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The Hamiltonian formalism is a formalism in Classical Mechanics. Besides Lagrangian Mechanics, it is an effective way of reformulating classical mechanics in a simple way. Very useful in Quantum Mechanics, specifically the Heisenberg and Schrodinger formulations. Unlike Lagrangian Mechanics, this formalism relies on a "Hamiltonian" instead of a Lagrangian, which differs from the Lagrangian through a Legendre transformation.

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Hamiltonian Field Theory in Peskin & Schroeder

In Section 2.2 of their QFT textbook, Peskin & Schroeder introduce the Lagrangian and Hamiltonian field theories of a classical scalar field. While defining the action $S[\phi]$ and deriving the Euler …
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5 votes
1 answer
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Quantization surface in QFT

What does the Quantization Surface mean here? Reference: H. Latal W. Schweiger (Eds.) - Methods of Quantization
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31 votes
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How to derive the formula for the quantum Hamiltonian $\hat H(\hat P,\hat Q)$ in terms of th...

While studying Path Integrals in Quantum Mechanics I have found that [Srednicki: Eqn. no. 6.6] the quantum Hamiltonian $\hat{H}(\hat{P},\hat{Q})$ can be given in terms of the classical Hamiltonian $H( …
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