Episode #125 of the Stack Overflow podcast is here. We talk Tilde Club and mechanical keyboards. Listen now

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.

704 questions
Filter by
Sorted by
Tagged with
44 views

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 ...
87 views

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 ...
54 views

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 ...
34 views

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 ...
30 views

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 ...
24 views

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, ...
14 views

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'...
51 views

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 ...
223 views

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 ...
51 views

41 views

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....
37 views

41 views

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, ...
65 views

62 views

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 $J_3|p,\sigma\rangle=\sigma|p,\sigma\rangle$ ...
64 views

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 ...
38 views

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 $45°$ ...
80 views

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?
53 views

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 ...
32 views

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 ...
48 views

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) ...
54 views

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 ...
50 views

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 ...
193 views

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 ${\mathbf{J }}=(J_1,J_2,J_3)$ ...
79 views

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 ...
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 ...
40 views

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? ...
50 views

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 ...
99 views

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. ...
24 views

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 ...
126 views

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 - ...
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 ...