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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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An indexed lorentz invariant that isn't constant

This is in light of the explanation here regarding lorentz invariants and scalars. Since its possible to have indexed quantities(that depend on space time) which aren't tensors, the aim is construct ...
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Is every Lorentz invariant a Lorentz scalar?

All examples of lorentz invariant quantities that I have come across seem to be scalars: rest mass, proper time, spacetime interval,dot product of two 4 vectors etc. Another thing is that these are ...
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Why is Lorentz symmetry considered sacred? [duplicate]

In almost all particle physics theories (except some effective field theories) why is it assumed that the Lagrangian of the theory should be Lorentz invariant? What is wrong with theories that ...
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Lorentz algebra and group question with regards to operator representaion of $M^{\mu\nu}$

1) Likely an Einstein summation confusion. Consider Lorentz transformation's defined in the following matter: I aim to consider the product $L^0{}_0(\Lambda_1\Lambda_2).$ Consider the following ...
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Covariance of the perfect fluid's stress tensor

In Special Relativity, for a perfect fluid (i.e. without heat transference or viscosity) we have a stress tensor $T_{\mu \nu}$ $$ T_{\mu \nu} = -p\eta_{\mu \nu} + (\rho + p)u_\mu u_\nu $$ It is said ...
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Finding commutators without cyclic permutations

I've been trying to solve Problem 2.4 in Srednicki's Quantum Field Theory textbook. This involves proving the identity $$[J_i,J_j]=i\hbar\epsilon_{ijk}J_k$$ where $J$ is the angular momentum operator, ...
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Invariant quantities? [duplicate]

Every phisical quantity is tensor quantity (special cases of tensors are vectors and scalars). There are transformation rules for tensors. For example for scalar quantity F transformation rule is F'(x'...
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What if the Lagrangian $\mathscr{L}$, a Lorentz scalar, is replaced by a Lorentz vector?

As an answer to this post, I made an impression that if $\mathscr{L}$ were not a Lorentz scalar in Eq.$(1)$ (see below), then Eq.$(1)$ would not be covariant. But now I think that is wrong! I state ...
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How can a proton travel the milky-way in 296 seconds? [closed]

In the Introductory Special Relativity book, by W. G. V. Rosser, the author presented an example about Lorentz Length contraction. In this example, a proton is crossing the milky-way galaxy and he is ...
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51 views

Correct transformation of left-handed Weyl spinor

In the book "Matthew D. Schwartz, Quantum Field Theory and the Standard Model", page 164, it says that a left-handed spinor transforms as $$\psi_L \rightarrow e^{\frac{1}{2}(i\vec{\theta} - \vec{\...
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Does charge conjugation symmetry sit in the Lorentz group?

We know the Lorentz group is $O(3,1)$ in 4 dimensional spacetime. We know that there are 4 disconnected components in Lorentz group $O(3,1)$, and https://math.stackexchange.com/q/2204349/ $$\pi_0(\...
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Spinor Understanding: QFT vs pure Representation Theory

I have some questions on terminology used in QM & QFT and (pure mathematical) representation theory treating the concept of "spinor". Let us focus on Dirac spinor as described in https://en....
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Generic parametrization of Lorentz transformation matrix?

A proper Lorentz transformation of a vector $\bf{x}$ is given by $$\bf{x}\to \bf{x}'=\Lambda\cdot\bf{x}$$ where $\Lambda$ is a matrix with the properties $$\Lambda^T\cdot\eta\cdot\Lambda=\eta~~~,~~~...
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Does a magnet moving in a uniform electric field experience torque?

Assume a uniform electric field of $E_y$ along $y$ in the lab frame of reference $(x,y,z,t)$. A simple magnet bar is set in motion at $v$ along $x$ in this electric field so that the alignment of the ...
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The role of Lorentz tranformations

My questions concern the role of Lorentz transformations in Special Relativity and General Relativity, as described in the following fragment of the series of GR lectures: https://www.youtube.com/...
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Twin Paradox in String Theoretical Backgrounds / Compactifications

It is a common exercise while learning special relativity to work out the resolution to the twin paradox. As an extension, I have looked at the twin paradox with compact dimensions, i.e. having an ...
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Time difference as a result of Lorentz boost

So I am given two clocks A and B moving in $S'$ frame with a velocity $V$ relative to $S$ frame. The two clocks are separated by a distance $L$ and are synchronized in $S'$ frame. The objective is to ...
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Find angle from two perpendicular relativistic Lorentz boosts

