1
vote
2answers
206 views

Lagrangian and hamiltonian of interaction

How to prove that lagrangian of interaction is equal to hamiltonian of interaction with minus sign? For example, I can't prove it for special case - quantum electrodynamics.
4
votes
1answer
418 views

Why does Quantum Field Theory use Lagrangians rather than Hamiltonains? [duplicate]

Why does Quantum Field Theory use usually Lagrangians rather than Hamiltonains? I heard many reasons, but I'm not sure which is true. Some say it's just a matter of beauty, so Lagrangians are more ...
0
votes
0answers
56 views

A posteriori solution to the Hamilton Jacobi equation

I was wondering about the following: For many simple systems it is far too cumbersome to solve the Hamilton Jacobi equation compared with the Hamilton or Lagrange formalism. Now I was wondering, ...
0
votes
2answers
308 views

Hamiltonian and non conservative force

I have to find the Hamiltonian of a charged particle in a uniform magnetic field; the potential vector is $ \vec {A}= B/2 (-y, x, 0)$. I know that $$H=\sum_i p_i \dot q_i -L$$ where $p_i$ is ...
2
votes
4answers
533 views

Why the Hamiltonian and the Lagrangian are used interchangeably in QFT perturbation calculations

Whenever one needs to calculate correlation functions in QFT using perturbations one encounters the following expression: $\langle 0| some\ operators \times \exp(iS_{(t)}) |0\rangle$ where, ...
3
votes
3answers
960 views

Is there a valid Lagrangian formulation for all classical systems?

Can one use the Lagrangian formalism for all classical systems, i.e. systems with a set of trajectories $\vec{x}_i(t)$ describing paths? On the wikipedia page of Lagrangian mechanics, there is an ...