Color charge

The color charge is a fundamental property of quarks, which causes them to experience the strong force (a.k.a. color force). There are 3 types of color charge: red ($$R$$), green ($$G$$) and blue ($$B$$).

Color charge can be represented by the Greek letter $$\chi$$, because it is the first letter of the Greek work chroma meaning 'color'. Color charge can be written as follows:


 * $$\chi = 3R + 5G + 2B$$

Therefore addition and subtraction can be easily performed on color charge. Multiplication by integers is also easy. Please note, however, that the multiple of each color component must be an integer.

The square of each color component is one:


 * $$R^2 = G^2 = B^2 = 1$$

However, the color components themselves are not equal to each other:


 * $$R \neq G \neq B$$

Finally, they all add up to 0:


 * $$R + G + B = 0$$

You can also take the absolute value of color charge. This is done as follows:


 * $$|\chi| = \sqrt{\chi_{R}^{2} + \chi_{G}^{2} + \chi_{B}^{2}}$$

An important operation on color charge is multiplication, e.g. in explaining the strong force. This can be easily done:


 * $$\chi_1 \chi_2 = r_1 r_2 + r_1 g_2 + r_1 b_2 + g_1 r_2 + g_1 g_2 + g_1 b_2 + b_1 r_2 + b_1 g_2 + b_1 b_2$$