Tagged Questions

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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?
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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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Reducing massive representation of the Poincare group to the massless one

I want to ask about the connection for massive and massless representation of the Poincare group. Sorry for the awkwardness. First I must to represent the formalism for both of cases. Massive ...
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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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Trying to rhyme Peskin and Schroeder with Weinberg

This is a follow up question of this one. In the Vol 1, Weinberg derives how a unitary operator $U(\Lambda)$ acts on one-particle states, which is given by equation (2.5.2): ...
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Question about Weinberg's derivation of a one-particle states under the Poincare group

I'm reading QFT: Vol 1 by Weinberg and I have a (perhaps trivial) question about a statement he makes on page 63. I can follow him to his derivation of equation (2.5.2): P^\mu ...
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How to show that higher derivative theories (mostly) breaks unitarity

How to show that higher derivative theories (mostly) breaks unitarity? Spinor field $\psi_{a_{1}...a_{n}\dot {b}_{1}..\dot {b}_{m}}$, which refer to the $\left( \frac{n}{2}, \frac{m}{2} \right)$ ...
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Spinor formalism in QFT

We can describe fields by two formalisms: vector and spinor. This is the result of possibility of representation of the Lorentz's group irreducible rep as straight cross product of two $SU(2)$ or two ...
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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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Poincaré group on quantum Klein-Gordon field (C*-algebraic scenario)

on the same topic as this question, I have been trying to fool around with the free real K-G field in flat spacetime on the C*-algebraic scenario (Haag-Kastler axioms, Weyl quantization, etc). Since ...
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Translations of field operators in QFT

A question in the book QFT of Srednicki: This concerns the relativistic QFT generalization $$\tag{2.21} {{e}^{-i\hat{P}x/\hbar}}\psi (0){{e}^{i\hat{P}x/\hbar}}~=~\psi (x)$$ of the formula ...
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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 ...
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Poincare Symmetry in QFT

Given that spacetime is not affine Minkowskispace, it does of course not possess Poincare symmetry. It is still sensible to speak of rotations and translations (parallel transport), but instead of ...
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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 PoincarĂ© group. The study of these representations allows to define the mass and the spin of the ...
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Identification of the state of particle types with representations of Poincare group

In the second chapter of the first volume of his books on QFT, Weinberg writes in the last paragraph of page 63: In general, it may be possible by using suitable linear combinations of the ...
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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 - ...
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 ...