All Questions
Tagged with quantum-field-theory fermions
399
questions
32
votes
5
answers
3k
views
Why do or don't neutrinos have antiparticles?
This was inspired by this question. According to Wikipedia, a Majorana neutrino must be its own antiparticle, while a Dirac neutrino cannot be its own antiparticle. Why is this true?
- 11.4k
29
votes
2
answers
1k
views
$\phi^4$ theory kinks as fermions?
In 1+1 dimensions there is duality between models of fermions and bosons called bosonization (or fermionization). For instance the sine-Gordon theory $$\mathcal{L}= \frac{1}{2}\partial_\mu \phi \...
- 8,815
26
votes
3
answers
6k
views
Grassmann paradox weirdness
I'm running into an annoying problem I am unable to resolve, although a friend has given me some guidance as to how the resolution might come about. Hopefully someone on here knows the answer.
It is ...
- 6,381
25
votes
3
answers
6k
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What is the fundamental reason of the fermion doubling?
Recall that the fermion doubling is the problem in taking the $a \to 0$ limit of a naively discretized fermionic theory (defined on a lattice with lattice spacing $a$). After such a limit one finds ...
- 23.7k
24
votes
1
answer
4k
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Classical Fermion and Grassmann number
In the theory of relativistic wave equations, we derive the Dirac equation and Klein-Gordon equation by using representation theory of Poincare algebra.
For example, in this paper
http://arxiv.org/abs/...
- 1,080
24
votes
1
answer
4k
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A reading list to build up to the spin statistics theorem
Wikipedia's article on the spin-statistics theorem sums it up thusly:
In quantum mechanics, the spin-statistics theorem relates the spin of a particle to the particle statistics it obeys. The spin ...
- 4,499
20
votes
3
answers
5k
views
Why cannot fermions have non-zero vacuum expectation value?
In quantum field theory, scalar can take non-zero vacuum expectation value (vev). And this way they break symmetry of the Lagrangian. Now my question is what will happen if the fermions in the theory ...
- 351
20
votes
3
answers
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Why do people say that neutrinos are either Dirac or Majorana fermions?
The question of whether a given particle "is" a Dirac or Majorana fermion is more subtle than is sometimes presented. For example, if we just consider the "old" Standard Model with massless neutrinos, ...
- 48.4k
18
votes
4
answers
6k
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Fermions, different species and (anti-)commutation rules
My question is straightforward:
Do fermionic operators associated to different species commute or anticommute? Even if these operators have different quantum numbers? How can one prove this fact in a ...
- 1,109
17
votes
1
answer
749
views
Intuition behind mass corrections to massless fermions
I'm trying to understand the intuition behind the mass correction to massless fermions. To be concrete lets consider a theory with a massless Weyl fermion ($\psi $), as well as two massive particles, ...
- 8,995
17
votes
0
answers
1k
views
Time Reversal, CPT, spin-statistics, mass gap and chirality of Euclidean fermion field theory
In Minkowski space even-dim (say $d+1$ D) spacetime dimension, we can write fermion-field theory as the Lagrangian:
$$
\mathcal{L}=\bar{\psi} (i\not \partial-m)\psi+ \bar{\psi} \phi_1 \psi+\bar{\psi} ...
- 7,848
16
votes
4
answers
2k
views
Spinning Tachyons
In all examples that I know, tachyons are described by scalar fields. I was wondering why you can't have a tachyon with spin 1. If this spinning tachyon were to condense to a vacuum, the vacuum wouldn'...
- 281
16
votes
3
answers
3k
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What are the mathematical problems in introducing Spin 3/2 fermions?
Can the physics complications of introducing spin 3/2 Rarita-Schwinger matter be put in geometric (or other) terms readily accessible to a mathematician?
- 365
15
votes
1
answer
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Why is there extra minus sign in Feynman's rules for every closed fermionic loop?
I know this is connected to the fact that fermions are represented by anticommuting operators, but I still cannot find the way to get this minus in Feynman rules.
- 2,586
14
votes
1
answer
2k
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What is the value of a quantum field?
As far as I'm aware (please correct me if I'm wrong) quantum fields are simply operators, constructed from a linear combination of creation and annihilation operators, which are defined at every point ...
- 1,978