# Tagged Questions

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### How to arrive at the Dirac Equation from Poincare Algebra?

For the case of Galilean group, the time translation is given by the generator $H$. Hence, $$\mid\psi(t)\rangle\to \mid\psi(t+s)\rangle =e^{-iHs}\mid\psi(t)\rangle$$ Which immediately is the ...
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### Five-component field

Recently I was reading about 5-component field $(\varphi , \psi_{\mu})$, for which $$\hat {p}^{\mu} \varphi = mc\psi^{\mu}, \quad \hat {p}_{\mu}\psi^{\mu} = mc\varphi .$$ This field refers to the ...
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### The Wigner angle for two-particle state

Suppose we have the Wigner angle $\theta (\mathbf k, \Lambda)$, which is defined through the Lorentz group transformation $U(\Lambda)$ of one-particle state $|\mathbf k , \sigma\rangle$ ($\sigma$ ...
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### Transformation of photons under Lorentz transformation

This question is a continuation of one of my earlier post. In this post,I asked about the transformation of photon fields under rotation. Here I generalize the question to Lorentz transformation, and ...
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### Generators of Poincare Groups

How can I determine the generators of the Poincare Group, $P(1,3)$ explicitly? Here $P(1,3)$ means a matrix Lie group.
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### Unitary Lorentz transformation on quantized Dirac spinor

I am stuck again on page 59 of Peskin and Schroeder. In particular, I do not know how they get equation (3.110). Let me first give some background in the way that I understand it (but I might be ...
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### Symmetry at quantum level in quantum field theory

In nonrelativistic quantum mechanics, a symmetry is a transformation on states in the Hilbert space which keeps the Hamiltonian invariant and this implies that the generator of the transformation must ...
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### Scalar operators In Quantum Field Theory

I am trying to learn Quantum Field Theory and I am stuck in a basic point. What is the definition of a scalar operator in QFT? That is, how does it transform under a Poincare transformation? Why do ...
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### General covariance and global Poincaré algebras

Reading an article (page 7) I read this: Just as ordinary general covariance may be regarded as the local gauge symmetry corresponding to the global Poincare algebra and local gauge invariance ...
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### Poincaré symmetry and linearized gravity

When working with linearized gravity, is Poincaré symetry assumed to be the symmetry of space-time?
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### From representations to field theories

The one-particle states as well as the fields in quantum field theory are regarded as representations of Poincare group, e.g. scalar, spinor, and vector representations. Is there any systematical ...
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### Representations of the Poincare group

Which type of states carry the irreducible unitary representations of the Poincare group? Multi-particle states or Single-particle states?
The Dirac equation may be interpreted as the action of projection operator $\frac{1 - \Delta}{2}\Psi = 0$, where  \Delta = \begin{pmatrix} 0 & \Delta_{b \dot {a}} \\ \Delta^{\dot {b}a} & 0 ...