All Questions
Tagged with group-theory poincare-symmetry
81
questions
1
vote
0
answers
29
views
Why every projective irreducible representation of $(ISO(2,1)^{\uparrow}=SO(2,1)^{\uparrow}\ltimes \mathbb{R}^3)$ is equivalent?
Why every projective irreducible representation of the connected poincare group $(ISO(2,1)^{\uparrow}=SO(2,1)^{\uparrow}\ltimes \mathbb{R}^3)$ is equivalent to a projective irreducible representation ...
- 374
2
votes
0
answers
95
views
Why representations? [duplicate]
I've been studying Talagrand's What is a Quantum Field Theory? lately and I have some questions regarding the scheme he presents.
Essentially the state of affairs as of where I am in the book is that ...
- 873
9
votes
6
answers
2k
views
What exactly is a quantum field?
As I understand it, a relativistic quantum field is an operator-valued function of spacetime that transforms under some finite dimensional irreducible representation of the Lorentz* group:
\begin{...
- 904
2
votes
1
answer
126
views
In what sense are fields representations of the Poincare group?
As far as I know, a representation is a homomorphism from the group to a vector space $V$ which preserves the group multiplication, i.e., if $(\pi,V)$ is a representation of the group $G$, then ...
- 904
3
votes
1
answer
113
views
What's the definition of spin for a particle in $d$-dimensional Minkowski spacetime?
Consider a relativistic quantum theory in d-dimensional flat spacetime. Neglecting possible internal symmetries, a particle is defined as a system whose Hilbert space furnishes the support of an ...
- 81
1
vote
0
answers
76
views
Why do we need to consider the full Poincare group to get unitary representations?
I am trying to study and understand QFT from the perspective of symmetries. I was referred to this super helpful answer by @ACuriousMind : https://physics.stackexchange.com/a/174908/50583. I still ...
2
votes
1
answer
243
views
Some question about the irreducible representation of Poincare group
I am writing a note about the Poincare group and I am trying to explain that argument that one-particle state transforms under irreducible unitary representations of the Poincare group. However, there ...
- 546
0
votes
0
answers
48
views
General element of the Poincare group
Consider the generators of the Poincare group are $M^{\mu\nu}$ and $P^\mu$. The Lorentz group elements are $g(\omega)\in SO(1,3)=e^{-\frac{i}{2}\omega_{\mu\nu}M^{\mu\nu}}$ and the translation group ...
- 534
3
votes
1
answer
180
views
Doubt in Poincare Algebra
So, I have been reading Lecture notes on "Supersymmetry and Extra Dimensions" (PDF), taken by Flip Tanedo (notes of the course of SUSY and Extra Dimension taken by Professor Quevedo, ...
- 85
2
votes
1
answer
227
views
Do generators of translations transform as *covariant* vectors under a homogeneous Lorentz transformation?
Using the composition law of Poincaré transformations, it is easy to see (cf. e.g. Ref. 1 this answer) that under a Lorentz transformation
$$\underbrace{U(\Lambda,0)P^\mu U(\Lambda,0)^{-1}}_{P'^{\mu}}=...
- 1,989
5
votes
3
answers
371
views
Why the Pauli-Lubansky and momentum operator build an irreducible representation of Poincarè group?
We know that particle states in QFT are identified with irreducible representation of Poincarè group, in particular they can be identified using Pauli-Lubansky and (squared) Momentum operator (wich ...
- 475
1
vote
0
answers
55
views
What are the discrete representations of the Poincare group, analogous to the $(j_1, j_2)$ representations of the Lorentz group?
The finite dimensional representations of the Lorentz group are given by two half-integers $(j_1, j_2)$. One can break up the Lorentz Lie algebra into two $\mathfrak{so}(3)$ Lie algebras, and the half-...
- 11.6k
2
votes
1
answer
466
views
In the Poincaré group, what are explicit representations of translations, boosts, and rotations?
Context
In [1], cowlicks asks, ``How can the Gallilean transformations form a group?''. In [1] Selene Routely explains that the Galilean transformations form a group of dimension 10. Routely explains ...
- 460
3
votes
3
answers
274
views
What we talk about when we talk about Lorentz transformations?
Context
In [1], cowlicks asks the question, ``How can the Gallilean transformations form a group?'' It is clear what a group is. Borrowing liberally from [2],
"A group is a set $G$ together with ...
- 460
3
votes
0
answers
60
views
Is every unitary representation of the Poincare group a direct sum of Wigner's irreducible representations?
Is Wigner's classification of unitary irreducible representations of the Poincare group [1] sufficient for constructing all unitary representations of the Poincare group by taking direct sums?
The ...
- 2,270