Questions tagged [quantum-field-theory]
Quantum Field Theory (QFT) is the theoretical framework describing the quantisation of classical fields which allows a Lorentz-invariant formulation of quantum mechanics. QFT is used both in high energy physics as well as condensed matter physics and closely related to statistical field theory. Use this tag for many-body quantum-mechanical problems and the theory of particle physics. Don’t combine with the [quantum-mechanics] tag.
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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} \...
- 88
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$2\pi$-rotation of fermionic states vs. fermionic operators
Given a fermionic state $|\Psi\rangle$, a $2\pi$ rotation should transform it as
\begin{equation}
|\Psi\rangle \quad\to\quad -|\Psi\rangle \,,
\end{equation}
On the other hand, given a fermionic ...
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Vacuum flucutuations = local entanglement between quantum fields?
I'm puzzled by this statement by Dieter Zeh: "Various types of quantum fluctuations (in particular vacuum fluctuations, often visualized in terms of 'virtual particles') are used to describe ...
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Questions about fundamental solutions and propagators for the Dirac operator
I thought that propagator is a synonym for fundamental solution. But that seems not to be the case since in this answer it is said that an expression with delta function on a surface has to be ...
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Compact scalar field - Polyakov textbook
This question is related with Polyakov, "Gauge Fields and Strings" section 4.2
In section 4.2, partition function is
\begin{equation}
Z=\sum_{n_{x,\delta}}\int_{-\pi}^{\pi}\prod_x\frac{d\...
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3
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573
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Path integral at large time
From the path integral of a QFT:
$$Z=\int D\phi e^{-S[\phi]}$$
What is a nice argument to say that when we study the theory at large time $T$, this behaves as:
$$ Z \to e^{-TE_0} $$
where $E_0$ is the ...
- 411
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1
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What does it mean to "resum" the large logarithms?
I am struggling to understand the concept of resummation of large logarithms in QFT; from what I learnt so far the problem relies on the fact that if a full theory defined in the UV contains much ...
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Path integral without wick rotation [closed]
As far as i know path integrals are usually evaluated by wick rotation to imaginary time, then making imaginary time finite and periodic/anti-periodic (bosons/fermions) with period beta=1/T (inverse ...
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How can I visualise a sphere with a negative radius? [closed]
I want to visualise the shape of the sphere , will having a negative radius turn the inside of the sphere outside or something other will happen ?
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Derivation of two-body Coulomb interaction in momentum space
$\newcommand{\vec}{\mathbf}$
In Condensed Matter Field Theory by Altland and Simons, they claim the two-body Coulomb interaction for the nearly-free electron model for a $d$-dimensional cube with side ...
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Static Patch Decomposition of Bunch Davies Vacuum
In the Jerusalem Lectures on Black Holes section 3.3 the author considers a QFT in Minkowski space. He then picks out a space coordiante, say $x$, and divides the Hilbert space $H$ of the QFT in two ...
- 505
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Physical observables in the XY/sine-Gordon duality
My question is, during the duality map, real physical quantities seem to acquire a prefactor of $i$ and become purely imaginary. And I feel uncomfortable.
Take bosonic current for example. Consider ...
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On the symmetry of changing the sign of helicity of incoming and outgoing particles in the invariant matrix element
Let $\Psi_\Lambda^{\{\mu\}}\propto U_\Lambda^{\{\mu\}}$ and $\psi_\lambda^{\{\nu\}}\propto u_\lambda^{\{\nu\}}$ be spinors of spin $s$ fermions where $s \geq 1/2$ with respective helicites $\Lambda$ ...
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Deriving the equal time anti-commutator of the Dirac fields [closed]
I am trying to solve an exercise on deriving the equal-time anti-commutator of the Dirac fields. But I got stuck somewhere and couldn't get the desired result.
I would like to show that
$$
\{\psi(x), \...
- 41
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1
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52
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Causality for gauge dependent operators in quantum field theories
Suppose that $\mathcal{A}_{ij...}(x)$ and $\mathcal{B}_{ij...}( x')$ are two gauge dependent (so non-observable) operator in some theory. If they are spacelike, should I impose the causality ...
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