Questions tagged [anticommutator]
The anticommutator tag has no usage guidance.
169
questions
0
votes
1
answer
125
views
Why do we only consider commutators and anticommutators in QFT?
While studying canonical quantization in QFT, I observed that we quantize fields either by a commutation or an anticommutation relation
\begin{equation}
[\phi(x), \phi(y)]_\pm := \phi(x) \phi(y) \pm \...
- 1,588
0
votes
0
answers
86
views
Relationship between anti-commutators and correlation
Ballentine (in his solution at the back of the book to his Problem 8.10) writes that
$$[Tr(\rho \{A,B\}/2)]^2$$
is related to the correlation between the observables represented by $A,B$, but gives no ...
- 1,095
1
vote
1
answer
66
views
Anticommutator Relation of Quantized Fermionic Field and Fermi–Dirac statistics: How are these related?
I'm reading the Wikipedia article about Fermionic field and have some troubles to understand the meaning following phrase:
We impose an anticommutator relation (as opposed to a commutation relation ...
- 1,395
2
votes
0
answers
68
views
Can Exceptional Jordan Quantum mechanics model field theory?
Exceptional Jordan Quantum mechanics is an interesting case in which observables are modelled with $3\times3$ Hermitian octonion matrices $\mathbb{J}_3(\mathbb{O})$. There is the Jordan product $A\...
user84158
0
votes
1
answer
79
views
What is the motivation for the Self-Dual Canonical Anticommutation Relation (CAR) algebra?
What exactly is the motivation for the use of the Self-Dual Canonical Anticommutation Relation (CAR) algebra in the context of infinite lattice systems? Why not remain with the CAR algebra, as both ...
- 71
2
votes
1
answer
70
views
Why can the commutator of a general expression be replaced by the anti-commutator in the $bc$ CFT theory?
Polchinski states in his equation 2.6.14 (in his book String Theory Vol. 1, Introduction to the Bosonic String) that for charges $Q_1$ and $Q_2$ the following equation holds, where $j_i$ is the ...
- 938
1
vote
0
answers
238
views
Commutation of kinetic energy operator with Hamiltonian
I am basically trying to calculate current energy operator $\hat{\mathbf{J}}_E(\mathbf{r})$ by using Heisenberg equation of motion as
$$
-\nabla\cdot \hat{\mathbf{J}}_E(\mathbf{r})=\frac{i}{\hbar}[H,\...
- 831
1
vote
1
answer
312
views
Anti-commutator of angular momentum operators for arbitrary spin
I know the commutator of angular momentum operators are
$$
[J_i,J_j]=\mathrm i\hbar \varepsilon_{ijk}J_k.
$$
For spin-1/2 particles, $J_i=\frac\hbar2\sigma_i$ where $\sigma_i$ are Pauli matrices, and ...
- 695
3
votes
1
answer
98
views
Contour integral for commutator of fermionic fields
Suppose we have primary fields $A$ and $B$ which have the OPE,
$$A(z) B(w) = \frac{1}{z-w} = -B(z)A(w), \quad |z| > |w|,\tag{1}$$
so they have fermionic statistics. Now I was curious how this would ...
- 721
2
votes
0
answers
123
views
About the Hilbert space that carries the representation of $\{\psi (x), \bar{\psi (y) }\}=i\delta (x-y) $?
What is this Hilbert space? Is it the complex Hilbert space of wavefunctionals spanned by using the spinor-field configurations as the basis vectors?
I know that the wavefunctional space carries a ...
- 6,355
0
votes
0
answers
116
views
Dirac spinor field anti-commutation
I am thinking the anti-commutation property of Dirac field! First, note that the equal time anti-commutation relation (from P&S's QFT):
$$\{ \psi_a(\mathbf{x}),\psi_b^{\dagger}(\mathbf{y}) \}=\...
- 1,421
3
votes
1
answer
128
views
Can Hadamard's formula be used for fermionic operators?
Can I use this special case of Hadamard's formula
$$e^\hat B \hat A e^{-\hat B}= A + [B,A]+\frac{1}{2!}[B, [B,A]] + \dots$$
for fermionic operators?
Suppose I have fermionic operators that obey ...
- 179
1
vote
0
answers
18
views
Adding a surface term to Dirac action modifies the canonical anticommutation relations [duplicate]
I'm dealing with the following issue: when describing a fermionic field, one can use the typical Dirac Lagrangian $$\mathcal{L}=\bar\psi(i\gamma^\mu\partial_\mu-m)\psi,\tag{1}$$ or the more symmetric ...
- 503
0
votes
0
answers
63
views
Why do fermions anti-commute in Ising model?
In my course fermions are given like a product of spin and (dual to spin) disorder parameter in 2D Ising square lattice. Then, using the properties of disorder parameter I can prove that fermions ...
- 509
1
vote
0
answers
72
views
Where do arbitrary phases of wavefunctions go under second-quantization?
As far as I understand, a second-quantized operator in QFT or condensed matter represents a many-body wavefunction (symmetrized for bosons or antisymmetrized for fermions). But every wavefunction is ...
