Invariance Definition and 454 Threads

Hi, this is probably a stupid question, but, does rotational invariance in ##d=2+1## mean to only rotate the spatial coordinates and not the time. I mean bascially I want to show that ## \int d^3 x \epsilon^{\mu\nu\rho}A_{\mu}\partial_{\nu}A_{\rho} ##, yes epsilon the antisymmetric tensor, is...

'Let’s first see what all of this means in the context of d = 3 + 1 dimensions. If we have rotational invariance then we can’t write down any terms linear in E or B. The first terms that we can write down are instead ...' Why is this? I don't understnad . My thoughts would be pictruing the set...

In an earlier question I asked if the EM field was truly a separate field from the matter field in QFT, as it's field structure is naturally complementary to phase changes in the matter field in just the right way to restore gauge invariance (poorly formed question, but hopefully you get the...

The Lorentz covariance of Maxwell equations was known before Einstein formulated special relativity. So what exactly special relativity brought new with respect to mere Lorentz covariance? Is special relativity just an interpretation of Lorentz invariance, in a sense in which Copenhagen...

In his book, "The greatest story ever told", Lawrence Krauss states: "Gauge invariance ... completely determines the nature of electromagnetism." My question is simple: How? I have gone back thru the math. Gauge invariance allows us to use the Lorenz gauge with the vector and scalar potentials...

I've been going through Bernard Schutz's A First Course in General Relativity, and I'm hung up on his "proof" of the invariance of the interval. At the beginning of section 1.6, he claims that he will prove the invariance of the interval, and after a few lines shows that the universality of the...

Why is that when there is lorentz invariance. Large 3-momentum corresponds to a large energy. And if there was no lorentz invariance. Large 3-momentum does not necessarily need to correspond to a large energy? What has Lorentz invariance got to do with 3-momentum having large energy or not?

Summary: Why is there no contradiction between energy as a non relativistic scalar and Galilean invariance? If energy is a non relativistic scalar, doesn't it mean that there is a contradiction with Galilean invariance? What i mean is that if i try to accelerate an object within the Galilean...

We're trying to reduce the tensor integral ##\int {\frac{{{d^4}k}}{{{{\left( {2\pi } \right)}^4}}}} \frac{{{k^\mu }{k^\nu }}}{{{{\left( {{k^2} - {\Delta ^2}} \right)}^n}}}{\rm{ }}## to a scalar integral (where ##{{\Delta ^2}}## is a scalar). We're told that the tensor integral is proportional...

From Weinberg, The Quantum Theory of Fields, Vol. 1, there is the statement that "the only way" to merge Lorentz invariance with the cluster decomposition property (a.k.a. locality) is through a field theory. He uses this argument basically to justify that any quantum theory at low energies...

Let's say we have a system of two point particles that can interact with each other by forces that are position and velocity dependent. The forces might or might not be derivable from a generalized potential. Assuming Isotropy of space and homogeneity of space and time, what are the constraints...

The Lagragian ##\mathcal L_e = e(\lambda)^{-1} \mathcal L - \frac{1}{2}m^2 e(\lambda)##, with ##\mathcal L## not depending on ##\lambda##, transform as ##\delta L_e = \frac{d}{d\lambda} (\epsilon (\lambda) \mathcal L_e)##* under the reparametrization ##\lambda \rightarrow \lambda +...

I use the ##(-,+,+,+)## signature. In the Schwarzschild solution $$ds^2=-\left(1-\frac{2m}{r}\right)dt^2+\left(1-\frac{2m}{r}\right)^{-1}dr^2+r^2d\Omega^2$$ with coordinates $$(t,r,\theta,\phi)$$ the timelike Killing vector $$K^a=\delta^a_0=\partial_0=(1,0,0,0)$$ has a norm squared of...

This is not a technical question. I'd like to have a more conceptual discussion about what - if anything - gauge invariance tells us about reality. If we could, please try to keep the discussion at the level of undergrad or beginning grad. To focus my questions and keep things elementary, I'd...

This is an example from "Noether's Theorem" by Neuenschwander. Chapter 5, example 4, page 74-75. He gives the Lagrangian for a charged particle in an electromagnetic field: ##L=\frac12 m \dot {\vec{r}}^2+e \dot{\vec{r}} \cdot \vec{A} -eV## And claims invariance invariance under the...

