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Results tagged with quantum-field-theory
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user 231049
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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Why is Gell-Mann and Low theorem valid only for non-degenerate non-perturbed states?
Second the Gell-Mann and Low theorem, if a quantum system has a hamiltnian $H = H_{0} + V$, and $H_{0} | \Phi_{0} \rangle = E_{0} | \Phi_{0} \rangle$, then the following quantity
$$
| \Psi \rangle = \ …
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The validity of the Gell-Mann and Low theorem for non-normalizable state $\phi_{0}$?
If we have a system with hamiltonian $H = H_{0} + H_{I}$, the Gell-Mann and Low theorem allow us to relate the exact state $\Psi$ of the interacting system with the ground state $\phi_{0}$ of the syst …
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Lehmann representation of Green function
The Lehmann representation of the Green function to a system with $N$ identical particles can be write as
$$G(\textbf{x}, \textbf{x}', E) = \sum_{n} \frac{\langle \Psi_{0}^{N} | \psi(\textbf{x})| \Ps …
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Interpretation of field operators
In the book Field Quantization of Greiner, in section 3.2 he introduces the field operators (for bosons), that are postuleted to satisfy the commutation relations $$[\hat{\psi}(\textbf{x},t), \hat{\ps …
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Generalization of Wick's Theorem [duplicate]
Wick's theorem allow us to write a time-ordering of creation and annihilation operators as a normal-ordering of contractions of these operators. I am studying a system that consists of two kinds of fe …
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The Gell-Mann and Low theorem and the expansion of the Green function
If we have a system with Hamiltonian $H = H_{0} + V$, with $| \Phi_{0} \rangle$ being the ground state of the system without the interaction, the Gell-Mann and Low theorem say that the quantite
$$ |\ …
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Expection values of the hamiltonian of Klein-Gordon field
The hamiltonian of the quantized Klein-Gordon field $\phi(\textbf{x},t)$ can be writting using the creation and annihilation operators: $$\hat{H} = \frac{1}{2} \int d^{3}\textbf{p} \ \omega_{p} (\hat …
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Completeness relations in propagators
Let's consider a system of $N$ identical fermions with a time-independent Hamiltonian $H$. We define the Green's function or propagator as
$$G(k_{1}, k_{2}, t, t') = -i \langle \Psi_{0}^{N} | T[c_{k_ …
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Normal-Ordering of operators of two different types of fermions
The normal-ordering of creation and annihilation operators is defined such that the creation operators are put to the left, with a minus sign for each permutation of two operators necessary to do this …
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Commutation of field operators with differents times
We know that field operators in the Heisemberg (or interacting) picture satisfy the commutation relations
$$\{ \hat{\psi}(\textbf{r},t), \hat{\psi}^{\dagger}(\textbf{r}',t) \} = \delta( \textbf{r} - …
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Contribution of a second-order Feynman diagram for the one-particle Green function
I am studyng how to construct Feynman diagams for the perturbative expansion of the one-particle Green function (or propagator) using the book "A Guide to Feynman Diagrams in the Many-Body Problem". O …
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