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3
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1answer
63 views

A nice overview (and maybe derivation) of the Poincaré transformations of the Vector Spherical Harmonics

With $Y_{lm}(\vartheta,\varphi)$ being the Spherical Harmonics and $z_l^{(j)}(r)$ being the Spherical Bessel functions ($j=1$), Neumann functions ($j=2$) or Hankel functions ($j=3,4$) defining ...
3
votes
0answers
83 views

Spectrum of a quantum relativistic “distance squared” operator

This question disusses the same concepts as that question (this time in quantum context). Consider a relativistic system in spacetime dimension $D$. Poincare symmetry yields the conserved charges $M$ ...
8
votes
1answer
562 views

Relativistic center of mass

Recently I realized the concept of center of mass makes sense in special relativity. Maybe it's explained in the textbooks, but I missed it. However, there's a puzzle regarding the zero mass case ...
7
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1answer
112 views

what compactifications of the Poincare group have been studied?

as we know the Poincare group is non-compact. Poincare invariance have been observed in velocities and energies up to $10^{20}$ eV in cosmic rays. The other day i was thinking in how $SU(2)$ ...
9
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2answers
2k views

Poincare group vs Galilean group

One can define the Poincare group as the group of isometries of the Minkowski space. Is its Lie algebra given either by the equations 2.4.12 to 2.4.14 (..as also given in this page - ...
7
votes
3answers
384 views

why certain superpositions of quantum states are supressed?

it has been said that the electron is the fundamental representation of the Poincare group, with only two conmuting observables, $( \sigma , p_{\mu})$. This question regards what is usually called the ...
1
vote
2answers
240 views

self-antiparticles and broken symmetries

certain particles (i.e: certain bosons like the photon) do not have an anti-particle, or rather, they are they own anti-particles. lets assume that such symmetry is only approximate and these ...
3
votes
1answer
79 views

Experimental limits on anisotropies in the $e/m_{e}$ ratio

Currently the charge-to-mass ratio of the electron is known to 10 orders of magnitude. However, i'm curious if: Are there any experiments trying to bound the anisotropy of this ratio for different ...