Journal of Modern Research Physics
Volume 10, Issue 1 (Spring and Summer 2025 2025)
JMRPh 2025, 10(1): 51-62 |
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Jafari A. Relativistic Hamiltonian and Poisson Bracket. JMRPh 2025; 10 (1) :51-62
URL: http://jmrph.khu.ac.ir/article-1-270-en.html
URL: http://jmrph.khu.ac.ir/article-1-270-en.html
Abstract: (54 Views)
In the relativistic regime, we propose a method for deriving the relativistic version of the Hamiltonian, assuming the Lagrangian is available. We demonstrate that a minor modification in the definition of the Lagrangian is sufficient to achieve this goal. We will investigate the ability of the obtained Hamiltonian to describe field theory, and, by referring to canonical and mechanical momenta, we will reproduce the theories of interest. From the relativistic Hamiltonian obtained through two different approaches, we will construct the theories of bosonic and fermionic fields and clarify their interconnection. We explain the mechanism of the Legendre transformation between configuration space and phase space, and we extend the Poisson product. After deriving the Hamiltonian and the equations of motion attributed to the relativistic Hamiltonian, we extend the phase space and show that the creation of a dual phase space, along with the redefinition of the derivatives on the dual phase space and the original phase space, and the modification of the Poisson product structure will be necessary to approach the relativistic Poisson product. To establish a complete Lorentzian phase space, modifications to classical theory and an effective realization of the relativistic Hamiltonian are necessary.
Keywords: Relativistic Systems, Relativistic Lagrangian and Hamiltonian, Bosonic and Fermionic Field Theory, Legendre Transform, Phase Dual Space, Relativistic Poisson Bracket
Type of Study: Research |
Subject:
Special
Received: 2025/09/14 | Accepted: 2025/10/19 | Published: 2025/09/22 | ePublished: 2025/09/22
Received: 2025/09/14 | Accepted: 2025/10/19 | Published: 2025/09/22 | ePublished: 2025/09/22
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