complex scalar field Homework Equations \hat{\phi}=\int\frac{d^3 \mathbf{k}}{(2\pi)^3 \sqrt{2\omega}}[\hat{a}(k)e^{-ik\cdot x} + b^\dagger(k)e^{ik\cdot x}]...

Hi, Are Einstein's field equations without the cosmological constant scale invariant? If so does the addition of the cosmological constant break the scale invariance? John

Homework Statement I must show that the one dimensional wave equation ##\frac{1}{c^2} \frac{\partial u}{\partial t^2}-\frac{\partial ^2 u}{\partial x^2}=0## is invariant under the Lorentz transformation ##t'=\gamma \left ( t-\frac{xv}{c^2} \right )## , ##x'=\gamma (x-vt)##Homework Equations...

Hello! Consider the law of addition of velocities for a particle moving in the x-y plane: u_x=\frac{u'_x+v}{1+u'_xv/c^2},\, u_y=\frac{u'_y}{\gamma(1+u'_xv/c^2)} In the book by Szekeres on mathematical physics on p.238 it is said that if u'=c, then it follows from the above formulae that...

[This is mostly about notation] I was working on a problem where I had to prove that div(B) remains invariant under lorentz transformations. That was not too hard, so I came up with div(B) = \partial_{\mu} B^{\mu} must equal div(B) = \partial'_{\mu} B'^{\mu} so I did a...

Hi, Since H^DaggerH is invariant under SU(2) X U(1), does this mean that H^DaggerH is invariant under rotations and translations? Thanks

I tried to look this up on the internet. I know there is a book about it but I forgot its title. I know that you can prove that the kinetic energy should be proportional to velocity squared by saying that this is the only Galilean invariant definition of kinetic energy. Can someone help me...

Hi! I have to prove that the amplitude of the process \gamma \gamma \to W^+ W^- does not depend on the gauge we will choose, R_{\xi}. So I use the most general expressions for the propagators and vertices. I find 5 diagrams. One that involves only the 4 fields and a vertex, 1 t and...

Homework Statement Homework Equations The Attempt at a Solution E2 - p2c2 = E02 I know that this is true. But how do i relate p1 to p1'? and same for energy as well. I expanded the LHS= E0,12 + E0,22 + 2E1E2 - 2(p1c)(p2c) for the RHS = E0,12 + E0,22 + 2E'1E'2 -...

Hi. I have trouble understanding an argument in Lewis H. Ryder's QFT (second edition) at page 325 where he wants to write down an equation similar to the renormalization group equation which expresses the invariance of the vertex function \Gamma^{(n)} under the change of scale. The relevant...

Homework Statement A gauge transformation is defined so as to leave the fields invariant. The gauge transformations are such that \vec{A}=\vec{A'}+\nabla\Lambda and \Phi=\Phi'-\frac{\partial\Lambda}{\partial t}. Consider the Coulomb Gauge \nabla\cdot\vec{A}=0. Find out what properties the...

Hi! I've seen it stated that because of Lorenz and translational invariance \langle 0| \phi(x) |0 \rangle has to be a constant and I wondered how to formally verify this?

Homework Statement Show that if a Hamiltonian H is invariant under all rotations, then the eigenstates of H are also eigenstates of L^{2} and they have a degeneracy of 2l+1. Homework Equations The professor told us to recall that J: \vec{L}=(L_x,L_y,L_z)...

Are photons partially non-local? Warping time-space to achieve this? Seems a bit confusing. I get that c is always supposed to be the same for all observers according to special relativity, but i am trying to picture what actually is supposedly happening there? Forgive me if...

I have been quite puzzled for some time with the concept of Diffeomorphic Invariance. Here is what I think about it, 1) Diffeomorphic Invariance is the invariance of the theory under general coordinate transformations. For instance the Einstein-Hilbert action is diffeomorphic invariant...

Hey, I'm trying to get my head around neutral Kaon oscillations. As far as I understand it neutral Kaons can change between K^0 and \overline{K^0} as they propagate. Going through the quantum mechanics of this implies that this oscillation must be facilitated by a mass difference between the...

Hello, My question is on coupling the photons to our Dirac field for electrons, we have the Dirac equation: (i\not{\partial -m })\psi=0 By Lorentz invariance we can change our space-time measure by: \partial ^\mu \rightarrow \partial ^\mu+ieA^\mu\equiv D^\mu Though I cannot see...

Homework Statement I am supposed to determine wether or not the discrete time system x[n] \rightarrow y[n] = x[-n] is time invariant or not. The Attempt at a Solution Let x_d[n] = x[n-n_0] y_d[n] = x_d[-n] = x[-(n-n_0)] = x[-n+n_0] y[n-n_0] = x[-(n-n_0)] = x[-n+n_0] Since y_d[n] =...

Homework Statement I've been reading through Spacetime Physics by Taylor & Wheeler, but this argument about the invariance of the y coordinate for inertial frames, one moving relative to the other on the x axis, is tripping me up. I'll just write the text word for word: I'm just not...

