# Tagged Questions

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### Are the partial derivatives of Lagrangian in the varied action functional derivatives?

In particle mechanics Lagrangian $L$ depends upon position, velocity (and may be explicitly on time), whereas in field theory the Lagrangian density ${\cal L}$ similarly (or analogously) depends upon ...
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### Beyond Hamiltonian and Lagrangian mechanics

Lagrangian and Hamiltonian formulations are the bedrock of particle and field theories, produce the same equations of motion, and are related through a Legendre transform. Are there more such ...
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### Geometric (topological?) structure and consequences of the canonical hamiltonian method

(1) Even though (I think) I understand the concept of a tangent bundle, I have trouble assimilating the idea of the configuration space being one and in relation to what that is the case. How can I ...
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### The consistency conditions of constrained Hamiltonian systems

I am studying the Hamiltonian description of a constrained system. There are some questions puzzled me for days, which I have been stuck on it. From the lagrangian, we can obtain the primary ...
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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 ...