Invariance Definition and 454 Threads

I was reading an article about the Aharonov - Bohm effect and gauge invariance ( J. Phys. A: Math. Gen. 16 (1983) 2173-2177 ) and there is something I really don't get it. The facts are: The problem is the familiar Aharonov-Bohm one, in which we have a cylinder and inside the cylinder \rho...

So whose quantum gravity theory will crash-and-burn if this is correct? http://physicsworld.com/cws/article/news/40834 Zz.

Let me propose a list of principles of classical dynamics, specifically designed for education, for introduction to novices: - In the absence of any force: objects in motion move along straight lines, covering equal distances in equal intervals of time - Composition of motion: position...

If the action of a theory is invariant under a transformation (i.e. a lorentz transformation or a spacetime translation), does this imply that the Lagrangian is also invariant under the transformation? L \to L + \delta L \;\;;\;\; \delta L = 0?

I'm trying to work through the proof of the Lorentz invariance of the Dirac bilinears. As an example, the simplest: \bar{\psi}^\prime\psi^\prime = \psi^{\prime\dagger}\gamma_0\psi^\prime = \psi^{\dagger}S^\dagger\gamma_0 S\psi = \psi^{\dagger}\gamma_0\gamma_0S^\dagger\gamma_0 S\psi =...

Hey guys, I was wondering how you would go about proving that the image of a transformation T, im(T), is invariant? And following that, how would you prove T(W1 \bigcap W2) is invariant if T(W1) and T(W2) are both invariant. On an unrelated note, another questions asks to show that TX =...

Hello, i have a question on the M point of a surface brioullin zone. why is that point a point with time-reversal invariance? Thanks

Homework Statement Let G be a group acting on a set X, and let g in G. Show that a subset Y of X is invariant under the action of the subgroup <g> of G iff gY=Y. When Y is finite, show that assuming gY is a subset of Y is enough. Homework Equations If Y is a subset of X, we write GY for...

Let's say I have a vector x in \mathcal{R}^3. Let's also suppose that any vector x undergoes the transformation x' = kx (where k is a positive real). Obviously, normalizing the vector will give us a quantity which is invariant to uniform scaling. In fact, \frac{\mathbf{x'}}{|\mathbf{x'}|} =...

Homework Statement So, I am working on a question that requires me to prove that s^2 = s'^2 from the Lorentz equations. It seemed like it'd be trivial... and then I ended up here a few hours later, not willing to waste any more time. Homework Equations By definition: s^2 = x^2 - (ct)^2 &...

Homework Statement I want to show explicitly that the Lagrangian... L_\Phi = (D_\mu \Phi)^\dagger (D^\mu \Phi) - \frac{m^2}{2\phi_0 ^2} [\Phi^\dagger \Phi - \phi_0 ^2]^2 where \Phi is a complex doublet of scalar fields, and D_\mu = (\partial_u + i \frac{g_1}{2} B_\mu) is the...

Hi! I have little questions about symmetries. I begin in the field, so... First about conformal symmetry. As I studied, in 2-d, a transformation (\tau, \sigma) \to (\tau', \sigma') changing the metric by a multiplicative factor implies that the transformation (\tau, \sigma) \to (\tau'...

According to Steven Weinberg ('The quantum theory of fields', vol.1), the principle of gauge invariance stems from the fact, that one cannot build the 4-vector field from the creation/annihilation operators of massless bosons with spin >= 1. This '4-vector field' ('vector potential'), if we...

I thought i had a basic to intermediate understanding of quantum physics and group theory, but when reading hamermesh's "group theory and it's application to physical problems" there's something in the introduction i don't understand. first of all, i know the parity (or space inversion)...

I understand that some do not accept LQG in particular, but any discrete spatial geometry in general, because that would be a violation of lorentz symmetry. It was explained to me as meaning that If a 2D plane were discretized into a grid or lattice, a vector would not have a continuous...

About the invariance of similar linear operators and their minimal polynomial Notations: F denotes a field V denotes a vector space over F L(V) denotes a vector space whose members are linear operators from V to V itself and its field is F, then L(V) is an algebra where multiplication is...

