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Results tagged with poincare-symmetry
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user 83398
0
votes
Is the antisymmetrisation of $a^{\mu}b^{\nu}\epsilon_{\mu\nu}= a^{[\mu}b^{\nu]}\epsilon_{\mu...
It's precisely the opposite of mandatory: it makes absolutely no difference.
Apparently in order to factor out the components of the antisymmetric tensor $\epsilon_{\mu\nu}$ the following antisymm …
- 105k
10
votes
Accepted
Why does having a representation of the Poincaré algebra imply conservation of energy, momen...
It does sound a bit weird, at first, that using the Poincare algebra alone can give nontrivial conservation laws. After all, that's not how other algebras work. Many physical system carry a representa …
- 105k
3
votes
Accepted
Does every Hilbert space contain the generators of the Poincaré algebra?
The two-dimensional Hilbert space of a qubit is simply not including any information about where the qubit is in space, so it is meaningless to talk about moving the qubit in space in this context. Ho …
- 105k
7
votes
How is it possible for quantum fields in different irreps of the Poincaré group to interact?
There are several confusions here. First, you seem to be mixing up particles (described by infinite-dimensional unitary irreps of the Poincare group) with fields (described by finite-dimensional, gene …
- 105k
2
votes
Accepted
Definition of particles in Schwartz, Quantum field theory and the standard model
The Poincare group has two pieces: translations and Lorentz transformations. The translations commute with each other, so we can simultaneously diagonalize them, leading to wavefunctions proportional …
- 105k
11
votes
Accepted
Why aren't infinite-dimensional representations of the Poincaré group classified by *two* ha...
I think most of the confusion is due to mixing up what the Lorentz and Poincare groups are typically acting on. When we talk about Lorentz irreps, we usually mean finite-dimensional non-unitary irreps …
- 105k
34
votes
What does it mean for particles to "be" the irreducible unitary representations of the Poinc...
Irreducible representations of the Poincare group are the smallest subspaces that are closed under the action of the Poincare group, which includes boosts, rotations, and translations. The point is th …
- 105k