I have a frame $s'$ moving with velocity $v_1$ along the x-direction with respect to a frame $s$. A frame $s''$ is moving with velocity $v_2$ along the y-direction with respect to $s'$. I want to ...
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Lorentz transformation boosts as matrices

I have seen Lorentz transformation boosts (say, along the x-direction) written as (in $c=1$ units): $$ \left[\begin{array}{cccc}{\gamma} & {-v \gamma} & {0} & {0} \\ {-v \gamma} & {\...
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Inertial frame and its transformation in anti-de Sitter spacetime

From the wikipedia, I learned and was able to follow mathematically the definition of anti-de Sitter space. As the maximally symmetric solution to field equations with negative cosmological constant, ...
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Lorentz transformations for time co-ordinates (STR)

I am little bit confused with the implication of Lorentz transformations for time co-ordinates or atleast how to apply those! Consider 2 frames of reference $O$ and $O'$ in which $O'$ is moving with $...
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As $SL(2,\mathbb{C})$ is a double cover of the Lorentz group, is $SL(2,\mathbb{Z})$ a discrete subgroup of the Lorentz group?

The group $SL(2,\mathbb{C})$, the group of $2 \times 2$ complex matrices with determinent $1$, is a double cover of the Lorentz group. (These transformations can be understood as Mobius ...
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$O(p,q)$ as transformations that conserve quadratic form

Let us try to define $O(p,q)$ in two different ways, which I want to show their equivalence. Define the symmetric bilinear quadratic form $[\cdot ,\cdot]$ which is given by $$[x,y]=\langle x,gy\...
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Is the ADM Mass for a boosted black hole $M$ or $\gamma M$?

If you were to take the metric for a Schwarzschild black hole and "boost" it, such that it were traveling with velocity $v$, would the ADM mass, corresponding to a time translation, be $M$ or $\gamma ...
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Applying a General Lorentz Boost to Multi-Partite Quantum State in Dirac Notation

I would like to apply a General Lorentz Boost to some Multi-partite Quantum State. I have read several papers (like this) on the theory of boosting quantum states, but I have a hard time applying ...
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Why all theories are Lorentz invariant?

Ok, in studying of Maxwell equations we have violation of Galilean relativity. This implies necessity of other transformations which make Maxwell equations covariant (invariant in form) under this ...
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Building the Lagrangian of electromagnetism from the Lorentz invariant?

The definition of the relativistic Action is $$ S=\int_a^b ds $$ The Lorentz invariant of electromagnetism is $$ s^2=\frac{1}{c^2}||\mathbf{E}||^2-||\mathbf{B}||^2-2i\frac{1}{c}(\mathbf{B}\cdot \...
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Thought experiment and possible contradiction between electromagnetism and special relativity (Part I)

I have designed a simple and qualitative thought experiment through which I believe that I have encountered an inconsistency in the relativistic electromagnetism. A point charge $+q$, with respect to ...
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$z$ component of angular momentum under Lorentz transformation for massless particle

This question is related to this Helicity states. Suppose we have $k=[\omega,0,0,\omega]$. In Weinberg's book The Quantum Theory of Fields: Volume I he defines the state $|k,\sigma\rangle$ as an ...
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Helicity states

On page 71 of Weinberg's book The Quantum Theory of Fields: Volume I, he defines the operators $$A=J_2+K_1$$and $$B=-J_1+K_2$$ where ${\mathbf{J }}=(J_1,J_2,J_3)$ are the rotation generators and ${\...
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Helicity under rotation

Suppose that the state $|p,\sigma\rangle$ (for a massless particle) has 3 momentum ${\bf p}=p_3$ (that is the momentum is in the $z$ direction) and that $J_3|p,\sigma\rangle=\sigma|p,\sigma\rangle$ ...
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Using Lorentz transformations with variable velocity

A particle is moving in a system of reference $S$. In its proper system of reference, say $S'$, the particle is still and it is described by the event $(c\tau,0,0,0)$. In the inertial frame $S$, the ...
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Spacetime rotation matrix using mostly minus conventions

When trying to find the Lorentz transformation in matrix form in the $x^2+x^3$-direction, I tried simply mapping the Lorentz boost in the $x^2$-direction to the $x+x^3$-direction by rotating it $45°$ ...
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Meaning of time derivative of the Lorentz factor $\gamma$?