The superpotential is basically a product of left chiral superfields, taking the \theta \theta component. However, under a supergauge transformation, the left chiral superfields change, and the superpotential does not seem to be supergauge invariant. In fact, under supergauge...

Homework Statement Suppose T is contained in the set of linear transformations from V to V. Prove that the intersection of any collection of subspaces of V invariant under T is invariant under T. Homework Equations The Attempt at a Solution Choose a basis for V. This basis...

Hello all, this is my first post so I hope the question I have is interesting, at least to a few, and that I can learn something from the discussion. I had problem for a class not long ago in which I had to prove that: \vec{E} \cdot \vec{B} and E^2 - c^2B^2 were Lorentz invariant. I was...

is proper time invariant? proof? thanks...

Hello, I have been reviewing some relativity notes, and I am confused over something. I apologize if this seems like a silly or obvious point, but humor me. When we are talking about Lagrangians in field theory and in regular mechanics, we are often looking at symmetries. Namely, almost...

Homework Statement A scalar function can be represented as a position on the x-y plane, or on the u-v plane, where u and v are axes rotated by θ from the x and y axes. Prove that the 2-dimensional \nabla^2 operator is invariant under a rotation of axes. ie, \frac{\partial^2 f}{\partial...

From: http://en.wikipedia.org/wiki/Quantum_mechanics#Mathematical_formulation ... In the mathematically rigorous formulation of quantum mechanics, developed by Paul Dirac[7] and John von Neumann[8], the possible states of a quantum mechanical system are represented by unit vectors (called...

Hi, what is the difference between Lorentz Invariance and Lorentz Covariance? From my lecture note (Group theory course) Invariance and Covariance where defined as follows: Invariance: refers to the property of objects being left unchanged by symmetry operations. Covariance: refers to...

I apologise if this question has been asked before, but I coudlnt find it, so: Is there some deeper reason for demanding gauge invariance other than that it allows us to include interactions between the gauge field and the fermions? I have seen people claim that it is "in keeping with the...

Hello, For spring break homework, I'm supposed to prove the Invariance of domain theorem (stating that continuous injective functions from an open set in R^n to R^n are open maps). Does anyone know of any books/sources of any kind which will help? Thanks!

Homework Statement I have two four vectors v and w with v^{2} = m^{2} > 0, v_{0} > 0 and w^{2} > m^{2}, w_{0} > 0 . Now we consider a system with w' = (w_{0}', \vec{0}) and v' = (v_{0}', \vec{v} \, ') and in addition we consider the quantity \lambda = \vert \vec{v}' \vert \, \sqrt{...

I don't understand why a diffeomorphism invariance allows the extention of the loops variables in the continuum limit. Can someone give me some detailed reference?

Hi, as you all know one can write the Maxwell-equations in covariant form, namely: \partial_a F^{ab} = \frac{4\pi }{c} j^{b} and \partial_a G^{ab}=0 where \textbf{G} is the dual Tensor to \textbf{F}. Now the two simple questions. I can see that they are invariant, because I...

Homework Statement Show that a^{\mu}b_{\mu} \equiv -a^0b^0 + \vec{a} \bullet \vec{b} is invariant under Lorentz transformations. Homework Equations \Lambda_{\nu}^{\mu} \equiv \left( \begin{array}{cccc} \gamma & -\beta \gamma & 0 & 0 \\ -\beta \gamma & \gamma & 0 & 0 \\ 0 & 0 & 1 &...

Cinsider please the invariance of the space-time interval in an one space dimension approach (x-0)2-c2(t-0)2=(x'-0)2-c2(t'-0)2 My question is: does it hold for arbitrary events (x,t) in I and (x',t') in I? Does it hold only in the case when the events are genertated in I and I' by the same...

The vector potential can be expressed in the following way: ∇^2 Ay-∂/∂y (∇∙A)=-μJy (Here only taking y components) Vector A is not determined uniquely. We may add derivatives of an arbitrary function (gradient) to the components of A, and the magnetic field does not change (curl of...

phase invariance? I read papers claiming that the phase of a plane wave (acoustic and electromagnetic) is not an invariant. Taking into account that invoking its invariance, we could derive formulas that account for well tested experimental facts (Doppler shift, aberratiion of light, wave...

