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Questions tagged [lorentz-symmetry]

Lorentz symmetry is a fundamental symmetry of [tag:special-relativity] describing the invariance of physics with respect to changes of orientation and boosts of inertial reference frames. These symmetry transformations are called transformations.

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How do u get Eq3 from Eq2&Eq1 [on hold]

I keep getting the wrong results by subbing eq1 into eq2 It’s from Kleppner’s an introduction to mechanics 2nd edition
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A charge moving relativistically in electric field [closed]

I need help in the following question: At $t=0$ a charged particle is moving at some speed $u$ in the X direction,and enters a constant electric field E in the direction of Y (all measured in lab ...
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Lorentz-transformation

I don't understand how to derive the matrix representing the Lorentz-transformation given two systems S and S': $$x' = \Lambda x$$ these transformations do not leave the differences $\Delta x^\mu$ ...
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The role of Lorentz transformation

I will assume that spacetime is flat four dimensional manifold equipped with a Lorentzian metric and define, Physical systems: any object that is capable of causing a response ( measurement) in the ...
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Combining two Lorentz boosts

Is it possible to express two Lorentz boosts $A_x(\beta)$ and $A_y(\beta)$ along the x/y-axis as one boost described by $A(\overrightarrow \delta)$? To answer this, I start by defining $\theta \equiv ...
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Is it possible to derive $2\times 2$ Lorentz transformation matrix from only eigenvectors?

As a preface, I am somewhat familiar with year 1 linear algebra but not too familiar with how one makes the connection to Lorentz transformation matrices so I apologize if the answer is obvious. One ...
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Connection between gauge invariance and Lorentz invariance

This question is presented in the context of Weinberg's QFT book treatment, in particular considering the electromagnetism chapter. It begins in chapter 5 where Weinberg argues that in order to have ...
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Dual space and Metric tensor

So I know that the dual space is the set of all linear transformations that map a vector from a vector space to the field of the space itself (the real number line, complex, quaternions). From YouTube ...
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Tensor index in special relativity?

I'm studying special relativity and I have some difficulties with tensor index. Take for example the Lorentz matrix, whose elements are written as $\Lambda^\mu{}_\nu$. $\Lambda^\mu{}_\nu(v) = \...
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Lorentz invariance of Maxwell's equations in matter

I know that Maxwell's equations of electromagnetism are Lorentz invariant in a vacuum. But what about in a generalized medium, e.g. a metal, a rubber, a dielectric, a magnet? I have read it comes down ...
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Questions about special relativity, index in the Lorentz matrix

I'm studying special relativity I have read this: We have $ x^u = (ct, x^1,x^2,x^3) $. If we apply Lorentz transformation we can write: $x'^u = \Lambda^{u}_{\hspace{0,2 cm}\nu} x^{\nu} $ $x'_u =...
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Intuitive explanation for the Lorentz transformation for time

I've recently started learning SR, and while the Lorentz transformation for space is pretty obvious, just the Galilean transformation combined with space contraction, I can't figure out the ...
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Error with generators of Lorentz group (basis of Lorentz Lie algebra) [closed]

Can someone help me figure out why my $J_y$ is incorrect? :/ It's supposed to be \begin{pmatrix} 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 1 \\ 0 & 0 & 0 & 0 \\ 0 & -...
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A simple proof covariance of Maxwell equations

I read that Maxwell equations are covariant under Lorentz transformations, but I can't find a proof. Or at least a proof understandable by someone that doesn't know higher mathematics (please don't ...
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Relativistic quantum mechanics ${}$

I am reading Weinberg's book "Quantum theory of field". Сould you explain to me the following things? Vol.1, page 60: How are we equating the coefficients? How we find the formula (2.4.8)? 2.3.10: ...
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Indices in Special Relativity

I am studying special relativity and I can't figure out what is the difference between the matrix - index notation between: $$ Λ_{α}{}^{β}, Λ^{α}{}_{β}, Λ^{αβ} ,Λ_{αβ} $$ Why do we introduce this ...
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Lorentz transformations: Distance vs “retarded distance”

Suppose I have a charge situated at rest in one inertial coordinate system. The field of that drops inversely with the square of the distance. If I perform a Lorentz boost where $$v^2« c^2$$ (not ...
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Do condensed-matter field theories with multiple fields generically have multiple speeds of sound?

