All Questions
11
questions
2
votes
1
answer
354
views
Is the expectation value of a Fermi field operator a Grassmann number?
It's often noted that Bosonic fields result from quantizing classical field theories defined on a regular numbers, whereas Fermionic fields arise when quantizing a classical field theory defined on ...
- 21
7
votes
1
answer
2k
views
What exactly are "Grassmann-valued fields"?
Peskin & Schroeder define a Grassmann field $\psi(x)$ as a function whose values are anticommuting numbers, that can be written as : [p.301 eq. 9.71]
$$\psi(x) = \sum\psi_i \phi_i(x),\tag{9.71}$$
...
- 456
8
votes
1
answer
339
views
What's the space of eigenvalues/field configurations for a fermion?
In the Schrödinger picture of quantum field theory, the field eigenstates of a real scalar field $\hat\phi(\mathbf x)$ with $\mathbf x \in\mathbb R^3$ are the states $\hat\phi(\mathbf x)|\phi\rangle=\...
- 970
1
vote
1
answer
453
views
Why is the Jacobian factor for fermionic variables different from that for bosonic ones?
In Srednicki's textbook Quantum Field Theory, Section 77 discusses anomalies and the path integral for fermions. The path integral over the Dirac field is defined to be
\begin{equation}
Z(A) \equiv \...
- 1,653
5
votes
1
answer
2k
views
Change of variables in path integral measure
In fermion's path integral we have a measure that you can write, in terms of the Grassmann variables $\psi, \bar{\psi}$ as
$$
D\bar{\psi}D\psi, \quad \psi(x) = \sum_n a_n\phi_n(x), \quad \bar{\psi}(x)...
- 1,597
4
votes
1
answer
323
views
Canonical Quantisation vs the Dirac Field, why does it even work?
Using the "Dirac Prescription", we can preserve the format of a differential equation in its QM form. If we define the canonical variables s.t. they have the same commutation relations times $i$ as ...
- 267
3
votes
2
answers
706
views
How are supersymmetry transformations even defined?
I am just starting to read about supersymmetry for the first time, and there is something bothering me. Supersymmetry transformations transform between bosonic fields and fermionic fields, but I don't ...
- 11.6k
1
vote
1
answer
200
views
Can Grassmann-number variations of operators be represented by operators?
In my previous question, I asked about how to handle Grassmann-number variations of operators. I read a book that uses those variations $\delta \Phi = c \mathbb{1}$, with $c$ being a grassmann number ...
- 6,763
2
votes
1
answer
568
views
Convert Grassmann numbers to real numbers [closed]
We know Grassmann numbers are complex numbers. Hence Grassmann integrals are also complex. How can we convert a Grassmann integral into real one, ie is there any transformation of converting complex ...
- 165
12
votes
4
answers
11k
views
Dirac equation as Hamiltonian system
Let us consider Dirac equation
$$(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
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