# Questions tagged [poincare-symmetry]

The tag has no usage guidance.

217 questions
Filter by
Sorted by
Tagged with
26 views

### Infinite dimensional representation of generators of the Lorentz group

I was reading Schwichtenberg's "Physics from Symmetry 2nd Edition". In Section 3.7.11, there is the discussion on the infinite dimensional representations. If we consider a transformation of ...
60 views

### Why the little group of a massless spin-1 particle is ISO(2) rather than SO(2)?

As the title suggests, after going through a lot of Wikipedia, and references of books, I have learned that: The little group of a massive spin-1 particle is SO(3), while the little group of a ...
47 views

### Commutator of tetrad and Lorentz generators

While reading "Four lectures on Poincaré gauge field theory" (available at RG) the authors present a relationship between a tetrad $e^i_{\;\gamma}$ (with Latin indices coordinates, Greek ...
33 views

90 views

### Representation of the Poincaré group by means of exponential

Let $(\Lambda,a)$ be a Poincaré coordinate transformation. Let $U$ be an unitary representation of the Poincaré group on some vector space. Is it always possible to express $U(\Lambda,a)$ in the ...
1k views

### What is CPT, really?

The naive statement for the "CPT theorem" one usually finds in the literature is "relativistic theories should be CPT invariant". It is clear that this statement is not true as written, e.g. ...
63 views

### Does $\partial^\mu X^\nu = \partial_\mu X_\nu$ (Neumann Boundary Conditions)?

Problem I am trying to prove that the Neumann boundary condition , $\partial_\sigma X_\mu=0$ , implies that no momentum flows out of the end of an open string. I'm told that the associated conserved ...
586 views

55 views

### Casimir operators for Poincare algebra

I have seen at various places the comment that the operator $P_\mu P^\mu$ is a Casimir operator of Lorentz algebra and thus it satisfies a on-shell condition like $P_\mu P^\mu=m^2$. Given the Poincare ...
53 views

82 views

### What is the problem with a generalized kinetic term as $K^{\mu\nu}(x)\partial_\mu\phi\partial_\nu\phi$?

For field theory in flat spacetime, the most general kinetic term that I can think of for a field is $$K^{\mu\nu}(x)\partial_\mu\phi\partial_\nu\phi$$ where $K^{\mu\nu}(x)$ is an arbitrary second rank ...
46 views

### Why do we use affine groups in gauge theory? What is the purpose?

When we study General Relativity in the frame of gauge theory, what's the importance of affine group?
46 views

### Poincaré Group element of pure spacetime translation

If we make a spacetime translation of the coordinates of a event $x^{\mu}$ such that $x' ^{\mu} = x ^{\mu} + a^{\mu}$, the element $\eta _{\mu \nu} x'^\mu x' ^\nu$. Must be invariant : \begin{...
31 views

### Can local rotations lead to a gauge theory?

I was reading about the relation between electromagnetism and the complex Klein-Gordon field. The KG field had a global $U(1)$ symmetry and upon demanding that even a local phase transformation must ...
114 views

### What is the value of $W_\mu W^\mu$ for massless particles?

What is the value of the quantity $W_\mu W^\mu$ for massless particles where $W^\mu$ is called Pauli-Lubanski vector defined as $W^\mu=\frac{1}{2}\epsilon^{\mu\nu\alpha\beta}P_\nu J_{\alpha\beta}$. ...
52 views

### Generators of $su(2) \oplus su(2)$ in the $(A, B)$ representation

Let us call the generators of $su(2)$ in the spin $A$ or spin $B$ representation $J^A_i$ and $J^B_i$ respectively. What are the generators of $su(2) \oplus su(2)$ in the $(A, B)$ representation ? ...