- #1
ndung200790
- 519
- 0
In &5.6 writes:
"An (A,A) field (A is spin) contains terms with only integer spins 2A,2A-1,...,0, and corresponds to a traceless symmetric tensor of rank 2A.(Note that the number of independent components of a symmetric tensor of rank 2A in four(space-time) dimensions is:
{4.5...(4+2A-1)}/(2A)!=(3+2A)!/6(2A)!
and the tracelessness condition reduces this to:
{(3+2A)!/6(2A)!}-{(1+2A)!/6(2A-2)!}=(2A+1)^2
as expected for an (A,A) field"
I can not derive the number of components of a tensor of rank 2A in four dimensions is
4.5...(4+2A-1) and the number of tracelessnes conditions is (1+2A)!/6(2A-2)!
"An (A,A) field (A is spin) contains terms with only integer spins 2A,2A-1,...,0, and corresponds to a traceless symmetric tensor of rank 2A.(Note that the number of independent components of a symmetric tensor of rank 2A in four(space-time) dimensions is:
{4.5...(4+2A-1)}/(2A)!=(3+2A)!/6(2A)!
and the tracelessness condition reduces this to:
{(3+2A)!/6(2A)!}-{(1+2A)!/6(2A-2)!}=(2A+1)^2
as expected for an (A,A) field"
I can not derive the number of components of a tensor of rank 2A in four dimensions is
4.5...(4+2A-1) and the number of tracelessnes conditions is (1+2A)!/6(2A-2)!