Hi. I'm reading an introductory text that somehow seems to confuse if ##E^2-(cp)^2=const## means that the left side is invariant (under Lorentz transformations) or conserved (doesn't change in time). As far as I understand it, they only prove Lorentz invariance. Are they both true? If so...

Does anybody know of examples, in which groups defined by ##[\varphi(X),\varphi(Y)]=[X,Y]## are investigated? The ##X,Y## are vectors of a Lie algebra, so imagine them to be differential operators, or vector fields, or as physicists tend to say: generators. The ##\varphi## are thus linear...

Homework Statement I have an assignment to prove that specific intensity over frequency cubed is Lorentz invariant. One of the main tasks there is to prove the invariance of phase space d^3q \ d^3p and I am trying to prove it with symplectic geometry. I am following Jorge V. Jose and Eugene J...

I have a really naive question that I didn't manage to explain to myself. If I consider SUSY theory without R-parity conservation there exist an operator that mediates proton decay. This operator is $$u^c d^c \tilde d^c $$ where ##\tilde d## is the scalar superpartner of down quark. Now...

Please tell me if Lorentz Transformation would be altered in any way if the invariance of c is explained, instead of postulated.

Hi there, I just saw some lectures where they claim that the Klein Gordon equation is the lowest order equation which is Lorentz invariant for a scalar field. But I could easily come up with a Lorentz invariant equation that is first order, e.g. $$ (M^\mu\partial_\mu + m^2)\phi=0 $$ where M is...

Hi, I've seen several explanations for sr on youtube. But they all start off explaining from a different perspective. I was wondering how the fundamental postulates of sr lead to the invariance of proper time between frames, and also what "order" everything is derived in. For example, does the...

Hi. In Newtonian physics, total mass is conserved, but open systems can obviously gain or lose mass, such as a rocket. But how can the term ##\dot{m}v## be Galilean invariant?

Homework Statement Hello Everyone I'm wondering, why in below product rule was not used for gradient of A where exponential is treated as constant for divergent of A and only for first term of equation we used the product rule? Homework Equations https://ibb.co/gHOauJ The Attempt at a Solution

Hello guys, I've came up with three statements in a discussion with a friend where we were trying to check if we had a clear vision of what isotropy and group invariance would imply in an arbitrary theory of gravity at the level of its matter lagrangian. We got stuck at some point so I came here...

Homework Statement Show that \int_{A} 1 = \int_{T(A)} 1 given A is an arbitrary region in R^n (not necessarily a rectangle) and T is a translation in R^n. Homework Equations Normally we find Riemann integrals by creating a rectangle R that includes A and set the function to be zero when x...

Homework Statement Question attached: Hi I am pretty stuck on part d. I've broken the fields into real and imaginary parts as asked to and tried to compare where they previously canceled to the situation now- see below. However I can't really see this giving me a hint of any sort unless...

I've been reading Straumann's book "General Relativity & Relativistic Astrophysics". In it, he claims that the twice contracted Bianchi identity: $$\nabla_{\mu}G^{\mu\nu}=0$$ (where ##G^{\mu\nu}=R^{\mu\nu}-\frac{1}{2}g^{\mu\nu}R##) is a consequence of the diffeomorphism (diff) invariance of the...

Can anyone briefly explain the difference between covariance and invariance in terms of special relativity? My understanding is that an invariant quantity is a value which does not change regardless of frame of reference it is being measured in. Covariance is a value which when measured in...

As I understand it Horava Lifschitz theory breaks lorentz invariance at high energies. Does this mean we should see photons from gamma ray bursts leave a signal of varying speeds of light for different frequencies?

Homework Statement In an inertial reference frame ##S## is given the four-potential: $$A^\mu=(e^{-kz}, e^{-ky},0,0)$$ with ##k## a real constant. ##A^\mu## fullfills the Lorentz gauge? And the Coulomb gauge? Which is the four-potential ##A'^\mu## in a reference frame ##S'## which is moving...

I am confused about tensor invariance as it applies to velocity and energy. My understanding is a tensor is a mathematical quantity that has the same value for all coordinate systems. I also understand that a vector is a first order tensor and energy is a zero order tensor. Thus, they should...

I'm reading a book on gauge symmetry, and in the discussion of the Aharanov-Bohm effect, the author says the following: But a paragraph later, he goes on to say: It seems to me like there is a contradiction here (indicated by phrases in bold). How can the a change in potential be...

