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Results tagged with quantum-field-theory
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user 36793
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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Evaluating Compton scattering cross-section
In deriving the cross-section of Compton scattering, we require to perform the polarization sum $$\sum\epsilon_{\mu}\epsilon_{\nu}\sum\epsilon_{\alpha}\epsilon_{\beta}$$ using the identity $\sum\epsil …
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Sources of zero point energy in quantum mechanics and free quantum field theory
A quantum linear harmonic oscillator has a definite non-zero ground state energy $E_0=\frac{1}{2}\hbar\omega\neq 0$. However, in this energy eigenstate, the position and momenta are uncertain and thei …
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Energy-momentum relation for dressed particles and how interactions change mass
When a free real scalar field $\phi(x)$ described by the Lagrangian \begin{equation}\mathscr{L}=\frac{1}{2}\partial_\mu\phi\partial^\mu\phi-\frac{1}{2}m^2\phi^2\end{equation} is quantized, a quanta wi …
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Particle picture in the path-integral formulation of Quantum Field Theory
In canonical quantization, the particles arise as quantized excitations on the vacuum $|0\rangle$. For example, a one-particle state with four momentum $p=(E,\textbf{p})$ is given by $$|p\rangle\sim a …
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quantum fluctuations and the virtual particles
In the introduction of chapter-12 of “An Introduction to Quantum Field Theory” by Peskin and Schroeder I encountered this line: “The quantum fluctuatuations at arbitrarily short distances appear in Fe …
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Classical vacuum and quantum vacuum
How to determine the ground state of a classical field, for example an electromagnetic field? What is the difference between the the ground state of a classical field and that of a quantum field?
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Physical understanding of the regularization of benign infinities in free field theories
Any continuum quantum field theory (QFT), free or interacting, has uncountably infinite number of degrees of freedom in spacetime.
Does it have anything to do with the appearance of infinities in QF …
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Why is the effective action $\Gamma[\phi_c] \propto -(VT)$ (spacetime volume)?
Use the following expansion of effective action
$$\Gamma[\phi_c]=\int d^4x [-V_{eff}(\phi_c)+(\partial_\mu\phi_c)^2A(\phi_c)+...]$$
where $...$ represents higher order derivatives of $\phi_c$. When …
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Complete renormalization in $\phi^4$-theory?
In the one-loop renormalization of $\phi^4$-theory, only 1PI vertex functions $\Gamma^{(2)}$ and $\Gamma^{(4)}$ are regularized and renormalized. But they do not exhaust all the irreducible connected …
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Understanding how is a field theory with a negative mass dimensional coupling becomes nonren...
A quantum field theory with a negative mass dimensional coupling (or equivalently, an operator having mass dimension $>4$) is nonrenormalizable. Therefore, it must be the case that (i) the divergences …
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Non-invariance of the Interaction term in QED lagrangian
The interaction term in the QED Lagrangian $$\mathcal{L}_{int}=e\bar\psi\gamma^\mu A_\mu\psi$$ changes under a gauge transformation $$A_\mu\rightarrow A_\mu+\partial_\mu\chi$$ Doesn’t it affect the QE …
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Formalism Of Quantum Field Theory vs Quantum Mechanics
How far can we extend the formalisms on quantum mechanics (QM) to quantum field theory (QFT)? In particular,
How is a Fock space $\mathcal{F}$ different from a Hilbert space $\mathcal{H}$? Can a gen …
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How will the (anti)commutation relation between two different fermion fields look like? [duplicate]
The anti-commutation relation between the components of a fermion field $\psi$ is given by $$[\psi
_\alpha(x),\psi_\beta^\dagger(y)]_+=\delta_{\alpha\beta}\delta^{(3)}(\textbf{x}-\textbf{y}).$$
In …
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About series expansion of effective potential and its justification
The books on quantum field theory often uses an expansion of the effective action $\Gamma[\phi_c]$ in terms of $\phi_{cl}$ and its derivatives given by $$
\Gamma[\phi_c]=\int d^4x[-V_{eff}(\phi_c)+Z(\ …
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What does it mean by a nonrenormalizable operator being induced in a Lagrangian?
I have heard that nonrenormalizable operators (i.e., mass dimension greater than 4) can be "induced" in the Lagrangian (that we started with) via loop effects. However, I do not understand what does i …
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