All Questions
Tagged with quantum-field-theory fermions
77
questions
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
12
votes
2
answers
5k
views
Why are anticommutators needed in quantization of Dirac fields?
Why is the anticommutator actually needed in the canonical quantization of free Dirac field?
- 335
12
votes
4
answers
11k
views
Dirac equation as Hamiltonian system
Let us consider Dirac equation
$$(i\gamma^\mu\partial_\mu -m)\psi ~=~0$$
as a classical field equation. Is it possible to introduce Poisson bracket on the space of spinors $\psi$ in such a way that ...
- 497
24
votes
1
answer
4k
views
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
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
14
votes
1
answer
2k
views
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
18
votes
4
answers
6k
views
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
10
votes
2
answers
1k
views
Can we treat $\psi^{c}$ as a field independent from $\psi$?
When we derive the Dirac equation from the Lagrangian, $$
\mathcal{L}=\overline{\psi}i\gamma^{\mu}\partial_{\mu}\psi-m\overline{\psi}\psi,
$$
we assume $\psi$ and $\overline{\psi}=\psi^{*^{T}}\gamma^{...
- 495
3
votes
2
answers
1k
views
Non-relativistic QFT Lagrangian for fermions
Take the ordinary Hamiltonian from non-relativistic quantum mechanics expressed in terms of the fermi fields $\psi(\mathbf{x})$ and $\psi^\dagger(\mathbf{x})$ (as derived, for example, by A. L. Fetter ...
- 31
11
votes
2
answers
3k
views
Sign in front of QFT kinetic terms
I'd like to understand if the sign in front of a kinetic term in QFT is physical. For the scalar field we conventionally write (in the $ + --- $ metric),
\begin{equation}
{\cal L} _{ kin} = \frac{1}{...
- 8,995
24
votes
1
answer
4k
views
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
4k
views
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
16
votes
3
answers
3k
views
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
11
votes
1
answer
7k
views
Why must fermions be antisymmetric? [closed]
I have read that fermions cannot exist in the same state simultaneously. I understand why indistinguishable particles with an antisymmetric superposition of states can't exist in the same state ...
- 1,386
9
votes
4
answers
645
views
Is there some special case where a fermion can mediate a force?
Looking at the comments of this questions
Does the gravitino contribute to the gravitational interaction? and even considering that the answers here in this other question Why are all force particles ...
- 1,943