infinite-dimensional

In the case of an irreducible representation of the space-time symmetry group, the orbit of a single state takes one through a sufficient number of orthogonal states to span the entire infinite-dimensional state space.

Archive 2009-02-01 Gordon McCabe 2009

Unfortunately, Wigner's irreducible representations are representations upon infinite-dimensional Hilbert spaces, whilst the Poincare group has only 10 dimensions.

Archive 2009-02-01 Gordon McCabe 2009

As for the amount of information, well, the Hilbert space that describes quantum mechanics is an infinite-dimensional space.

Quantum Diavlog Sean 2008

Free particles live in an infinite-dimensional space, and the usual basis for this space is plane waves.

Everything You Ever Wanted to Know About Quantum Mechanics, But Were Afraid to Ask Sean 2008

So, at the very least, the Hilbert space (under these assumptions) must be infinite-dimensional.

What if Time Really Exists? Sean 2008

The first is that the modal interpretation, as stated thus far, was never in a position to deal with quantum mechanics in infinite-dimensional Hilbert spaces.

Modal Interpretations of Quantum Mechanics Dickson, Michael 2007

(Their results are not all applicable to the infinite-dimensional case, however).

Modal Interpretations of Quantum Mechanics Dickson, Michael 2007

States of physical systems are associated with normalized vectors in a Hilbert space, a complex, infinite-dimensional, complete and separable linear vector space equipped with a scalar product.

Collapse Theories Ghirardi, Giancarlo 2007

It would seem at first sight that a lattice formulation could never reproduce this, since in finite volume (e.g. on the 4-torus) the space of lattice spinor fields is finite-dimensional but to have a non-trivial index theory the operators generally must be acting on an infinite-dimensional vectorspace.

String Theory is Losing the Public Debate Sean 2007

Even standard non-relativistic quantum theory occurs in the arena of infinite-dimensional Hilbert spaces, not to mention quantum field theory.

Modal Interpretations of Quantum Mechanics Dickson, Michael 2007