# Tag Info

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1) Are we able to perform perturbative analysis and use diagrammatic expansion, Green function etc. – all these field-theoretical stuff [for bosons]? In general, the field-theoretic methods (at finite or zero temperature) can be applied to both bosons and fermions with slight differences which originate from the Fermi-Dirac and Bose-Einstein ...

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It's true that "the perturbative series is valid only when the perturbed state is qualitatively similar to the unperturbed state". Generally perturbation theory is acceptable when the coupling is weak, in which case the coupling can be treated as a small perturbation of the free field theory at all energies (for example Yukawa theory and $\phi^{4}$ theory. ...

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1) I should note that most perturbative expansions that are of interest in physics are not formally convergent (and more often than not, not Borel-resummable either). 2) There are many examples of useful perturbative calculations for bosons. The oldest example (probably) in Many-Body physics is the calculation of the energy per particle of the weakly ...

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Neutrino can interact only by exchange of electroweak boson. So in each reaction with neutrino $W^\pm$ or $Z$ bosons must be involved. Also, Standard Model neutrino is assumed to be massless, so there is defined handedness: neutrino is left-handed and antineutrino is right-handed. Consequence of it is that left-handed neutrino will interact only with ...

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In the reaction that you ask about the exchange boson is space-like (meaning that for that particle $E^2 - (pc)^2$ takes on a negative value. In cases like that there is no unique way to decide if you have a $W^-$ going from the nucleon to the lepton or a $W^+$ going from the lepton to the nucleon, and the drawing is usually annotated only with a $W$. ...

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BEC qubits are set up by splitting one harmonic condensate trap into a double-well trap by means of a suitable laser or microwave field. See for instance pg.6 on these LANL slides: Quantum dynamics, measurement and decoherence in Bose-Einstein condensates. Under strong enough separation the overall ground state becomes two-fold degenerate and the two ...

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The terminology of a mode of a free quantum field $\phi(x)$ comes from writing it as a Fourier transform, often also called mode expansion: $$\phi(\vec x) = \int \frac{\mathrm{d}^3 p}{(2\pi)^3}\frac{1}{\sqrt{2\omega_p}}\left(a(\vec p)\mathrm{e}^{\mathrm{i}\vec x\cdot\vec p} + b(\vec p)^\dagger\mathrm{e}^{-\mathrm{i}\vec x\cdot\vec p}\right)$$ where for a ...

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The term mode is used to define a particular state of a system and may refer for instance to its spin, wavevector, polarisation, charge etc. If we wanted to create a boson at position $x$ with an up-spin and with wavevector $k$, we may use the field operator $\hat{a}^\dagger(x, k, \uparrow)$ on the vacuum state $\vert0\rangle$. The most clear distinction ...

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