Consider the following equations pmu mualpha deltamubeta pm

Consider the following equations: p^mu = mu^alpha delta^mu_beta p^mu n_muv P^v + m^2 = 0 dp^mu/dt = 0 for a free particle Which of these equations violate Rule 1 about free indices? Write \"OK\" or \"violates\" next to each equation, as appropriate. Consider the following examples of renaming an index: A^alpha_beta A^beta = A\' alpha renamed to A^alpha_beta A^beta = A\'^mu n_mu vA^mu B^v = 0 renamed to n_mumu A^mu B^mu = 0 eng_alpha beta = eng_mu v A^mu_alpha A^v_beta renamed to eng_mu v = eng_alpha beta A^alpha_mu A^beta_v delta^alpha_mu delta^beta_v F^mu v = F^alpha beta renamed to delta^mu_mu delta^v_mu F^mu v = F^mu v Which of these equations violate Rule 2 about renaming indices? Write \"OK\" or \"violates\" next to each equation, as appropriate.

Solution

Rule 1 about free indices is as given below:

\"The indices must be lower case Latin or Greek letters.\"

a) Ok. As, in the given equation all the superscripts (, and ) used are lower case Greek letters.

b) Ok. As, in the given equation all the subscript and superscripts ( and ) are lower case Greek letters.

c) Ok. As, in the given equation the superscripts used is and is lower case Greek letter.

d) Ok. As, in the given equation all the subscript and superscripts (, , and ) used are lower case Greek letters.

e) Ok. As, in the given equation all the subscript and superscripts (, and ) used are lower case Greek letters.