# Questions tagged [hamiltonian]

The central term in the hamiltonian formalism. Can be interpreted as an energy input, or "true" energy.

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### Temperature in the Hamiltonian limit

There is a well known connection between statistical mechanics in D spatial dimensions and quantum field theory in D-1 spatial dimensions. Changing the temperature in statistical mechanics corresponds ...
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### Topological Quantum Field Theories

I've asked this on Math.SE, but with no avail. So, I decided to ask it here. I was wondering about the following after reading the Wikipedia article on TQFTs. It is said that TQFTs have vanishing ...
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### How the supercharge operators act on superfields in quantum mechanics, and the adjoints of supercharges?

I'm watching this lecture on introductory Supersymmetry (Clay Cordova, 2019 TASI lecture 2 on Supersymmetry). My question relates to the first 20minutes or so. The lecturer is introducing Superfields ...
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### $S$-matrix commutation with Hamiltonian

I know from scattering theory that $S$-matrix and the free Hamiltonian $H_{0}$ commute due to energy conservation of incident and outgoing asymptotic states, but can the $S$-matrix and $H = H_{0} + V$,...
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### Hamiltonian eigenvalues in a transformed reference frame

Under a time-dependent unitary transformation $V(t)$ of the state vectors $|{\psi}\rangle$ $$|\psi'(t)\rangle = V(t) |\psi(t)\rangle$$ The Hamiltonian $H(t)$ has to ...
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### Projection operator (relative angular momentum) in FQHE Toy hamiltonian

I am working on Fractional Quantum Hall Effect and reading these lecture notes http://www.damtp.cam.ac.uk/user/tong/qhe/qhe.pdf. As all others sources I have found, none of them precisely define the ...
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### Imaginary Hamiltonian

The Hamiltonian for nuclear spin independent parity violation in atoms is given by: $$H_{PV} = Q_w\frac{G_F}{\sqrt{8}}\gamma_5\rho(r)$$ Here $Q_w$ is the weak charge of the nucleus (which is a scalar),...
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### Mechanical systems with their configuration space being a Lie group

In Marsden, Ratiu - Introduction To Mechanics And Symmetry there is a certain focus on reducing cotangent bundles of Lie groups. More precisely, if $G$ is a Lie group, then $T^*G$ is naturally a ...
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### Meaning of the concept of external parameters in Statistical Mechanics

I'm confused about the meaning of the concept of external parameter in Statistical Mechanics. According to my textbook, the Hamiltonian of a system is a function that depends on the generalized ...
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### Physical meaning of gapped path between Hamiltonians in the same phase

I'm reading this famous paper about the classification of quantum phases, and I'm wondering about the physical meaning of the definition of phases the authors use. They say that two Hamiltonians $H_0$ ...
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### Utility of the Magnus expansion (preserving symplectic form?)

There are (at least) two ways to perturbatively solve a matrix initial value problem: the Dyson expansion and the Magnus expansion To be explicit, suppose you're solving for a (interaction-picture) ...
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### Is Schrieffer-Wolff transformation equivalent to Feynman diagram and Path integral?

In high energy community, people usually use path integral (or Feynman diagram) to derive effective action (or effective Hamiltonian). However, in condensed matter or AMO community, people usually use ...
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I am looking for a proof of the next theorem: "If the higher order time derivative Lagrangian is non-degenerate, there is at least one linear instability in the Hamiltonian of this system." Where ...
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### What is the interpretation of the eigenvalues of $e^{-\beta (H-\mu N)}$?

In quantum statistical mechanics, the equilibrium state is characterized by a density matrix $\rho$. Let me focus on the grand canonical ensemble, although the question also holds for the canonical ...
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### Are all physically realistic Hamiltonians local?

My understanding of modern physics is that physicists think that, fundamentally, physical laws are local. For system A to interact with system B, they either need to be very close to each other or ...
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### Finite temperature greens function in grand canonical ensemble

I see this question was asked several times before but I don't think any answer can explain the issue perfectly. I am studying many body theory and encounters finite temperature Green's function. At ...
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I have a momentum space Hamiltonian $H(\vec k)$ for a Kagome lattice and I want to find its eigenvalues which may be dependent on $\vec k$. Now, I'm told that one of the eigenvalues for such ...