All Questions
Tagged with non-locality variational-principle
5
questions
2
votes
1
answer
142
views
Energy and canonical momentum conservation in non-local classical field theory
Assume we have the following Lagrangian field density where $x, x'$ both three dimensional real vectors are coordinates and $t$ represents time, field is given by $\phi$. Assume for the sake of ...
0
votes
1
answer
70
views
Finding the cost functional of a car-following model [closed]
I have a car-following model with delay
$\ddot{x}_n(t)=\lambda [\dot{x}_{n-1}(t-T)-\dot{x}_{n}(t-T)]$,
where $\ddot{x}$ is the acceletation, $\dot{x}_{n-1}-\dot{x}_{n}$ is the relative velocity, $\...
- 111
1
vote
2
answers
552
views
An inconsistency in Hamiltonian formulation for non-local Lagrangian: what am I doing wrong?
This question is based on a previous question I asked, Q. [1]
In this question, I proposed an example of a non-local Lagrangian (functional), I'm revisiting it here:
$$\mathbb{L}=\frac{1}{2}\int^t_0 ...
- 411
5
votes
1
answer
569
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Legendre transform for non-local Lagrangians, or Hamiltonian of non-local Lagrangian and their properties
This is sort of a multi-part question, mostly dealing with how to treat non-local Hamiltonians and how the corresponding properties of Hamiltonians work in a non-local framework. I proposed an example ...
- 411
5
votes
2
answers
523
views
Non-local Lagrangian contact interaction
Conside a contact interaction given by a delta function on their worldlines. Use a gauge fixed Lagrangian for two point particles in terms of their proper times $t$ and $t^{\prime}$. Is it possible to ...
- 3,206