Massive Sa : Yr 03 / M = 0, 1, 2, 3 And . Che . For S=0,1; And * . Consider The Intend Spin Quantum Numbers Of The Following Elementary Particles: S=0: $(X), S=1: An (X) And S=2 % With P = 1, 2, 3, 4 Which Are There Associated Fields Those - Particle States Described By Those Fields Have 2sti Internal States. • This Number Is Equal To The Degre Ees Of

Consider the internal spin quantum numbers of the following elementary particles: S = 0 5= 12: ((x), 5 = = = 4, (x) : with 4= 0,1,2,3 and Those One , massive S=1: A (x) and S = 2 : 4(x) 2: "HP" 1 = 1,2,3,4, which are there associated Fields: 2- particle states described by those Fields have 25+1 internal states. This number equal to the degrees of Freedom N that is associated to the original classical Field. The degrees of freed om N are obtained as follows. N = NF - Nc for S = 0,1,... and N = N - = Nc for s= 1. 1. where No is the # of (Reall constraints on the Field that follow from the Field NF is the # of (Real) Field components The Gamma malvices satisfy the Clifford property: 1a) What is N for a for {4141 = 0, 1, 2, 3} real ((x) Field eq. and 16) What is N for a complex f(x) Field and what is the interpretation of this number in terms of the number of internal states of particles and anti particles with spin S = 0 ? 1C) Now, consider a spiner field 4(x) that has s = and obeyes the Dovic: ie ifth d 4 - my = o , where We left out the Spinor Indices B Prove that every (Complex) Component of 4() solves the KG (2x + m ) 4 = 0 By acting with (ig" do ton) on the Dirac eq. .eq. For this Spino Field eg. 1 d.) Now again calculate the # N using * and also give an interpretation. of this number in terms of particles and antiparticles.