# Tag Info

11

It's c for constant or celeritas, which means speed in Latin. Everyone uses it because it's convention. You could use $\xi$ or $\zeta$ or $\gamma$ or any other symbol you wanted, but then you'd have to explain what it meant, and people would have to go through the trouble to remember this every time they read your papers. Better to go with convention and ...

10

The no-go results from Algebraic and Constructive QFT you mention deal with related but slightly different matters. (Edit: the previous version of the following paragraph was slightly misleading - Haag's theorem is actually stronger than I stated before; see below for details) Haag's theorem (which actually slightly predates the inception of Algebraic ...

10

Indeed most examples of unambiguously labeling chiral states fall back on having another pre-labeled chiral object on hand. For a long time it seemed as though "left" and "right" were entirely interchangeable labels. This symmetry is known as parity. However it turns out there is a way to distinguish left from right in a fundamental way; parity is not ...

10

A particle is said to be on-shell if it satisfies the relativistic dispersion relation, $$E^2 = p^2 +m^2$$ in units wherein $c=\hbar=1$. If you graph it, you obtain a parabolic surface for massive particles, and a cone for massless particles, like a photon. This is known as the mass shell, it is quite literally a shell or surface. The momentum of a real ...

9

I say "ee-vee per see-squared" or "ee-vee over see-squared." If it's convenient to assume $c=1$, I'll say "ee-vee" or "electron volts." I can't remember ever having said "electron volts over see-squared." For MeV and GeV I'll say "em ee vee" or "gee ee vee." I know people who say "mev" or "jev", to rhyme with the first syllable of "Beverley", but in ...

7

People have essentially explained the details, but let me make an attempt to formulate it in a language more familiar to a mathematician. I will ignore subtleties that enter for more general Lie superalgebras. Let $\mathfrak g$ be a Lie superalgebra with the $\mathbb Z_2$ grading $\mathfrak g = \mathfrak g_e\oplus\mathfrak g_o$, where the two factors are ...

7

Lenses and glass bottles are transparent. As you quoted above, the different has to do with diffusion. Here is an example of an image through a transparent object: Here is an example of a translucent object: This is an example of how diffusion causes translucency: As light passes through a translucent object, it either enters or exists a rough ...

7

Such an ordering arises from the fact that they are arranged chronologically, i.e., according to the dates they were "discovered". The principle quantum number $n$ entered the picture with Bohr's theory of the Hydrogen atom in 1913.Bohr introduced $n$ in his quantization of angular momentum postulate where $n$ is the allowed orbit. Mathematically, $L = ... 7 The "shift in the meaning" refers to some attempts to reinterpret the terminology that were made by a metrological document, ISO 5725, in 2008. That may be described as a bureaucratic effort by a few officials – really bureaucrats of a sort – and as far as I know, the "shift in the meaning" hasn't penetrated to the community of professionals. The people ... 6 The quadrature is a process – any process – of turning something into a "square". "Quadro" in Latin is "make square", "quadrus" is a "square". It comes from "quattors", four, because that's the number of vertices of a square. So integration of a function is also known as "quadrature" because we are calculating the area i.e. looking for a well-known area ... 6 "They" are probably talking about symplectic integrators. Most numerical integrators for (partial) differential equations do not specifically consider the energy of the system; they are generic integrators capable of solving any set of DEs, and not all DE's have a concept like "energy". When these are applied to a classical dynamics problem concerning ... 6 Your question is kind of vague but I will try to respond. Acceleration is defined as the time rate of change of velocity. Since velocity has both magnitude and direction, so does acceleration. In other words, acceleration is a vector. The length of the vector is its magnitude. Its direction is the direction of the vector. So the magnitude of ... 6 The more common names for what you are talking about are the abbreviated action $$S_0[q] := \int p \mathrm{d}q$$ versus the action $$S[q] := \int_{t_1}^{t_2}L(q,\dot q,t)\mathrm{d}t$$ Both are used in different formulations of classical mechanics, and deliver a different "flavor" of solutions. On both one can do variations calculus and obtains the ... 6 A 'moment' is quite a general term, and its use ranges from electrostatics (e.g. dipole and other multipole moments) to mechanics (moment of force but also moment of inertia) to huge stretches of statistics. The general intuition is that you have some amount of 'stuff' (charge, force, mass, probability) with some distribution function$s(x)$, and the various ... 6 The term 'equation of motion' is somewhat subjective as it depends on the context, but for any given context there is usually one single equation, or set of equations, which can be described as an equation of motion. These are typically differential equations in time, usually of second order, and for simple objects in Newtonian mechanics they do not involve ... 6$mr^2\dot\theta$is the angular momentum, which is conserved. The quantity$r^2\dot\theta$is conserved if$m$is independent of time, but it doesn't have a name that I know of. 6 Microscopically, i.e. in the quantum theory the scattering with radiation is a collision of particles with photons such as $$e^- + \gamma \to e^- + \gamma$$ The momentum vectors of the particles above are $$\vec p_1+\vec p_2= \vec p_3 + \vec p_4$$ where the identity holds due to momentum conservation. But in general$\vec p_1\neq \vec p_3$and$\vec ...

