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7

Yes, your confusion is wholly caused by you thinking classically ;) In a hand-wavy way, particles are certain localized excitations of the quantized fields. The QFT picture contains the particle picture in the perturbative approach known as Feynman diagrams (and, relatedly, the LSZ formalism). There, we are given the action of our theory dependent on some ...


5

The QFT is strongly based on the group theory formalism. Often when people say about some QFT theory they primarily say about the symmetries of the theory - invariance of lagrangian of theory (or about covariance of equations of motion) under sets of transformations. The group theory formalize these statements and help to construct theories which corresponds ...


5

Unitarity says that the probabilities of any event is less then $1$. This is obviously an essential requirement for a given quantum theory and if a theory is not unitary then for it to describe Nature, it is necessarily missing some information that will fix this issue (such as new states and/or interactions). Renormalizability just says that the theory ...


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Fundamental fermions like quarks and leptons are described by the spinor field, while gauge bosons like photons are described by the vector field. They together with the Higgs bosons are currently what we have in the Standard Model for elementary particles.


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The type of field that you have depends on the way that your field transforms. The fields that you encounter in quantum field theory usually are: Scalar fields, these describe spin-0 particles such as the Higgs boson. Spinor fields, these describe spin-1/2 particles, these describe for example the elementary fermions, like the leptons and quarks. Vector ...


3

The field theory is fully analogous for Hermitian and non-Hermitian fields The Hermitian operator $\varphi$ still creates and/or annihilates particles and the number of these particles $N$ is still well-defined (at least if we ignore interactions and problems with loops and divergences). The only difference from the non-Hermitian field is that the ...


2

Correct me if I'm wrong, but your line of thinking goes like this... Since quantum fields do not commute in general one can have finite variances for, e.g., particle number. Since the vacuum states defines a probability distribution we can find the corresponding entropy. However, here we are dealing with quantum physics. The entropy is in general $S ...


2

The second-quantised description of the electromagnetic field in terms of oscillators holds in QED as well. The part that is modified is the single particle description of charged particles. In other words, (virtual and real) pair-creation is permitted in QED. So for energy scales less than $2mc^2$ as well as low intensities (see Schwinger limit), where ...


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Typically, when you calculate quantum effects, you will put some cut-off $\Lambda$, and typical integrals, say for a $ \lambda \phi^4$ theory, are, at first order, going in $\log \Lambda$ (ex : $\int \frac{d^4k}{k^2 (p-k)^2}$) While defining renormalized quantities at some energy scale $p_0$, you may remove the cut-off, and get typically equations like (at ...


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To put it simply: Renormalizability is the feature that the theory you know at low energy scales can be extrapolated to "arbitrarily high" energy scales, without losing consistency. Now some observations: When you say that a theory comes with a cutoff and seemingly doesn't work beyond that cutoff, then you're seeing something (that is scale dependent) ...



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