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Tagged with quantum-field-theory hilbert-space
681
questions
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3
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Unitarily Inequivalent Representations
The definition of unitarily equivalent representations I am using is the one given here: https://en.wikipedia.org/wiki/Haag%27s_theorem.
Now in this text http://www.sa.infn.it/Massimo.Blasone/...
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7
votes
2
answers
1k
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Hermitian conjugation in Radial Quantization
I'm a little confused about Hermitian conjugation in a radially quantized CFT. Now, in the Minkowski theory, Hermitian conjugation leaves the coordinates invariant, i.e. $t^\dagger = t$ and $x^\dagger ...
0
votes
0
answers
40
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About momentum states covariant normalization
I'm following QFT of Schwrtz and I have a doubt about Eq. (2.72).
In particular, from Eq. (2.69): $$[a_k,a_p^\dagger]=(2\pi)^3\delta^3(\vec{p}-\vec{k}),\tag{2.69}$$ and Eq. (2.70): $$a_p^\dagger|0\...
- 207k
2
votes
0
answers
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Asymptotic states and physical states in QFT scattering theory
Context
In the scattering theory of QFT, one may impose the asymptotic conditions on the field:
\begin{align}
\lim_{t\to\pm\infty} \langle \alpha | \hat{\phi}(t,\mathbf{x}) | \beta \rangle = \sqrt{Z} \...
- 207k
0
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0
answers
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Why the Slavnov operator is self-adjoint? [duplicate]
In the context of BRST we can define the Slavnov operator $\Delta_{BRST}$ which generates BRST transformations. My lecture notes claim that $\Delta_{BRST}$ is self-adjoint, but I don't see why.
- 207k
0
votes
2
answers
116
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Do different bases of Fock space commute?
$\newcommand\dag\dagger$
Suppose we have a Fock space $\mathcal{F}$ with two different bases of creation and annihilation operators $\{a_\lambda, a^\dag_\lambda\}$ and $\{a_{\tilde \lambda}, a^\dag_{\...
- 5,989
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1
answer
44
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Bogoliubov transformation of Bunch-Davies vacuum
Let $\left|0\right>$ be the Bunch-Davies vacuum state of a QFT, for example a free scalar field, in de Sitter space. The creation and annihilation operators w.r.t. this state is a vacuum, i.e. $a^...
- 505
3
votes
1
answer
266
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Clarifications on the assumptions made for QFT interactions
I am reading about scattering and $S$-matrix in the context of quantum field theory and although I understand the math and the physical interpretation of the final results, I am confused about some ...
- 207k
0
votes
1
answer
576
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Anticommutation relations for fermionic operators in Fock space
In second quantization, creation and annihilation operators are defined on Fock space as follows:
\begin{align}
\begin{cases}a_j^\dagger|n_1,n_2,...,n_j,...\rangle=\xi^{s_j}\sqrt{n_j+1}|n_1,n_2,...,...
CommunityBot
- 1
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votes
1
answer
67
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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, ...
- 207k
0
votes
2
answers
58
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How can I construct a trivial product state in the continuum?
When working on the lattice it is easy to define a trivial product state. A state $|\psi\rangle$ is a trivial product state if it admits the following tensor decomposition,
\begin{equation}
|\psi\...
5
votes
2
answers
482
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About sending time to infinity in a slightly imaginary direction in QFT
I am going through the Peskin and Schroeder QFT book. While proving the Gell-Mann and Low theorem in chapter 4 of their book, the authors started with the equation
\begin{equation}
e^{-iHT}|0\rangle = ...
- 207k
17
votes
2
answers
685
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Is there an analogue of the LSZ reduction formula in quantum mechanics?
In quantum field theory the LSZ reduction formula gives us a method of calculating S-matrix elements. In order to understand better scattering in QFT, I will study scattering in non-relativistic ...
CommunityBot
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1
vote
0
answers
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In the path integral formulation of QFT, how do we get quantized particles out of a field?
Every QFT textbook starts by basically postulating that we have discrete states connected by creation and annihilation operators. In Quantum Mechanics, we started from a differential equation and ...
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