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For the leptons, the gauge group can be written SU(2) l × U(1) L × U(1) R. The two U(1) factors can be combined into U(1) Y × U(1) l, where l is the lepton number. Gauging of the lepton number is ruled out by experiment, leaving only the possible gauge group SU(2) L × U(1) Y. A similar argument in the quark sector also gives the same result ...
Y W is the weak hypercharge – the generator of the U(1) group, W → μ is the 3-component SU(2) gauge field, L are the Pauli matrices – infinitesimal generators of the SU(2) group – with subscript L to indicate that they only act on left-chiral fermions, g' and g are the U(1) and SU(2) coupling constants respectively,
Rotation formalisms are focused on proper (orientation-preserving) motions of the Euclidean space with one fixed point, that a rotation refers to.Although physical motions with a fixed point are an important case (such as ones described in the center-of-mass frame, or motions of a joint), this approach creates a knowledge about all motions.
The Tusi couple (also known as Tusi's mechanism [1] [2] [3]) is a mathematical device in which a small circle rotates inside a larger circle twice the diameter of the smaller circle. Rotations of the circles cause a point on the circumference of the smaller circle to oscillate back and forth in linear motion along a diameter of the larger circle.
The space R 3 is endowed with a scalar product , . Time is a scalar which is the same in all space E 3 and is denoted as t. The ordered set { t} is called a time axis. Motion (also path or trajectory) is a function r : Δ → R 3 that maps a point in the interval Δ from the time axis to a position (radius vector) in R 3.
Linear motion, also called rectilinear motion, [1] is one-dimensional motion along a straight line, and can therefore be described mathematically using only one spatial dimension. The linear motion can be of two types: uniform linear motion , with constant velocity (zero acceleration ); and non-uniform linear motion , with variable velocity ...
Therefore, the unit metre per second squared is equivalent to newton per kilogram, N·kg −1, or N/kg. [2] Thus, the Earth's gravitational field (near ground level) can be quoted as 9.8 metres per second squared, or the equivalent 9.8 N/kg. Acceleration can be measured in ratios to gravity, such as g-force, and peak ground acceleration in ...
A delta system arrangement provides only one voltage, but it has a greater redundancy as it may continue to operate normally with one of the three supply windings offline, albeit at 57.7% of total capacity. [1] Harmonic current in the neutral may become very large if nonlinear loads are connected.