# Tag Info

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Actually there are terminological subtleties when you are talking about that. Particles in the accelerator's tube are gathered in a sequence of little "bunches". For the proton-proton mode there was roughly ~3000 bunches per beam. And each bunch contained roughly $\simeq 10^{11}$ protons. So, at the largest level what you actually have during the ...

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Theoretical physics is the field that develops theories about how nature operates. It is fundamentally physics, in that the ultimate goal is to describe reality. It is informed by experiment, and at the same time it extends the results of experiments, making predictions about what has not been physically tested. This is accomplished using the language of ...

9

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 ...

8

A theory is a collection of concepts, laws, and equations in science that is meant to explain some particular subset of observations. It's also used for theories describing gedanken worlds that differ from ours. There is also a related word "model" that differs by a theory by being really specific while a "theory" may leave some details adjustable, and ...

7

Elementary particles are characterized by quantum numbers, some of them esoteric, which have organized the known particles and resonances into specific multiplets of SU(3) or SU(2). Different interactions conserve different quantum numbers, but the term "annihilation" is reserved for the annihilation of specific quantum numbers. In the case of proton ...

7

If I create an electron on earth and someone else creates an electron on Andromeda, they're identical particles. They have the same quantum numbers, they're both excitations of the electron field. However they're distinguishable by means of their spatial separation. Their wavefunctions don't overlap. Edit: perhaps I should add that not everyone uses the ...

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"Host star", or "host" for short, seems to fit the bill.

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Great question! I don't think there is anything obvious at play here. In quantum mechanics, we assume that that state of any system is a normalized element of a Hilbert space $\mathcal H$. I'm going to limit the discussion to systems characterized by finite-dimensional Hilbert spaces for conceptual and mathematical simplicity. Each observable quantity ...

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 ...

6

INCLUDING AN EXTENSION $\psi_o$ is, as mentioned previously, the normalisation constant which is calculated by doing the integral $\int_V|\psi|^2dV$ and setting its value equal to 1 (hence normalization). This will give you the equation for $\psi_o$. If your interest is to find the probablity amplitude for a particle in a volume V, for example, then you ...

6

[Converted from my comments, as suggested] Mathematical physics and theoretical physics are two very distinct disciplines, as can be checked by browsing a random issue of Communications in Mathematical Physics. Mathematical Physics is bona fide mathematics, but applied to physics questions: the papers have the traditional Lemma/Proposition/Theorem structure ...

6

An ultra-relativistic particle is any particle you observe to have almost all its energy stored in the form of momentum. In other words, we are talking about particles that have only a very tiny fraction of their total energy stored in (rest)mass. The relativistic mass-energy-momentum relationship $$E^2 - c^2 \ p^2 \ = \ c^4 \ m^2$$ is valid for a ...

6

Lasers typically operate in two regimes: as CW or continuous wave (the radiation leaving the laser cavity or resonator continuously by a partially reflecting mirror, or as you put it, forming an uninterrupted wave) or as a laser pulse (the radiation leaving the cavity during a short time at a repetition rate, that is, as a burst of short pulses very separted ...

5

It is a matter of confusing terminology , at the present times when so much differentiation has happened in physics related scientific disciplines. Radiation was a general terminology assigned to transfer of energy radially, to start with with waves: acoustic waves, waves in water. Then came Maxwell's equations and the discovery of electromagnetic waves, ...

5

Mathematical physics is what is done by mathematical physicists, and published in mathematical physics journals. Theoretical physics is what is done by theoretical physicists, and published in physics journals. I believe the actual dividing line between the two fields was delineated largely by the historical development of these fields. Certainly, ...

5

$H$, sometimes called the Hubble "constant" should actually be called properly: the Hubble parameter. It is a function of the scale factor $a(t)$ of the Universe or of the redshift $z=1/a-1$ and depends on the cosmological parameters. It gives the rate of change of the size of the Universe with respect to its size. Through the Friedmann equations it is ...

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: $$H(a) = H_0 ... 5 In signal processing, the Nyquist–Shannon sampling theorem says you need at least 2 samples of a frequency to be able to perfectly reconstruct it. So in your question, a sampling rate of 200\: \mathrm{MHz} means you can perfectly reconstruct frequencies in the range of 0 - 100\: \mathrm{MHz}. So what happens when frequencies above 100\: \mathrm{MHz} ... 4 Refraction: is specifically the redirection/bending of waves caused by things like changes in density, or material. Reflection: when the wave returns from the medium it came from. Scattering: more general, blanket term for any type of change in direction (but not being absorbed). Absorption: the energy of the waves being absorbed by a material they ... 4 If I'm not mistaken, "moose models" are an alternative name for quiver gauge theories. A quiver gauge theory consists of multiple gauge groups, [like U(1) \times U(1) in your example] and "matter" fields charged under multiple gauge groups. For example, quarks in the standard model carry charges under U(1)_{EM}, SU(2)_{Weak} and SU(3)_{Colour}.. That ... 4 To add to what @Qmechanic says, note also that for a representation \rho:\mathfrak g\to \mathfrak{gl}(V) of a Lie algebra \mathfrak g acting on a vector space V, a vector subspace W of V is called an invariant subspace of the representation provided \rho(X)w\in W for all X\in\mathfrak g and w\in W. A representation \rho is said to be ... 4 Well, for starters, time + flat space, as you put it, isn't necessarily curved. The obvious example being Minkowski space, of course. It can be curved though, depending on how you join the two to form a spacetime. For example, flat space can be joined with a time coordinate to form a hyperbolic space with metric$$ds^2 = \frac{-dt^2 + dx^2 + dy^2 ...

4

User twistor59 has addressed the part regarding the "generator" terminology, but let me give a bit more detail on the second part of the question. I'm going to restrict the discussion to matrix Lie groups for simplicity. Some background. Given a Lie group $G$ with Lie algebra $\mathfrak g$, there exist two mappings $\mathrm{Ad}$ and $\mathrm{ad}$, both ...

4

Yes, Newton was definitely using the term "mass". His Principia were written in Latin but the English translation of his Latin definition of gravity said: Every particle of matter in the universe attracts every other particle with a force that is directly proportional to the product of the masses of the particles and inversely proportional to the square ...

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

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

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

"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 ...

3

Galmeida, I think you are thinking of a Jones vector polarization formalism, which works for plane waves in a homogeneous, linear, anisotropic medium (like air, amorphous glass, or vacuum). The reasons they are defined this way are the following Any electric field can classically be decomposed into a superposition of plane waves via a Fourier transform. ...

3

Here is my hypothesis. Consider a hose that is shaped like the diagram below, with two straight sections linked by a section of constant curvature: The thick black arrows indicate the velocity of the flow. The flow in the second straight section has been deflected, so a force must have acted on it. The fluid dynamics of the situation might be complicated ...

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