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9
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2answers
1k views

Irreducible Representations Of Lorentz Group

In Weinberg's The Theory of Quantum Fields Volume 1, he considers classification one-particle states under inhomogeneous Lorentz group. My question only considers pages 62-64. He define states as ...
0
votes
1answer
353 views

Lorentz transformation problem

In the equation (1.18) they omitted the translation vector $a^\mu$, but why?
3
votes
1answer
1k views

Klein-Gordon inner product

Studying the scalar field and Klein-Gordon equation in quantum field theory I came across this definition for the inner product in the space of the solutions of the K.G. equation: $\langle \Phi_1 | ...
7
votes
1answer
271 views

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 ...
3
votes
1answer
183 views

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 ...
2
votes
4answers
513 views

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 ...
2
votes
2answers
733 views

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 ...
5
votes
2answers
320 views

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 ...
14
votes
1answer
1k views

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 ...
10
votes
1answer
907 views

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 ...
3
votes
1answer
68 views

A nice overview (and maybe derivation) of the Poincaré transformations of the Vector Spherical Harmonics

With $Y_{lm}(\vartheta,\varphi)$ being the Spherical Harmonics and $z_l^{(j)}(r)$ being the Spherical Bessel functions ($j=1$), Neumann functions ($j=2$) or Hankel functions ($j=3,4$) defining ...
3
votes
0answers
87 views

Spectrum of a quantum relativistic “distance squared” operator

This question disusses the same concepts as that question (this time in quantum context). Consider a relativistic system in spacetime dimension $D$. Poincare symmetry yields the conserved charges $M$ ...
8
votes
1answer
703 views

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 ...
7
votes
1answer
128 views

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 $SU(2)$ ...
9
votes
2answers
2k views

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 - ...
7
votes
3answers
412 views

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 ...
1
vote
2answers
251 views

self-antiparticles and broken symmetries

certain particles (i.e: certain bosons like the photon) do not have an anti-particle, or rather, they are they own anti-particles. lets assume that such symmetry is only approximate and these ...
4
votes
1answer
83 views

Experimental limits on anisotropies in the $e/m_{e}$ ratio

Currently the charge-to-mass ratio of the electron is known to 10 orders of magnitude. However, i'm curious if: Are there any experiments trying to bound the anisotropy of this ratio for different ...