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In mathematics and physics, the plate trick, also known as Dirac's string trick (after Paul Dirac, who introduced and popularized it), [1] [2] the belt trick, or the Balinese cup trick (it appears in the Balinese candle dance), is any of several demonstrations of the idea that rotating an object with strings attached to it by 360 degrees does not return the system to its original state, while ...
A unit with spin number n is called an n-unit and has angular momentum nħ/2, where ħ is the reduced Planck constant. For bosons, such as photons and gluons, n is an even number. For fermions, such as electrons and quarks, n is odd. Given any closed spin network, a non-negative integer can be calculated which is called the norm of the
Here, 1 / 2 σ μν and F μν stand for the Lorentz group generators in the Dirac space, and the electromagnetic tensor respectively, while A μ is the electromagnetic four-potential. An example for such a particle [9] is the spin 1 / 2 companion to spin 3 / 2 in the D (½,1) ⊕ D (1,½) representation space of the ...
The sum over r covers other degrees of freedom specific for the field, such as polarization or spin; it usually comes out as a sum from 1 to 2 or from 1 to 3. E p is the relativistic energy for a momentum p quantum of the field, = m 2 c 4 + c 2 p 2 {\textstyle ={\sqrt {m^{2}c^{4}+c^{2}\mathbf {p} ^{2}}}} when the rest mass is m .
In mathematical physics, the Dirac algebra is the Clifford algebra, ().This was introduced by the mathematical physicist P. A. M. Dirac in 1928 in developing the Dirac equation for spin- 1 / 2 particles with a matrix representation of the gamma matrices, which represent the generators of the algebra.
There are two kinds of heterotic strings differing in their ten-dimensional gauge groups: the heterotic E 8 ×E 8 string and the heterotic SO(32) string. (The name heterotic SO(32) is slightly inaccurate since among the SO(32) Lie groups , string theory singles out a quotient Spin(32)/Z 2 that is not equivalent to SO(32).)
Using the Dirac adjoint, the probability four-current J for a spin-1/2 particle field can be written as J μ = c ψ ¯ γ μ ψ {\displaystyle J^{\mu }=c{\bar {\psi }}\gamma ^{\mu }\psi } where c is the speed of light and the components of J represent the probability density ρ and the probability 3-current j :
The extension to 2n + 1 (n integer) gamma matrices, is found by placing two gamma-5s after (say) the 2n-th gamma-matrix in the trace, commuting one out to the right (giving a minus sign) and commuting the other gamma-5 2n steps out to the left [with sign change (-1)^2n = 1].
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