ISSN:
1089-7658
Source:
AIP Digital Archive
Topics:
Mathematics
,
Physics
Notes:
In the framework of two-particle relativistic quantum mechanics, a Poincaré-invariant scalar product and the corresponding physical Hilbert space of states are constructed. This is achieved by finding a tensor current of rank 2, jμν(x1,x2), satisfying two independent conservation laws, relative to particles 1 and 2, respectively. Then the scalar product is obtained by integrating the current jμν over two three-dimensional spacelike hypersurfaces. The Hermiticity of the Poincaré group generators is ensured by the fact that the kernel of the current jμν is translation invariant and covariant. A simple expression of the scalar product is obtained when one chooses for the two spacelike hypersurfaces two constant parallel hyperplanes. The positivity of the norm is, in general, ensured if the spectrum of the eigenvalues of the total mass squared operator comes out to be positive.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1063/1.527910
