Gauge invariance Definition and 73 Threads

I know what gauge invariance is, but I'm not sure what gauge covariance is. Is it that a given field has a gauge covariant derivative? And under which circumstances do we get a field that is gauge invariant but not gauge covariant? And I would appreciate an example (other than the one...

If only left handed fields couple in the weak force, and we can boost to a frame that changes left handed fields to right handed ones, how can that theory be relativistically invariant? thanks for the help!

Hello all ! My question: Does fibre bundles are necessary for describing gauge invariance in electromagnetic case? Or fibre bundles uses only for describing gauge invariance in cases of weak, electroweak and strong interactions? Thanks

Hi, excuse the funny title :). In his book on quantum field theory Zee says (pag 245, fouth line) that QED gauge symmetry follows from the conservation of the current j=ψ γ^μ ψ (with the bar on the first spinor). I'm confused because that current is the noether current resulting from the...

I am trying to understand the derivation of the covariant derivative in Peskin/Schroeder (chapter 15.1, page 483). This is the important stuff: n^\mu\partial_\mu\psi=\lim_{\epsilon \rightarrow 0} \frac{1}{\epsilon}\left[\psi(x+\epsilon n)-\psi(x)\right] Scalar quantity: U(y,x): U(y,x)...

Hi everybody, i have a question concerning potential energy (in all its forms, which basically means all forms of energy except the kinetic one). The kinetic energy of a system is always well defined: in the rest frame it is m² (convention c=1), in a frame moving at a relative speed v compared...

Hello, I don't understand two steps in solution to the problem: I. Homework Statement Show that QED action is invariant under gauge transformation. II. Relevant equations QED action: S= \int{d^{4} x \left[\overline{\Psi}\left(i\gamma^{\mu} D_{\mu} -m \right)\Psi...

I have been trying to teach myself Lagrangian mechanics from a textbook “Lagrangian and Hamiltonian Mechanics” by MC Calkin. It has covered virtual displacements, generalised coordinates, d’Alembert’s principle, the definition of the Lagrangian, the Euler-Lagrange differential equation and how...

First of all, let me remind about an older thread on this topic: https://www.physicsforums.com/showthread.php?t=330517 Here I'd like to thank again to everybody, who participated in that discussion. However, I still find myself at a deadlock with some questions about Gauge Invariance (GI)...

Short intro.: I'm a 2nd year M.Sc. student in particle physics, with basic quantum field theory and knowledge of the SM and perhaps a bit more. I've read the forums before and tried to find questions/answers that were similar to my own until I decided, "why not just join so I can ask exactly...

After the first explanation of superconductivity by Bardeen, Cooper and Schrieffer, it was for several years a matter of concern to render the theory charge conserving and gauge invariant. I have been reading the article by Y. Nambu, Phys. Rev. Vol. 117, p. 648 (1960) who uses Ward identities to...

Homework Statement So I was doing a problem out of Merzbacher 3rd edition (end of chapter 4 problem 3); the homework set has already been turned in but I wanted to run this by you all and see what you thought. I am essentially working with a particle in a 1-d ring constrained to the x-y plane...

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...

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...

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...

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...

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...

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...

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...

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)...

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...