On the particle level of Galilean Quantum field theories

G. Puccini, H. Vucetich

Antonio Díaz Miranda

Steven Corley, Oscar Wallace Greenberg

We consider the nonrelativistic quantum mechanics of a model of two spinless fermions interacting via a two-body potential. We introduce quantum fields associated with the two particles as well as the expansion of these fields in asymptotic “in” and “out” fields, including such fields for bound states, in principle. We limit our explicit discussion to a two-body bound state. In this context we discuss the implications of the Galilean invariance of the model and, in particular, show how to include bound states in a strictly Galilean-invariant quantum field theory.

L. Lanz, Luigi A. Lugiato, G. Ramella +1 more

Meinard Kuhlmann, Manfred Stöckler

Masanori Kobayashi, M. de Montigny, F. C. Khanna

We define Galilean invariant delta functions by using the Takahashi formulation, which describes particles with arbitrary spin. The direct calculation of the Galilean invariant delta functions in the (N+1)-dimensional Galilean covariant extended manifolds reveals that, for N odd, there exists a surface on which these delta functions vanish. This feature corresponds to the spacelike separation in the relativistic quantum field theory, and it enables us to discuss a connection between spin and statistics in the Galilean covariant theories. These results show that a spin-statistics connection holds for even-dimensional Galilean covariant extended manifolds; that is, for N-dimensional space-times with odd N≥5. Likewise, we observe that there is no such connection for odd-dimensional Galilean covariant extended manifolds; that is, for N-dimensional space-times with even N≥4. Thus, our results support the claim that there is no connection between spin and statistics in the usual nonrelativistic theory, for which N=4.