5

I know we've had this discussion on the Astronomy SE site, but let me try to elaborate on my answer. Dark matter is an altogether different component of the universe from baryonic matter. It does cause the same overall dynamics when it comes to the universe as a whole. What I mean by this is that the hubble parameter: $$H(a) = H_0 ... 5 In signal processing, the Nyquist–Shannon sampling theorem says you need at least 2 samples of a frequency to be able to perfectly reconstruct it. So in your question, a sampling rate of 200\: \mathrm{MHz} means you can perfectly reconstruct frequencies in the range of 0 - 100\: \mathrm{MHz}. So what happens when frequencies above 100\: \mathrm{MHz} ... 5 See this article on the history of phase space. Assuming the article is to be trusted, Boltzmann noted that in a 2-D system the trajectories looked like Lissajous figures, and the shape of the Lissajous figure is determined by the relative phase of the two input signals. He then used the work phase to refer to that part of the configuration that was ... 4 Some examples come to my mind: Fourier's law of heat conduction \vec{J} = -c\vec{\nabla}T in crystalline solids is a good example of a phenomenological law. It is an ampirical law easy to verify in a broad range of materials in various phases and yet, as explained in this presentation, there is no derivation of it from first principles in solids and ... 4 You have pinpointed an important nuance of quantum information theory. A perfectly entangled state is, in some sense, like a single bit in a one time pad: just two copies of a shared random bit. In fact, the teleportation protocol is perfectly analogous — not the same, but certainly analogous — to transmitting a message securely using a one-time ... 4 The neutral current is electrically neutral. To see why, one must first understand what the current is. It is a composite field or (in the quantum theory) an operator, something like$$ J^{\mathrm{(NC)}\mu}(f) = \bar{u}_{f}\gamma^{\mu}\frac{1}{2}\left(g^{f}_{V}-g^{f}_{A}\gamma^{5}\right)u_{f}, $$where u_f is the Dirac field for the fermion f. Note that ... 4 "Coupling" is just a particle physicist's (but also a rather generic other physicist's) favorite word for an "interaction". In a theory given by a Lagrangian, degrees of freedom (e.g. fields but not necessarily fields) f,g are coupled if there exist terms in the Lagrangian that depend both on f and g, typically (in field theory) on their product or a ... 4 This is called entanglement, the 'spooky' action-at-a-distance phenomenon. 4 The doppler shift causes a shift in wavelength at the origin of the wave (the frequency of the source never changes). This results in a shift in frequency for the observer. In the link below you can see the emission of the wave for a moving source causes the wavelength to be shorter in front and longer behind. The actual source isn't changing in ... 4 It started with conservation of quantum numbers, from baryon number when we did not know about quarks, to lepton number, when we discovered the positron.For the neutrino momentum and energy conservation played a role too, since it is only seen as a missing mass. In time the symmetries in the assignments of the quantum numbers became more and more evident ... 4 "Equilibrium" means thermal equilibrium. The solid has one well defined temperature, and a constant Fermi energy. The Fermi energy is an energy value against which energy levels are compared to determine how fully occupied (or not) an energy level is. Generally when the Fermi level is constant throughout a solid electrons diffuse equally in all ... 4 Refs. 1 and 2 define a canonical transformation (CT)$$\tag{1} (q^i,p_i)~\longrightarrow~ (Q^i,P_i)$$[together with choices of Hamiltonian H(q,p,t) and Kamiltonian K(Q,P,t)] as satisfying$$ \tag{2} (p_i\mathrm{d}q^i-H\mathrm{d}t)-(P_i\mathrm{d}Q^i -K\mathrm{d}t) ~=~\mathrm{d}F$$for some generating function F. On the other hand, Wikipedia (March ... 4 The term "shell" originally derives from the non-relativistic version of the answer by @JamalS. In a non-relativistic theory, a free particle satisfies the following dispersion relation$$ E = \frac{ {\bf p}^2 }{ 2m } $$For a fixed energy a particle satisfies$$ {\bf p}_x^2 + {\bf p}_y^2 + {\bf p}_z^2 = 2 m E  In momentum space, this is precisely the ...

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