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Results tagged with quantum-field-theory
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user 288281
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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Deriving a toy model for a particle in a potential interacting with a neutral scalar field
In section 6.2 of Folland's Quantum Field Theory, he constructs a toy model for a particle of mass $M$ moving in a potential $V$ interacting with a neutral scalar field. Here he takes space to be cont …
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Interpreting scattering operators
The following is from Talagrand's What is a Quantum Field Theory (Section 12.2). He lets $H$ be the Hamiltonian
$$H = H_0 + V$$
where $H_0$ is the Hamiltonian of the free particle and $V$ is some pote …
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What is lattice regularization and how is it carried out? [duplicate]
I am new to QFT, and so far I have studied dimensional regularization and Pauli-Villars regularization. These seem to be the only two regularization techniques discussed in most introductory textbooks …
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How to read renormalization group flow plots?
From what I know, the renormalization group tells us how the coupling constants of a theory change as the energy scale is varied. Thus as you vary the energy scale you trace out a path or flow in the …
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How do we know Schwinger functions exist?
Let $\mathcal{D}'(\mathbb{R}^n)$ denote the dual of $C^\infty_C(\mathbb{R}^n)$, that is distributions on the set of infinitely differentiable functions with compact support. If $d\mu$ is a probability …
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Divergences in tree-level diagrams?
Consider the Feynman diagram in $\phi^4$ theory where there are three incoming momenta ($p_1$, $p_2$, and $p_3$), three outgoing momenta ($q_1$, $q_2$, and $q_3$), and one internal line so that this i …
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Is the magnitude of the $\beta$ function important?
I am currently studying the renormalization group in quantum field theory and have gotten up to computing the $\beta$ function perturbatively . While I only have a basic understanding of it so far, th …
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What is the interpretation of the $\beta$ and $\gamma$ functions in the renormalization group?
Let $M$ be a renormalization/momentum scale, $\lambda$ a coupling, $G^{(n)}$ the $n$-point Green's function, $Z$ the field strength, and $\Lambda$ a momentum cutoff.
When studying the renormalization …
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Why is particle creation and annihilation not observed on a macro scale?
I am new to QFT and the idea of particle creation/annihilation so this will likely be a soft question. I have read that due to special relativity, particles come in and out of existence (and some sour …
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Calculating the contraction of a field operator and a creation operator
In Folland's Quantum Field Theory (section 6.4) he considers a field:
$$\phi_\pi = \sum_\tau \int f(\textbf{q})\big[u(\textbf{q}, \tau, \pi)a(\textbf{q}, \tau, \pi) e^{-iq_\mu x^\mu} + v(\textbf{q}, …
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Why does QFT require operator-valued distributions? [duplicate]
I am new to QFT, and so far I have only gone through the basics up to defining what a quantum field is, which is an operator valued distribution. I have been struggling so far understanding why operat …
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Motivation behind introducing creation/annihilation operators into the Dirac equation
When studying the Klein-Gordon equation, the introduction of creation/annihilation operators was justified by recognizing a harmonic-oscillator-like equation which we know how to quantize. Is there a …
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Calculation of one-loop diagram in $\phi^4$ theory
In Folland's book Quantum Field Theory, page 207, he gives the value of the amputated one-loop $\phi^4$ diagram as
$$I(p) = \frac{(-i\lambda)^2}{2} \int \frac{-i}{-q^2 + m^2 - i\epsilon} \cdot \frac{- …
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How is the source term chosen when using path integrals?
Suppose I would like to compute (time ordered) vacuum expectation values for a quantum field theory by using the path integral approach. Using the Lagrangian for the theory, we define a generating fun …
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Expanding the generating functional $W[J]$ for connected diagrams as a power series in $\hbar$
This is a follow up of a recent post I made (Making sense of stationary phase method for the path integral), but here I will work in Euclidean space, i.e. a Wick rotation has been performed.
Let
$$Z[J …
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