This question about the Lorentz factor $\gamma$ in special relativity. I know what $\gamma$ means and how to drive. I'm wondering if I have time derivative of $\gamma$, what dose it mean conceptually?
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Lorentz group in 1+1 dimension

Consider the Minkowski 2D metric $\eta = \text{diag}(-1, 1)$. The Lorentz group is the set of matrices such that, for a transformation $\Lambda$, we get $$\eta = \Lambda^T \eta \Lambda$$ This means ...
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Lorentz invariant probability from the Dirac equation

My question is regarding a proof given in Greiner's "Relatavistic Quantum Mechanics", 3rd Edition textbook. On pg 148, he proves that the current density $j^{\nu}(x)$ is invariant to a Lorentz ...
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Lorentz boost in light-cone coordinates

Consider a particle with momentum $p^{\mu}=(p^+,p^-,p_{\perp})$, where the momentum is written in light cone coordinates defined as, \begin{align} n^{\mu}&=(1,0,0,1)& \bar{n}^{\mu}=(1,0,0,-1) ...
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Why does the charge conjugation of the spinor transform as a spinor?

I have come across (in QFT Nutshell, A. Zee) how the charge conjugation of the spinor, $\psi_c \equiv \gamma^2 \psi^*$, transform (where $\gamma^2=\sigma^2\otimes i\tau^2$ is the component of the ...
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A question about Lorentz invariant argument when writing down the Dirac equation [duplicate]

According to the chapter II.1 in "Quantum Field Theory in a Nutshell" by A. Zee, Dirac was trying to write down the relativistic wave equation linear in spacetime derivative. The author stated that ...
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Why helicity for massless particles is Lorentz invariant?

By definition helicity is projection of spin onto the 3 momentum. $$h={\bf J} \cdot {\mathbf{P }} $$ where ${\mathbf{P }}=(P_1,P_2,P_3)$ is the momentum operator and ${\mathbf{J }}=(J_1,J_2,J_3)$ ...
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The Proof of $\cos\phi=\gamma$ Equation in Special Relativity [closed]

In the Introductory Special Relativity book, by W. G. V. Rosser, page 182, Section 7.3, the author is defining the 4-vector methods using complex numbers. In his derivation, he writes the following ...
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112 views

Orthochronous indefinite orthogonal group $O^+(m, n)$ forms a group

My question is based on Qmechanic's answer here which proves that $O^+(m, 1)$ forms a group -- that if two Lorentz transformations have positive time-time co-ordinate, so does their product. The key ...
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Effectively Lorentz-invariant interacting Lagrangians in solid state?

Are there any known examples in solid state physics when an essentially non-relativistic system in certain regime may be described by a relativistically invariant Lagrangian with an interaction? ...
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Has this group something to do with the cone of light?

Consider the group $V=(-1,1)$ with addition $+_{rel}:V\times V\to V$ defined as: $$v+_{rel}w=\frac{v+w}{1+vw}$$ This group is analogous to the relativistic velocities where the speed of light equals ...
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Lorentz transformations: new actual notation for a $4$-vector [duplicate]

For the Lorentz trasformations I use this notation \begin{equation*} \left\{\begin{aligned} x&=\gamma (x'+\beta ct')\\ y&=y'\\ z&=z'\\ ct&=\gamma (ct'+\beta x')\\ \end{aligned}\right. ...
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Velocity composition effect of moving line charges acting on a moving charge - By what velocity (boost) is the E-field unchanged along the boost?

Claim 1) An infinitely long line current can be modeled as the linear superposition of two infinitely long line charges. Claim 2) An infinitely long line current can exert forces on charges with ...
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Why would a spinor transform under Lorentz transformations?

From my understanding of spinors, they arise as projective representations of $SO_0(1,3)$ that do not correspond to representations of $SO_0(1,3)$. But still one says here - and virtually everywhere - ...
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Trying proving that energy and momentum are conserved in every inertial frame

I'm trying to show, using Lorentz transformations, that if relativistic energy and momentum are conserved in $S$, then they are conserved in $S'$ too. A wrong proof Let's suppose I know that in ...
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About elements “factorization” in Clifford Algebras

the article linked below is very instructive and advanced about real Clifford Algebras, and their relationship with Lorentz group. After a general introduction of a Clifford algebra, $\mathcal{Cl}(V,\...
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Lorentz boost tensor notation confusion

I have been given this$$ \delta X^{\mu}=\omega_{\mu \nu}\left(M^{\mu \mu}\right)_{\sigma}^{\rho} X^{\sigma} $$ and I think it should be equal to this but I'm confused if I'm doing it correctly $$ \...