All Questions
26
questions
1
vote
0
answers
122
views
On which bundle do QFT fields live?
In QFT, there is a vector field of electromagnetism, usually notated by $A$, which transforms as a 1-form under coordinate changes. Since quantum fields are operator-valued, I thought it is a section ...
- 61
2
votes
1
answer
93
views
Equivalent definitions of Wick ordering
Let $\phi$ denote a field consisting of creation and annihilation operators. In physics, the Wick ordering of $\phi$, denoted $:\phi:$, is defined so that all creation are to the left of all ...
- 3,350
0
votes
1
answer
67
views
Is integral of energy-momentum tensor in QFT over a region $R$ self-adjoint?
Consider a quantum field theory in flat 1+1D spacetime for simplicity. Let $T_{\mu\nu}$ be the conserved symmetric stress tensor. One writes operators by integrating the tensor over the whole space, ...
- 184
1
vote
0
answers
73
views
Convergence of series of elements in a quasi-local algebra
I am studying the quasi-local algebra on Bratteli and Robinson Operator Algebras and Quantum Statistical Mechanics, but there is one thing that is not clear to me at the moment. Let's say that the ...
- 159
3
votes
1
answer
213
views
Haag-Kastler axioms
In the Haag-Kastler axioms, an algebra of observables $A(O)$ is associated to each open spacetime region $O$ of the Minkowski space. In several treatments, the algebra $A(O)$ is a $C^{*}$ algebra, and ...
- 689
2
votes
0
answers
163
views
Can quantum fields be smeared in space (rather than spacetime)?
I am interested in what is known about the possibility of smearing interacting quantum fields on a Cauchy slice. This is easy to do for free fields and their conjugate momentum, and indeed this is ...
5
votes
1
answer
217
views
Quantum Fields living in finite dimensional non-unitary irreducible representations of the Lorentz group
In Non-unitary, finite dimensional representations of the Lorentz group it got clarified that the finite dimensional non-unitary reps of the Lorentz group are completely reducible. In physics, we use ...
- 689
11
votes
2
answers
764
views
Path integral in QM vs QFT
On page 282 of Peskin and Schroeder discussing functional quantization of scalar fields, the authors use expression 9.12, the path integral in ordinary quantum mechanics
$$U(q_a,q_b;T)= $$
$$\bigg(\...
- 789
6
votes
2
answers
251
views
How do *-Algebras correspond to operators on a Hilbert space?
In algebraic quantum field theory, a theory is defined through a net of observables $\mathcal{O} \mapsto \mathcal{A}(\mathcal{O})$ fulfilling the Haag-Kastler axioms (see e.g. this introduction, sec. ...
- 1,618
2
votes
0
answers
91
views
Does microcausality plus the time-slice property imply local primitive causality?
In quantum field theory, observables are associated with regions of spacetime. One of the basic principles of relativistic quantum field theory is microcausality, which says that observables ...
- 54.5k
2
votes
0
answers
45
views
Given a positive element, $a$, of a $C$*-algebra, why does there exists a pure state, $p$, on $A$ such that $p(a)=||a||$? [duplicate]
I'm reading secondary literature where they make this claim, however, I cannot see why it holds true. This is a reformulation from a previous question that I didn't specify good enough.
- 41
3
votes
1
answer
275
views
Normal ordering by contour integral in CFT
In chapter 6 of Di Francesco, they introduce the normal ordering
$$
(AB)(w) = \oint_w \frac{ dz }{ 2\pi i (z-w) }A(z) B(w)\ .\tag{6.130}$$
So far so good. But then starting eq (6.139)
$$
\oint_w \...
- 669
1
vote
1
answer
276
views
Normal ordered products of operators and inverses
I have been reading this paper ("Operator ordering in quantum optics
theory and the development of Dirac’s
symbolic method" by Hong-yi Fan), and on page 3 (right-hand column) the author writes that $:...
- 3,063
2
votes
1
answer
808
views
Utility of the time-ordered exponential
Is the time-ordered exponential
$$ \mathcal{T}\exp\left\{-i\int_{t_0}^tdt'V(t')\right\}\tag{1} $$
just a mnemonic device for the series
$$
\begin{aligned} 1 + (-i)\int_{t_0}^tdt_1 \, V(t_1) +{} &...
- 5,220
2
votes
1
answer
193
views
States in algebraic QFT, and non-diagonal matrix elements
Let $\mathcal A$ be a $C^*$ algebra in the sense of Haag and Kastler. We define a state as an element of the space dual to $\mathcal A$, that is,
$$
\phi\colon\mathcal A\to\mathbb C
$$
This ...
