Questions tagged [momentum]
In introductory mechanics, the momentum of a particle is its mass times its velocity. In electrodynamics, the momentum of a field is proportional to the cross-product of the electric field with the magnetic field. In special relativity, momentum is generalized to four-momentum.
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What's the momentum-space vacuum wave-functional of a fermion?
In the Schrödinger picture, the field eigenstates of a real scalar field $\hat\phi(\mathbf x)$ with $\mathbf x \in\mathbb R^3$ are the states $\hat\phi(\mathbf x)|\phi\rangle=\phi(\mathbf x)|\phi\...
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Weinberg QFT problem 2.1: transformation of quantum states
I'm solving the following problem in Weinberg's QFT textbook: an observer sees a particle of spin 1 and mass $M$ move with momentum $\mathbf{p}$ in the $y$-direction, and spin $z$-component $\sigma$. ...
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Is there a general formula to translate from *canonical* to *physical* momentum?
In Peskin and Schroeder, after having derived a conserved tensor $T^{\mu \nu}$ associated with translations in space-time (the stress-energy tensor), it is said that the charges $\int d^3 x T^{0i}$: $$...
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Interpreting $4D$ massive scalar momentum space action as a gauge-field action in 1D?
Consider the following action for massive scalar as follows
$$S = \int d^4x \left(-\frac{1}{2}\partial^{\mu}\phi\partial_{\mu}\phi-\frac{1}{2}m^2\phi^2\right) \tag{1}$$
with Minkowski signature $(-,+,+...
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How does the Hong-Ou-Mandel (HOM) effect conserve photon momentum?
HOM is a two-photon interference effect where temporally overlapped identical photons coming perpendicular to a beam splitter must leave it in the same direction.
How is momentum conserved in this ...
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Does every curved spacetime have non-commuting generators of translations?
If we define the generators of translations in a general spacetime to be $P_\mu$, is it true that in every curved spacetime we have $[P_\mu,P_\nu]\neq0$? Is it also true that for every spacetime where ...
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What are pre-collisions and post-collisions in forces and momentum?
What are pre-collision and post-collision exactly? I assume it is before collision and after collision. I can not find an answer on google.
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Lagrangian with vanishing conjugate momentum, independent variables
Given a Lagrangian density $\mathcal L(\phi_r,\partial_\mu\phi_r,\phi_n,\partial_\mu\phi_n)$, for which we find out that for some $\phi_n$ its conjugate momentum vanishes:
$$\pi_n=\frac{\partial\...
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Why is mass nonnegative/is the nonnegativity of mass a convention?
In An Introduction to Tensor Calculus and Relativity, Lawden provides the definition of mass by considering a collision between two massive particles $p$ and $q$ with masses $m_p$ and $m_q$, ...
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Weinberg, off the mass shell Feynman diagrams
In section 6.4 of Weinberg QFT, the book says on page 286:
It is important to also consider Feynman diagrams "off the mass shell", for which the external line energies like the energies ...
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Generalized momentum in terms of wavefunction: Is it always $-i\hbar \partial/\partial q$?
I saw this kind of derivation several times in different notes/review/educational articles.
(For example https://arxiv.org/abs/1904.06560 or http://wcchew.ece.illinois.edu/chew/course/QMALL20121005....
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Momenta basis for a quantum system with configuration space $\mathbb{R}\mathrm{P}^2$
Let $\mathcal{X}$ be the configuration space of a (quantum) system.
When $\mathcal{X} = S^1 \simeq \mathrm{SO}(2)$, a momenta basis is $$\{ |\ell\rangle : \ell \in \mathbb{Z} \}.$$
When $\mathcal{X} ...
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Intuitive explanation on why velocity = 0 for a inverted pendulum on a wheel system
I believe I have solved below problem. I am not looking for help on problem-solving per se. I am just looking for an intuitive explanation.
Problem statement: wheel mass = $m_1$, even mass rod BC mass ...
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Why can $\hbar q_x$ and $\hbar q_y$ be replaced by $\hat{p}_x=-i\hbar\frac{\partial}{\partial x}$ and $\hat{p}_y=-i\hbar\frac{\partial}{\partial y}$?
It is written in the book The Physics of Graphene (Page 10 and 17) that when the intervalley scattering is neglected, we can make the following substitution in the Hamiltonian of the graphene when ...
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Momentum Vectors in Bondi coordinates
In the Bondi-Sachs formalism, we can define the notion of 'retarded' time via a coordinate transformation of the usual Minkowski metric
$$
d s^{2}=\eta_{\mu \nu} d x^{\mu} d x^{\nu}=-\left(d x^{0}\...
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