# Tagged Questions

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### Finding the speed of electrons in a magnetic field

So I'm trying to solve this problem in which an electron beam is "drawing a picture" on a TV screen. The electrons are accelerated to a voltage of $3 kV$ by wire coils and are then directed to ...
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### Hamilton's equations of motion on Dirac's formalism

I'm having several doubts about the procedure proposed by the Dirac-Bergmann algorithm in order to get the correct equations of motion of electrodynamics (Maxwell's equations). Suppose I've already ...
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### General form for functional derivatives

Working on the hamiltonian formalism applied to canonical field theory, how do I deduce the general form for the functional derivatives $\frac{\delta}{\delta \pi}$ and $\frac{\delta}{\delta \phi}$ (...
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### How do (and don’t) particles emerge from fields?

I am aware of the following field- and particle-like notions: QFT particle, a unit of excitation in (the Fock space of) a QFT; SR field, an extremal $A = A(\mathbf x)$ of a Lorentz-invariant action; ...
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### Classical Klein-Gordon theory is a free relativistic theory

The classical Klein-Gordon theory for a real scalar field is called a relativistic free theory. It is called a free theory because the dynamics of the degrees of freedom in the momentum space of the ...
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### Placement of indices in canonical commutation relations of coordinates and conjugate momenta as well as fields and conjugate momenta

The canonical commutation relations between generalised coordinates $q_a$ and their conjugate momenta $p^a$ are given by $[q_a,q_b]=[p^a,p^b]=0$ $[q_a,p^b]=i\delta^b_a$. Furthermore, the canonical ...
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### Electric potential inside a shell

Inside a shell, electric field is zero. Then does it have a constant electric potential inside the shell? If $V=\dfrac Ed$, then since field is zero, potential should also have been zero. Please ...
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### Do Weyl fermions carry electric charge?

Do Weyl fermions carry ordinary electric charge? That is, do they interact with, for instance, electrons or photons?
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### Why don't people use Hamilton's equations for a relativistic free charged particle?

A charged relativistic free particle has the Hamiltonian in general: $$\mathcal{H} = \sqrt{p^2c^2+m^2c^4}.$$ I read somewhere that says, it is possible to go further and say that the EoM are ...
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### Higher than Lagrangian/action?

When you begin learning physics, you start with equations of motion applied to various physics systems. In classical mechanics course you learn, that exists Lagrangian/action of a system, which gives ...
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### Why is a theory Lorentz invariant if the Lagrangian is Lorentz invariant?

For if I started by trying to make the Hamiltonian Lorentz invariant, I would have failed. Indeed, the Hamiltonian is part of a covariant tensor. But how do I know that the Lagrangian is not a part of ...
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### Active transformation and passive transformation of a scalar field

For the Lorentz transformation $x \to x'=\Lambda x$, the active transformation is $\phi(x) \to \phi'(x)=\phi(\Lambda^{-1}x)$ and the passive transformation is $\phi(x) \to \phi'(x)=\phi(\Lambda x)$. ...
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### QFT: prove Dirac lagrangian is invariant under C, P, T separately

As it is stated in Peskin, $\mathcal{L}=\bar\Psi(i\gamma_{\mu}\partial^{\mu}-m)\Psi$ is invariant under C,P and T transformation separately. I have some problems to see how the partial derivative is ...
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### Why Different charges attract while they should repel? [closed]

When I started studying magnetic fields, my teacher was always telling me that strong fields push the bodies to weaker fields, so i tried to apply the same concept to charges in the following picture: ...
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### How do I obtain the SUSY Transformations from Poisson Brackets?

In Friedman's and Van Proyen's Supergravity textbook it is explained how one can get the supersymmetry transformations using the conserved currents. Specifically this is in section 6 where we are ...
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### Field theory on a lattice, what is this?

I only have the training of undergraduate quantum mechanics and solid state physics. For me, field theory is defined on a continuous space. So, what does lattice field theory mean? Is it similar to ...
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### Cosmology: equation of motion for a scalar field in conformal time [closed]

So, I've derived the equation of motion for a scalar field in "normal" time, $t$: $$\ddot{\phi}+3H\dot{\phi}+\frac{dV(\phi)}{d\phi}$$ Then, using the expressions for the scalar field density, \$\...
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### Transformation of self-dual and anti-self-dual tensors and irreducibility of representations

I am working out exercise 2.5 of Maggiore's book. Part of the exercise is the following: Verify that self-dual and anti-self-dual tensors are irreducible representations of (real) dimension three of ...
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### Why is stat mech involved in mean field theory?

Mean field theory involves approximating an interacting system by a non-interacting one, by replacing some operators with their expectation value. However, to my surprise, free energy is involved in ...