The poincare-symmetry tag has no wiki summary.
8
votes
2answers
877 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
279 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 ...
7
votes
1answer
202 views
alternatives to supersymmetry and Coleman-Mandule theorem
Humour me for a minute here and let's imagine that all interesting and plausible supersymmetry models have been "cornered" out by the experimental data;
what sort of alternatives are there for having ...
7
votes
1answer
253 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
...
6
votes
1answer
66 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 $SU(2)$ ...
5
votes
2answers
189 views
Poincare Symmetry in QFT
Given that spacetime is not affine Minkowskispace, it does of course not possess Poincare symmetry. It is still sensible to speak of rotations and translations (parallel transport), but instead of
...
3
votes
2answers
201 views
Irreducible Representations Of Lorentz Group
In Weinberg's The Theory of Quantum Fields Volume 1, he considers classification one-particle states under inhomogeneous Lorentz group. My question only considers pages 62-64.
He define states as ...
3
votes
1answer
191 views
Klein-Gordon inner product
Studying the scalar field and Klein-Gordon equation in quantum field theory I came across this definition for the inner product in the space of the solutions of the K.G. equation:
$\langle \Phi_1 | ...
3
votes
1answer
107 views
Poincaré group on quantum Klein-Gordon field (C*-algebraic scenario)
on the same topic as this question, I have been trying to fool around with the free real K-G field in flat spacetime on the C*-algebraic scenario (Haag-Kastler axioms, Weyl quantization, etc).
Since ...
3
votes
1answer
38 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
41 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 $M$ ...
3
votes
1answer
72 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 ...
2
votes
4answers
219 views
Translations of field operators in QFT
A question in the book QFT of Srednicki: This concerns the relativistic QFT generalization
$$\tag{2.21} {{e}^{-i\hat{P}x/\hbar}}\psi (0){{e}^{i\hat{P}x/\hbar}}~=~\psi (x)$$
of the formula
...
2
votes
2answers
233 views
Effects of a non-Lorentz-invariant vacuum state
I'm here asking about real or though experiments (i.e., physical effects) where, at least in principle, one can see some consequence of a non-Lorentz-invariant vacuum state in an otherwise Poincare ...
1
vote
2answers
171 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 ...
0
votes
1answer
114 views
Lorentz transformation problem
In the equation (1.18) they omitted the translation vector $a^\mu$, but why?
