# Tag Info

### Are all fields in the universe we know of quantum fields?

Currently all fundamental fields are quantum, except for gravity. For this reason Quantum Gravity is a hot area of research, but the full Quantum Gravity theory has not been developed yet. Why not? ...
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### How does canonical quantization work with Grassmann variables?

When you are dealing with Grassmann numbers you have a "left derivative" and a "right" derivative. A left derivative removes the variable from the left, a right derivative removes it from the right. ...

### Why can't $p^0$ change sign under a proper orthochronous Lorentz transformation?

Sometimes, diagrams are more useful than equations! Note that $p^2 = - (p^0)^2 + |\vec{p}|^2$ remains unchanged under any Lorentz transformation. Suppose that $p^2 < 0$ (say $p^2 = -1$). A plot of ...

### Invariance of Action vs. Lagrangian in Noether's theorem?

No, they are not the same. To see why, even in classical mechanics, suppose we have symmetry transformation $q \rightarrow q + \epsilon K$ that leaves the Lagrangian invariant. This means that we must ...
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### Classical field limit of the electron quantum field

The classical limit of bosonic quantum mechanical systems with both finite and infinite degrees of freedom is pretty well understood from a mathematical standpoint (with complete rigour, and for quite ...
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### What is the actual form of Noether current in field theory?

Eq. (5) is (up to factors of the infinitesimal parameter $\varepsilon$) the standard expression for the full Noether current. Here: $\delta x^{\mu}$ is the so-called horizontal component of the ...

### Why is action a functional of $q$ only?

The notation $q$ in the functional $S[q]$ stands for the whole parametrized curve/path $q:[t_i,t_f]\to \mathbb{R}$, not just a single position. In particular, the parametrized path already carries all ...
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### Hamiltonian Field Theory in Peskin & Schroeder

When you transform from the Lagrangian to the Hamiltonian picture, you necessarily must choose a particular foliation of spacetime -- that is, you must single out a particular time direction, and ...
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### What is "gradient energy" in classical field theory?

The best intuition is from the example of a "loaded string": a set of $N$ masses that are connected by a massless elastic string. If we imagine the limit as $N \to \infty$ but with the ...
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### Euclidean geometry in non-inertial frame

What is wrong is the idea that one can actually make the disk rotate; and it will remain perfectly rigid. In reality, what this correct argument shows is that relativity doesn't admit the existence ...
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### Why is a nonzero VEV for a spinor field said to break Lorentz invariance?

The $v$ you write is itself a spinor, not a scalar. A non-zero spinor is obviously not invariant under Lorentz transformations, so a non-zero spinorial VEV breaks Lorentz invariance of the 1-point ...

### Klein gordon field and positive/negative energy solutions

You say you're doing classical field theory, but the terminology comes from QM: these terms are only positive and negative energy if you interpret the field $\phi$ as a wavefunction, as people did ...
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### Uniqueness of the definition of Noether current

In Noether's first theorem, the continuity equation$^1$ $$d_{\mu} J^{\mu}~\approx~0 \tag{*}$$ is an on-shell equation, i.e. it holds if the EOMs [= Euler-Lagrange (EL) equations] are satisfied. It ...
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### Charged particle as observed from an inertial and a non-inertial frame of reference

First, I'll note that unless the non-inertial frame has a changing acceleration, there is some doubt as to whether it radiates at all. https://en.wikipedia.org/wiki/...
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### What is a gauge theory?

A gauge symmetry is simply a symmetry transformation of the action that depends non-trivially on spacetime. You can ask for all physical theories whether such transformations exist. For the case of ...
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### Most general Lagrangian in CFT in 0+1D

Classically a theory is invariant under a transformation if its action is invariant (up to boundary terms). In our case a conformal transformation is given by $$t'=\lambda t\\ Q'=\lambda ^{-\Delta}Q$$...
TL;DR: Generically$^1$ an action principle gets destroyed if we apply EOMs in the action. Examples: This is particularly clear if we try to vary wrt. a dynamical variable that no longer appears in ...