# Tagged Questions

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### What is a general definition of the spin of a particle?

In quantum field theory, one defines a particle as a unitary irreducible representations of the Poincaré group. The study of these representations allows to define the mass and the spin of the ...
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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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### 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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### 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 - http://en....
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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?
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### Spin state after boost

I am working through Weinberg's QFT book, and in problem 1 in chapter 2 I ran into copious amounts of algebra, so I am trying to "cheat" a little by using some assumptions, but am unsure of their ...
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### 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 ...
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### Why do we say that irreducible representation of Poincare group represents the one-particle state?

Only because Rep is unitary, so saves positive-definite norm (for possibility density), Casimir operators of the group have eigenvalues $m^{2}$ and $m^2s(s + 1)$, so characterizes mass and spin, and ...
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### 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 $SU(2)$ ...
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### 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 ...
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### 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 ...
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### Poincare representations for interacting field theory

I was going through Rudolf Haag's memoir http://link.springer.com/article/10.1140%2Fepjh%2Fe2010-10032-4 and came across these lines: '..in quantum ﬁeld theory (or for any system of interacting ...
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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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### 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 ...
Let $P_0$ be the generator for temporal translation and $P_1, P_2, P_3$ be for spatial translations. Let $p_μ$ be the momentum operator in the $x_μ=x^μ$ direction. I watched a lecture where the guy ...