A Hamiltonian-like formalism that treats one spatial coordinate --
rather than time -- differently
- URL: http://arxiv.org/abs/2108.11330v1
- Date: Tue, 24 Aug 2021 10:25:49 GMT
- Title: A Hamiltonian-like formalism that treats one spatial coordinate --
rather than time -- differently
- Authors: Sivapalan Chelvaniththilan
- Abstract summary: The Hamiltonian and Lagrangian formalisms of Qunatum Field Theory (QFT) are equivalent.
While Lorentz invariance can be clearly seen in the Lagrangian formalism, it is not so explicit in the Hamiltonian one.
This is because time is treated a little differently from the spatial coordinates in the Hamiltonian formalism.
- Score: 0.0
- License: http://creativecommons.org/licenses/by-nc-sa/4.0/
- Abstract: The Hamiltonian and Lagrangian formalisms of Qunatum Field Theory (QFT) are
equivalent. But while Lorentz invariance can be clearly seen in the Lagrangian
formalism, it is not so explicit in the Hamiltonian one. This is because time
is treated a little differently from the spatial coordinates in the Hamiltonian
formalism. In this paper, I explore whether it is possible to devise another
formalism that is just like the Hamiltonian one (with operators and state
vectors) but which treats time on an equal footing with two of the spatial
coordinates, while the third one is treated differently, the way time is in the
usual Hamiltonian formalism.
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