Recently, over in the relativity forum, Micromass contributed a post: https://www.physicsforums.com/showpost.php?p=4168973&postcount=89 giving a proof that the most general coordinate transformation preserving the property of zero acceleration (i.e., maps straight lines to straight lines) is...

These are notes I made when I was studying the subject 20 years ago. They seem fine considering that I was student then. I believe they can be useful for those who are studying Yang-Mills and other related material. Sam

In addition to my Faddeev-Popov Trick thread, I'm still tying up a few other loose ends before going into Part III of Peskin and Schroeder. I was able to show that the other Lagrangians introduced thus far are indeed invariant under the transformations given. But, I am hung up on what I think...

Homework Statement The problem asked us to show that the Euler-Lagrange's equations are invariant under a point transformation q_{i}=q_{i}(s_{1},...,s_{n},t), i=1...n. Give a physical interpretation. Homework Equations \frac{d}{dt}(\frac{\partial L}{\partial \dot{s_{j}}})=\frac{\partial...

Homework Statement Show that the Lagrangian \mathcal{L}=\frac{m}{2}\vec{\dot{r}}^2 \, \frac{1}{(1+g \vec{r}^2)^2} is invariant under the Transformation \vec{r} \rightarrow \tilde{r}=\vec{r}+\vec{a}(1-g\vec{r}^2)+2g\vec{r}(\vec{r} \cdot \vec{a}) where b is a constant and \vec{a} are...

does SR change the direction of light and if yes is it then possible to find a transformation keeping the velocity of light invariant and not only its speed ?

im trying to prove the galileo invariance of s.e. But i get stuck with an extra term prop.to v*d/dx in fact i get invariance only for scaling x' equ. ax and t' equ. at. Where does the mistake hide ?

I've read that gauge invariance leads to a fundamental phenomenon.What is that? Thanks

For free EM field: L=-\frac{1}{4}FabFab Then the stress-energy tensor is given by: Tmn=-Fml∂vAl+\frac{1}{4}gmnFabFab The author then redefines Tmn - he adds ∂lΩlmn to it, where Ωlmn=-Ωmln. The redefined tensor is: Tmn=-FmlFvl+gmv\frac{1}{4}FabFab It is gauge invariant and still satisfies...

Suppose you have a particle in one dimension in an energy eigenstate, i.e. Hψ(x)=Eψ(x) for some E. For an observer B in a coordinate frame with the origin translated some distance K to the right, the wavefunction of the particle looks like ψ'(x) = ψ(x+K). Surely, we expect the energy that B...

Homework Statement The invariance of physical laws to a coordinate change suggests a symmetry group structure. Can the operations of cordinate transformation be written as group operations? What is the group? Homework Equations The Attempt at a Solution At the moment I do not...

Homework Statement How do I know that vector is invariant to changes of coordinate systems if i only have the components of the vector and not the basis vectors? Homework Equations let the vector in reference frame 1 be ds and the same vector in the reference frame 2 be ds1 The...

Can the metric of special relativity be derived from requiring the infinitesimal line segment, dτ, to be invariant in space and time? If we parameterize a line segment by the variable τ marked off along the line (that exists in space and time dimensions) is the length in τ of that line segment...

My understanding of the S&G relativity is that one theory deals with reference frames at speeds near the speed of light while the other deals with reference frames that are approaching the speed of light. There are variances in observation between the two reference frames arising from their...

In several textbooks of QM I have read that Lorentz invariance is manifest in Heisnberg picture. How can we deduce that?

Hi, so I was going over my lectures notes and I was looking at the Invariance, S2 for space time. I was just wondering why they call it time-like for S2<0 and space-like for S2>0 because, S2>0 says that there is an inertial frame where events occur at the same time (this has to do with...

Hello, I've been spending a lot of time trying to solve this problem but I can't figure out a good solution. I have to show that the action of a non-relativistic particle ( Schrodinger density Lagrangian ) is invariant under Galilean boost with the form...

Consider a random walk (in any dimension) with N steps and a step size of 1. Take a real number \alpha > 0 and consider another random walk which takes \alpha^2 N steps but wil step size \frac{1}{\alpha}. I immediately noticed that the mean deviation after the full walk in both cases is the...

I was reading Mandle QFT book, and it says: "If we require the vacuum states to be invariant under Lorentz transformations and under translations, then this field must be a scalar field, $\phi(x)$, and its vacuum expectation value must be constant". Could anybody explain to me why is that?

Homework Statement I just have a general question about what one of my professors had written on the board today in class. He was writing down examples where we had to determine whether the given statement was time invariant or not. One example was written as follows, x(-t) = y(t)...

My understanding is that for electrons, there is a standard argument that the electromagnetic interaction between them is required, not optional. Since they're identical particles, we should be able to take the wavefunction of two electrons and mix up their identities by any amount we like, and...