It is well known that a local, unitary Poincaré-invariant 2D quantum field theory with a global scaling symmetry and a discrete non-negative spectrum of scaling dimensions necessarily has both a left and a right local conformal symmetry. In this Letter, we consider a chiral situation beginning with only a left global scaling symmetry and do not assume Lorentz invariance. We find that a left con...

We propose a solution to the problem of compatibility of Bose-Fermi statistics with symmetry transformations implemented by compact quantum groups of Drinfel’d type. We use unitary transformations to conjugate multiparticle symmetry postulates, so as to obtain a twisted realization of the symmetric groups Sn. *A. v. Humboldt-fellow e-mail: Fiore, Schupp @ ls-wess.physik.uni-muenchen.de

Particle systems admit a variety of tensor product structures (TPSs) depending on the algebra of observables chosen for analysis. Global symmetry transformations and dynamical transformations may be resolved into local unitary operators with respect to certain TPSs and not with respect to others. Symmetry-invariant and dynamical-invariant TPSs are defined and various notions of entanglement are...

The theory of corepresentations of non-unitary groups G = G + a0G, where G denotes a unitary group and a0 is an antiunitary element, was formulated by Wigner [26], to whom belong the first applications of corepresentations in quantum mechanics. Space groups with antiunitary operations and their corepresentations subsequently found important applications in solid state physics. Lie groups with a...

We construct a class of multipartite states possessing rotational SO(3) symmetry – these are states of K spin-jA particles and K spin-jB particles. The construction of symmetric states follows our two recent papers devoted to unitary and orthogonal multipartite symmetry. We study basic properties of multipartite SO(3) symmetric states: separability criteria and multi-PPT conditions.

The Lieb-Schultz-Mattis theorem and its higher-dimensional generalizations by Oshikawa and Hastings require that translationally invariant 2D spin systems with a half-integer spin per unit cell must either have a continuum of low energy excitations, spontaneously break some symmetries, or exhibit topological order with anyonic excitations. We establish a connection between these constraints and...

We discuss the differing definitions of complex and quaternionic projective group representations employed by us and by Emch. The definition of Emch (termed here a strong projective representation) is too restrictive to accommodate quaternionic Hilbert space embeddings of complex projective representations. Our definition (termed here a weak projective representation) encompasses such embedding...