# Questions tagged [poisson-brackets]

In phase-space classical Hamiltonian mechanics, the Poisson bracket is an antisymmetric binary operation acting like a derivative.

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### Poisson brackets for a field theory

I'm performing a calculation involving Dirac constraints theory, and I need to calculate the Poisson brackets between constraints and the total Hamiltonian. The starting theory is described by a ...
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### Commutator Constant

I have seen a lot of commutators in quantum mechanics having a constant factor $i\hbar$. I have read about Dirac supplanting Poisson Brackets with commutators having a constant $i\hbar$. I want to ...
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### Equivalence of symplectic condition and canonical transformation

In Goldstein's "Classical Mechanics", at page 384 it is claimed that given a point-transformation of phase space $$\underline{\zeta} = \underline{\zeta}(\underline{\eta}, t),\tag{9.59}$$ ...
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### A problem understanding primary constraints meaning

I have some problems understanding the meaning of a function that vanishes weakly. As far as I can understand, when somebody writes that a function $F$ in the phase space vanishes weakly, that means ...
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### Is there any classical correspondence of the Jacobi identity? [closed]

In QM, the commutator were closely related to the poison bracket, so much so that to promote the classical operators to the quantum operators were often associated as \begin{equation} \{A,B\} \text{(...
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### The different generators of canonical transformations

Consider the phase space of a one degree of freedom mechanical system. We can pass from one phase space coordinates to another phase space coordinates via a canonical transformation. I want to focus ...
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### Canonical Realization of Poincare Symmetry of Dirac Spinor

I have a maybe stupid question about Noether charges and the Poisson bracket. If a classical field theory has a Poincare symmetry, then by using the Noether's theorem, one can write down its ...
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### What are the conserved currents and charges in QFT - operator form of Noether currents?

I can't figure out how to define/compute conserved charges and currents in Quantum Field Theory. I am following Peskin & Schroeder's Introduction to Quantum Field Theory, and in the second chapter ...
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### What does it mean for two variables to be canonically conjugate?

The word "canonical" has been used in many of my classes (canonical ensemble, canonical transformations, canonical conjugate variables) and I am not really sure what it means physically. ...
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### Functional derivative acts on covariant derivative

I'm confusing about how functional derivatives act on a covariant derivative. I'm doing such a calculation: In ADM formalism, let $h_{ij}(x)$ be the spatial metric while $\pi^{ij}(x)$ is its momentum ...
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### System vector, angular momentum, and rotation

In Goldstein 3rd edision p. 409, it is stated that $$\partial \mathbf{F}=[\mathbf{F}, \mathbf{L}\cdot\mathbf{n}]=\mathbf{n}\times\mathbf{F}\tag{9.121}$$ if $\mathbf{F}$ is a function of system ...
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### How can you confirm that two variables are canonically conjugate using Poisson brackets?

Suppose you have two conjugate variables $q$ and $p$ that are canonically transformed into two other variables $Q$ and $P$. What needs to hold true for these variables in terms of Poisson brackets? I ...
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