# I Relativistic dynamics in the Hamiltonian formulation

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1. Jan 7, 2019

### Alex Petrosyan

hi all!

I’m trying to generalise the Caldeira-Leggett Hamiltonian (heat bath + particle) to the case of high velocities. Naturally, the multi-oscillator Hamiltonian needs to change and I have a gnawing suspicion that the multi-particle Hamiltonian is just the sum of single-particle hamiltonians with $$H = \sqrt{P^2 + m^2}$$

In natural units ofc.

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Can you offer guidance or do you also need help?