It is well known that the low-energy physics of many non-relativistic condensed matter systems can be described by field theories that display emergent Lorentz symmetry. The heuristic way to figure ...
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Is this a right approach to show that $\partial_{\mu} \phi \partial^{\mu} \phi $ is Lorentz Invariant?

When trying to convince myself that $\partial_{\mu} \phi \partial^{\mu} \phi $ is Lorentz Invariant, I stumbled upon this approach: The last equation should read - $\partial_{i} \phi \partial^{i} \...
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Massive chiral fermions

The main question is: why does nobody care about massive chiral fermions? It is well-known that in QFT (in the axiomatic framework of Garding & Wightman) the quantum field transform according (...
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Rapidity in 4-vector Transformation

In Lorentz transformation we have a concept of rapidity as related to boost. Rapidity is defined as a hyperbolic angle α such that $$\tanh(α)=v/c .$$ This further defines a matrix for Lorentz ...
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Is the metric $ds^2=g_{\mu\nu}(x)dx^\mu dx^\nu$ Lorentz invariant?

Postulate of Special Relativity leads to the conclusion that the metric in flat Minkowski space $$ds^2=c^2t^2-\textbf{r}^2=\eta_{\mu\nu}dx^\mu dx^\nu\tag{1}$$ is Lorentz invariant. This follows as a ...
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Lorentz transformation of a Weyl Spinor?

A left handed Weyl Spinor belongs to the $(\frac{1}{2},0)$ representation of the Lorentz group. So given the Spinor, the unitary representation of the Lorentz transformation should look like $\exp{iA\...
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Is Lorentz symmetry broken if SUSY is broken?

I have seemingly convinced myself that the entire Poincare group is spontaneously broken if one of the supersymmetric charges is spontaneously broken. We know that if one of the supersymmetric ...
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How do time-like separated points preserve temporal ordering under orthochronous Lorentz Transformations?

How do time-like separated points preserve temporal ordering under orthochronous Lorentz Transformations? This question has already been asked in this Phys.SE post but I want to derive this result in ...
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Do Lorentz invariance and General covariance always hold at low energies, or are they sometimes violated?

This is motivated by Weinberg’s folk theorem, where the construction of our perturbative expansion (and choice of theory space) is mostly safe given that we only have to enforce very general symmetry ...
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The chain rule and velocity transformation in relativity

From elementary calculus, we have that the chain rule occurs when we differentiate a function like $f(y(x)) \equiv f(x)$: $$\frac{\mathrm{d}}{\mathrm{dx}}[f] = \frac{\mathrm{d}}{\mathrm{dx}}[f(y(x))] ...
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Lattice gauge theory under a Lorentz transformation

Taking a grid of 'evenly-spaced' space-time points. e.g. at integer values of (x,y,z,t). Now do a Lorentz boost on this grid. We end up with a grid of points which are much closer together. It is ...
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How do the creation operators transform under Lorentz transformation?

In Weinberg's QFT book In chapter 4, the change of creation operator under Lorentz transformation is describe by (4.2.12), $$\begin{aligned} U_{0}(\Lambda, \alpha) a^{\dagger}(\mathbf{p} \sigma n) ...
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Tensor decomposition v.s helicity amplitude

It is common to write e.g photon two point function in terms of manifest transverse and longitudinal form factors with lorentz structure factored out, e.g via explicit tensor decomposition $$\Pi^{\mu \...
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A question about Lorentz transformations in spinor representation

For $$\Lambda^{\mu}{}_{\nu}= \frac{1}{2} Tr(\bar{\sigma}^{\mu} S \sigma_{\nu}S^{\dagger}) $$ We need to prove that $$\Lambda (S)= \Lambda (-S)$$ Am I naive to say that by adding $-S$, $S^{\dagger}...
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Trying to prove the Wess Zumino invariance under a SUSY transformation

I have the Lagrangian density $$L=-\partial_\mu \phi^\star \partial^\mu \phi - \bar{\chi}_R \gamma^\mu \partial_\mu \chi_L - \bar{\chi}_L\gamma^\mu\partial_\mu \chi_R.$$ where $\epsilon$ is the ...
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Infinitesimal parameter of Lorentz transformation

I'm working through the SUSY lecture notes by Lambert, and he does something which seems strange to me during the calculation of the Wess Zumino model. He says the spinor $\psi$ has the ...
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If infinitesimal transformations commute why don't the generators of the Lorentz group commute?

