User:Quietly/Chalkboard

the CHALKBOARD

Maxwell's equations:

Name	Differential form	Integral form
Gauss's law:	$\nabla \cdot \mathbf {D} =\rho$	$\oint _{S}\mathbf {D} \cdot d\mathbf {A} =\int _{V}\rho dV$
Gauss' law for magnetism (absence of magnetic monopoles):	$\nabla \cdot \mathbf {B} =0$	$\oint _{S}\mathbf {B} \cdot d\mathbf {A} =0$
Faraday's law of induction:	$\nabla \times \mathbf {E} =-{\frac {\partial \mathbf {B} }{\partial t}}$	$\oint _{C}\mathbf {E} \cdot d\mathbf {l} =-\ {d \over dt}\int _{S}\mathbf {B} \cdot d\mathbf {A}$
Ampère's law (with Maxwell's extension):	$\nabla \times \mathbf {H} =\mathbf {J} +{\frac {\partial \mathbf {D} }{\partial t}}$	$\oint _{C}\mathbf {H} \cdot d\mathbf {l} =\int _{S}\mathbf {J} \cdot d\mathbf {A} +{d \over dt}\int _{S}\mathbf {D} \cdot d\mathbf {A}$

Fermions (half-integer spin)

Fermions have half-integer spin; for all known elementary fermions this is ½. Each fermion has its own distinct antiparticle. Fermions are the basic building blocks of all matter. They are classified according to whether they interact via the colour force or not. According to the Standard Model, there are 12 flavors of elementary fermions: six quarks and six leptons.

• Quarks interact via the color force. Their respective antiparticles are known as antiquarks. Quarks exist in six flavors:

Generation	Name/Flavor		Electric charge (e)	Mass (MeV)	Antiquark
1	Up	(u)	+2/3	1.5 to 4	antiup quark	$({\overline {u}})$
	Down	(d)	−1/3	4 to 8	antidown quark	$({\overline {d}})$
2	Strange	(s)	−1/3	80 to 130	antistrange quark	$({\overline {s}})$
	Charm	(c)	+2/3	1,150 to 1,350	anticharm quark	$({\overline {c}})$
3	Bottom	(b)	−1/3	4,100 to 4,400	antibottom quark	$({\overline {b}})$
	Top	(t)	+2/3	171,400 ± 2,100	antitop quark	$({\overline {t}})$

• Leptons do not interact via the color force. Their respective antiparticles are known as antileptons (although the antiparticle of the electron is called the positron for historical reasons). Leptons also exist in six flavors:

Charged lepton / antiparticle					Neutrino / antineutrino
Name	Symbol	Electric charge (e)	Mass (MeV)		Name	Symbol	Electric charge (e)	Mass (MeV)
Electron / Positron	$e^{-}\,/\,e^{+}$	−1 / +1	0.511		Electron neutrino / Electron antineutrino	$\nu _{e}\,/\,{\overline {\nu }}_{e}$	0	< 0.0000022
Muon	$\mu ^{-}\,/\,\mu ^{+}$	−1 / +1	105.7		Muon neutrino / Muon antineutrino	$\nu _{\mu }\,/\,{\overline {\nu }}_{\mu }$	0	< 0.17
Tau lepton	$\tau ^{-}\,/\,\tau ^{+}$	−1 / +1	1,777		Tau neutrino / Tau antineutrino	$\nu _{\tau }\,/\,{\overline {\nu }}_{\tau }$	0	< 15.5

Note that the neutrino masses are known to be non-zero because of neutrino oscillation, but their masses are sufficiently light that they have not been measured directly as of 2006.

Bosons (integer spin)

Bosons have whole number spins. The fundamental forces of nature are mediated by gauge bosons, and mass is hypothesized to be created by the Higgs boson. According to the Standard Model the elementary bosons are:

Name	Charge (e)	Spin	Mass (GeV)	Force mediated
Photon	0	1	0	Electromagnetism
W±	±1	1	80.4	Weak nuclear
Z0	0	1	91.2	Weak nuclear
Gluon	0	1	0	Strong nuclear
Higgs	0	0	>112	See below

The Higgs boson (spin-0) is predicted by electroweak theory, and is the only Standard Model particle not yet observed. In the Higgs mechanism of the Standard Model, the massive Higgs boson is created by spontaneous symmetry breaking of the Higgs field. The intrinsic masses of the elementary particles (particularly the massive W^± and Z⁰ bosons) would be explained by their interactions with this field. Many physicists expect the Higgs to be discovered at the Large Hadron Collider (LHC) particle accelerator now under construction at CERN.

Polynomials

$a_{1}x^{n}+a_{2}x^{n-1}+a_{3}x^{n-2}+...+a_{n-2}x^{2}+a_{n-1}x+a_{n}=0$

Particles

An overview of the various families of elementary and composite particles, and the theories describing their interactions

Side-by-side setup

(See rationalwiki for details.)

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