# Tagged Questions

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### Significance of symplectic form in classical field theory

I'm trying to understand the significance of construction presented to me in field theory class. Let me first briefly describe it and then ask questions. Given two solutions $\phi_1$, $\phi_2$ of the ...
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### Are all forces given by a field conservative forces?

When teaching us electromagnetism, our professor first introduced us to the concept of "field". Several lessons later, he proved that electric field force is a conservative force. But I think the ...
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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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### Do gravitational waves have field components like electromagnetic waves?

One way I've been led to understand electromagnetic waves (and I accept that this might be a misconception I have) is that they 'self propagate' through empty space by virtue of the wave consisting of ...
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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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### Mass spectrum of field theory

How can I find the mass spectrum of a field theory given a Lagrangian made of a canonical kinetic term and a potential. I mean, I think I have to find the matrix of the quadratic terms in all the ...
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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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### Sign of Feynman rules with derivative couplings

Feynman rules for derivative couplings always make me confused. For example, the derivative in $gV^\mu\phi^+\partial_\mu\phi^-$ will give you $\pm ip_{-\mu}$, where $\pm$ depends on whether the ...
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; ...