If infinitesimal transformations commute as proved e.g. on this mathworld.wolfram page, why are the commutators for the generators of the Lorentz group nonzero?
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Is there a “special” inertial frame determined by the value of E and B at a point in an EM field?

Given the facts that $(E^2 - B^2)$ and $(E\cdot B)$ are Lorentz invariants of the EM field, and that the energy density $(E^2 + B^2)$ is not invariant, it seems that at each point in an EM field there ...
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An invariant for transformations of Lorentz

Exist a physical demonstration why $$E^2- p^2c^2 =m^2c^4=E'^2- p'^2c^2 $$ is an invariant for transformations of Lorentz? N.B.: $m$ is mass; $E$ is the energy and $p$ is momentum in the frame $\...
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The transformations of Lorentz as a general case of the transformations of Galileo

Starting from the transformations of Lorentz, $$ \left\{\begin{aligned} x&=\gamma (x'+\beta ct)\\ y&=y'\\ z&=z\\ ct&=\gamma (ct'+\beta x')\\ \end{aligned}\right. \quad \tag{*}$$ I ...
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How can I prove this relationship between the S-matrix and the Gamma matrices?

For an infinitesimal Lorentz transformation: $$ S(\Lambda)=1+i\epsilon_{\rho\sigma}s^{\rho\sigma} $$ $$ S(\Lambda)^{-1}=1-i\epsilon_{\rho\sigma}s^{\rho\sigma} $$ and apparently if we just plug that ...
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Invariance of $ds^2$ from invariance of all null intervals

Is this linear algebra statement true? Let $\eta= \begin{pmatrix}1&0&0&0\\0&-1&0&0\\0&0&-1&0\\0&0&0&-1\end{pmatrix}$. If $x^T (\Lambda^T\eta\Lambda) x$...
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Computing correlation functions sandwiched between momentum eigenstates

Suppose I have a free scalar theory, and I want to compute the following correlation function $<p|\phi(\zeta)\phi(0)|p>$ where $|p>$ is a momentum eigenstate in my quantum field theory. My ...
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Geometric derivation of Lorentz boosts

In two dimensions a very nice parametrization of the rotation group is obtained by the following line of arguments: The group of rotations is connected and compact. Therefore the exponential is ...
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Is Lorentz transform a tensor?

I am confused whether Lorentz transform is a tensor or not, since it is a linear transform. If yes how can I verify that?
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What does Lorentz index structure say about a full-fledged correlator?

I have a probably dumb question. Consider the following position space correlation function in a YM-theory (with or without matter fields): $$f_{\mu_1\cdots \mu_n}^{a_1\cdots a_n}(x_1,\ldots,x_n)=\...
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Check that the Poincaré's transformations form a group structure

How can I answer to this question ? I know that this is a Lorentz transformation + a translation but I don't know how to start. What's the difference between group/group structure ?
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How is Inönü-wigner contraction done?

I have read that little group for the massive particles is $SO(3)$ and for the massless particles is $E(2)$ in 4 dimensions. How does one take zero mass limits for the representations and show that it ...
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Solution to invariance equation when deriving Lorentz transformation

Requiring that the spacetime interval (1 spatial dimension) between the origin and an event $(t,\, x)$ stays constant under a transformation between reference frames: $$c^2t^2-x^2= c^2t'^2- x'^2$$ we ...
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Transformation of $4-$velocity

Notation: a greek index indicates four labels; spacetime coordinates $\mu = (0,1,2,3)$. A latin index indicates three labels; spatial coordinates $i = (1,2,3)$. $$* * *$$ A quantity, to be ...
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Weyl spinor representations and the Lorentz group

I'm currently trying to read up on the Lorentz-group and it's representations. I've found a couple of posts here on stack-exchange that I find helpful and confusing at the same time, so I would be ...
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Invariance of measure under Lorentz transformations without the four dimensional expression

Ticciati's book Quantum Field Theory for Mathematicians states that the invariance of the measure $$\int\frac{\text{d}^3\vec{k}}{2\sqrt{\left\|\vec{k}\right\|^2+\mu^2}}$$ can be shown by direct ...
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Measuring the lorentz transform generators $J$, $K$, and providing evidence that photons have no internal continuous d.o.f

I am reading Weinberg's first QFT book. We looked for (and I suppose found) unitary representations of the Lorentz group: $$U(\Lambda) = 1 - i (\vec{\theta}\cdot\vec{J}-\vec{\eta}\cdot \vec{K})$$ ...