I am working through the first chapter of Lessons on Particle Physics by Luis Anchordoqui and Francis Halzen. The link is https://arxiv.org/PS_cache/arxiv/pdf/0906/0906.1271v2.pdf I am on page 22. Equation 1.5.61: ##L_{Dirac}=\psi \bar ( i\gamma^\mu \partial_\mu-m)\psi## where ##\psi bar =...

I am working through Lessons in Particle Physics by Luis Anchordoqui and Francis Halzen; the link is https://arxiv.org/PS_cache/arxiv/pdf/0906/0906.1271v2.pdf. I am on page 11, equation 1.3.20. The authors have defined an operator ##L_{\mu\nu} = i( x_\mu \partial \nu - x_\nu \partial \mu)##...

[Mentors' note - this thread was split off from https://www.physicsforums.com/threads/invariance-of-force-and-mass.939025/] Are force and mass both invariant, or is it just the force divided by mass value which is invariant?

Hi! How do I check if the equation of motion of the particle, with a given potential, is invariant under time reversal? For a 2D pointlike particle with potential that is e.g $$V(x) = ae^(-x^2) + b (x^2 + y^2) +cy', where a,b,c >0$$ Can it be done by arguing rather then computing? Thanks!

The problem: $$\mathcal{L} = F^{\mu \nu} F_{\mu \nu} + m^2 /2 \ A_{\mu} A^{\mu} $$ with: $$ F_{\mu \nu} = \partial_{\nu}A_{\mu} - \partial_{\mu}A_{\nu} $$ 1. Show that this lagrangian density is not gauge invariance 2.Derive the equations of motion, why is the Lorentzcondition still...

https://arxiv.org/pdf/1710.11425.pdf The dark matter/dark energy issues has not made any sense to me since 1996 when it was evident that the ratio of dark matter increased as the volume of space measured increased. This was an obvious affect of empty space in the dark matter question that was...

https://www.sciencedaily.com/releases/2017/11/171122113013.htm A University of Geneva researcher has recently shown that the accelerating expansion of the universe and the movement of the stars in the galaxies can be explained without drawing on the concepts of dark matter and dark energy…...

Homework Statement Homework EquationsThe Attempt at a Solution ok so for w' i am getting since the s' is only moving in x direction ## \omega' = \omega \gamma (1 + \beta) ## is this correct then i am having some trouble in dealing with the dot product to derive for ## \bf {ck'} ##

The invariance of the laws of physics in space-time is a corner stone of physics and all science. A.Is this an axiom or can be derived from other more fundamental axioms? B. Are there any books that discuss how science could be if the laws of physics could be changed (for example if we could...

Let's assume that a and b charges are moving. now in our lab frame there will be a electric+magnetic force whereas in a rest frame of either of the charges, there will be only an electric force. So, two inertial observers will measure different forces?

I've commonly heard it said that Lorentz invariance is equivalent to saying that special relativity is obeyed, although I also recall discussions arguing that this is not precisely and technically correct, although the two concepts heavily overlap. I also understand that Lorentz invariance has...

Homework Statement Imagine two inertial frames, S and S'. Inertial frame S' moves with velocity v0 = 5 m = s in the upward (positive y) direction as seen by an observer in frame S. Now imagine that a person at rest in frame S throws a ball with mass m straight up into the air with initial...

Suppose you have two samples of white noise of equal amplitude. If you add them together ((sub)sample-by-(sub)sample that is), do you get one sample of white noise with twice the amplitude? How about pink noise?

This is an interesting question that popped through my mind. Some of us should know what is meant by „gauge transformations”, „gauge invariance/symmetry” and are used to seeing these terms whenever lectures on quantum field theory are read. But the electromagnetic field in vacuum (described in a...

it is often stated in texts on general relativity that the theory is diffeomorphism invariant, i.e. if the universe is represented by a manifold ##\mathcal{M}## with metric ##g_{\mu\nu}## and matter fields ##\psi## and ##\phi:\mathcal{M}\rightarrow\mathcal{M}## is a diffeomorphism, then the sets...

Consider the Dirac Lagrangian, L =\overline{\psi}\left(i\gamma^{\mu}\partial_{\mu}-m\right)\psi, where \overline{\psi}=\psi^{\dagger}\gamma^{0} , and show that, for \alpha\in\mathbb{R} and in the limit m\rightarrow0 , it is invariant under the chiral transformation...

At non-relativistic speeds is the elastic potential energy of a compressed spring frame-invariant? That is, would all reference frames agree on how much elastic potential energy is stored in the spring?