Hi everyone, This is my first post and I hope to get some better understanding of something that has been bugging me. I understand (global) gauge invariance in the sense that |\psi\rangle denotes the same (physical) state as e^{i\varphi}|\psi\rangle, or more generally, the physical state...

In classical e&m, for gauge invariance you can choose div[A]=0 or div[A]=dV/dt, where A is vector potential and V is the scalar potential; however, in qft you multiply your wavefunction by a phase factor that is dependent on space time. My question is that is there any parallel that can be drawn...

Let us restrict ourselves to SR for the moment at least. So we have a flat spacetime. Now consider a proper force of the form: \frac{dp^\mu}{d\tau} = a v^\mu where a is a scalar. It seems to be coordinate system independent due to the definition being in tensor notation. But it seems to...

Homework Statement Let W be a complex finite dimensional vector space with a hermitian scalar product and let T: W -> W be linear and normal. Prove that U is a T-invariant subspace of W if and only if V is a T*-invariant subspace, where V is the orthogonal complement of U. The attempt at a...

If we introduce four-dimensional coordinate sistem with component of four-momentum on axis, then dp1*dp2*dp3 can be considered as zeroth component of an element of hypersurface given by p^2=m^2*c^2. Element of this hypersurface is parallel to 4-vector of momentum so we have that dp1*dp2*dp3/E is...

Homework Statement I'm solving Goldstein's problems. I have proved by direct substitution that Lagrange equations of motion are not effected by gauge transformation of the Lagrangian: L' = L + \frac{dF(q_i,t)}{dt} Now I'm trying to prove that Hamilton equations of motion are not affected...

Imagine a beam of light being turned on at the surface of a massive body such as a neutron star, the beam of light travels along a geodesic path towards a mirror located at radius r from the planet's surface, when the light beam hits the mirror, the light bounces back to the observer located at...

Why is local gauge invariance needed in qft? I read that is allows interactions whereas global gauge invariance does not but was given no reason.

Hi folks! Another stupid question: Consider a Yukawa coupling \lambda \bar{\psi}_1 \psi_2 \phi where \phi is a scalar field in the (2,-\frac{1}{2}) representation and \psi_1 and \psi_2 are lh. Weyl fields in the (2,-\frac{1}{2}) and (1,1) representation of \mathrm{SU}(2) \times \mathrm{U}(1)...

Is weak interaction invaraint under CPT Symmetry? Why?

[SOLVED] Quantum Field Theory: Field Operators and Lorentz invariance Hi there, I am currently working my way through a book an QFT (Aitchison/Hey) and am a bit stuck on an important step in the derivation of the Feynman Propagator. My problem is obviously that I am not a hard core expert...

I kind of get the connection, but could someone elaborate the necessity for time translation invariance for the existence of a unique vacuum state.

Sorry to bring up again a question that I asked before but I am still confused about this. In SR we have Lorentz invariance. Now we go to GR and one says that the theory is invariant under general coordinate transformations (GCTs). But, as far as I understand, this is simply stating that...

Hello, I'm currently doing a project that is concerned with the hopeful discovery of the Higgs Boson at LHC. I'll be running some code that my supervisor has produced, but before that he wanted me to understand more of the physics that is behind the Higgs mechanism. He has proposed a...

I initially posted this question in the Beyond the Standard Model forum since diffeomorphism invariance is a key ingredient of loop quantum gravity but it was suggested that I post the question here. Why is Einstein's theory diffeomorphism invariant? A diffeomorphism is basically a map of...

I was watching one of Smolin's online lecture (the link was provided by Marcus in the thread "What's new that's happening in quantum gravity" or something to that effect) and Smolin makes a big deal on the difference between diffeomorphism invariance and invariance under general coordinate...

Hello, I need help showing that the Euler-Lagrange equations are Lorentz invariant (if Einstein's extended energy concept is used). Is there an easy way to show this? Any help would be very much appreciated.