A Euclidean formulation of QFT incorporating finite rotations

A

bstract

We formulate thermal quantum field theory on a finite spatial periodic volume incorporating finite rotations. Traditional compactifications at finite temperature without rotations typically involve

as the space-time manifold within a path integral formulation and also moving frames can be accommodated by shifted boundary conditions on the same space. We show that consistent descriptions of certain finite rotations are possible on space-time manifolds with topology different from

$$ {\mathbbm{T}}^4 $$ T 4

but still flat and without boundary and we classify all possible geometries. The non-trivial topology may be implemented by rotated boundary conditions allowing for a path integral formulation. The purely imaginary angular velocity in temperature units cannot be arbitrary but several discrete values are possible. We also discuss finite volume effects in detail.