# Questions tagged [hamiltonian-formalism]

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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### Weyl Quantization Integral

I have some doubts when calculating the integral for Weyl Quantization symbol. If I understand correctly, quantization using the Weyl symbol takes a function in phase space and takes it to an operator ...
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### Extrinsic curvature, Gauss equation and Christoffel symbol contribution

This question is in the context of geometry of hypersurfaces and ADM formalism. In a $4$-dimensional manifold, we define a $3$-hypersurface with space-like tangent basis $e_a$, $a=1,2,3$, and a normal ...
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### Evolution of volumes in Phase-Space

Liouville's theorem states that the volume occupied by an ensemble does not change as the ensemble evolves. My question regards the volume of the smallest sphere that contains the ensemble. Is there a ...
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### Lagrangian equal to Hamiltonian - is it possible?

In one calculation, I got a result where the Hamiltonian equals the Lagrangian, with both values constant. Eventually I found the error and corrected it, but I began to wonder whether there could even ...
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In this question (1.a), you are asked to find the hamiltonian of the system described above. I understand where the Lagrangian comes from, but I don't understand why the generalized momentum related ...
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### How does Poisson bracket vanish in this equation?

I am studying the book "Lectures on Quantum Field Theory", by Ashok Das. I am stuck in the last step of equation (10.36) as I will explain below. Under section 10.2 (Dirac method and Dirac ...
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### How to determine which coordinates to use for calculating the Hamiltonian? [closed]

In my classical mechanics course, I was tasked with finding the Hamiltonian of a pendulum of variable length $l$, where $\frac{dl}{dt} = -\alpha$ ($\alpha$ is a constant, so $l = c - \alpha t$.). I ...
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### Calculating Poisson brackets in classical non-relativistic Hamiltonian field theory

Summary of the question: How can I prove the equal-time Poisson bracket relations for the classical Hamiltonian field theory? I.e $$[q(x,t),H(t)]_\mathrm{PB}=\dot{q}(x,t)\tag{1}$$ for a field $q$ and ...
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### How are Lie series used as canonical transformations in perturbation theory?

I have a few questions on how to use Lie series as a canonical transformation, which are widely used in perturbation theory (celestial mechanics). I know that these series are related to a Taylor ...
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