A bstract We determine the unitary and anti-unitary Lagrangian quantum symmetries of arbitrary abelian Chern-Simons theories. The depend sensitively on arithmetic properties (e.g. prime factorization) matrix levels, revealing interesting connections with number theory. give a complete characterization topological field theories along way find many that are non-trivially time-reversal invariant ...

We show that a quantum system possessing an exact antilinear symmetry, in particular PT -symmetry, is equivalent to a quantum system having a Hermitian Hamiltonian. We construct the unitary operator relating an arbitrary non-Hermitian Hamiltonian with exact PT -symmetry to a Hermitian Hamiltonian. We apply our general results to PT symmetry in finite-dimensions and give the explicit form of the...

The duality symmetries of WZW and coset models are discussed. The exact underlying symmetry responsible for semiclassical duality is identified with the symmetry under affine Weyl transformations. This identification unifies the treatement of duality symmetries and shows that in the compact and unitary case they are exact symmetries of string theory to all orders in α′ and in the string couplin...

We investigate representations of the conformal group that describe “massless” particles in the interior and at the boundary of anti-de Sitter space. It turns out that massless gauge excitations in anti-de Sitter are gauge “current” operators at the boundary. Conversely, massless excitations at the boundary are topological singletons in the interior. These representations lie at the threshold o...

We show that dynamical symmetry methods can be applied to Hamiltonians with periodic potentials. We construct dynamical symmetry Hamiltonians for the Scarf potential and its extensions using representations of su(1, 1) and so(2, 2). Energy bands and gaps are readily understood in terms of representation theory. We compute the transfer matrices and dispersion relations for these systems, and fin...

The general theme of these lectures is the use of the tools of string theory, in particular D-branes [1] and holography [2], to study chiral symmetry breaking in the strong interactions. Recall that QCD with Nf falvors of massless quarks with left and right-handed components qL, qR has a symmetry group U(Nf )L × U(Nf)R which acts as independent unitary rotations of qL, qR. We know from the iden...

the unitary cayley graph xn has vertex set zn = {0, 1,…, n-1} and vertices u and v areadjacent, if gcd(uv, n) = 1. in [a. ilić, the energy of unitary cayley graphs, linear algebraappl. 431 (2009) 1881–1889], the energy of unitary cayley graphs is computed. in this paperthe wiener and hyperwiener index of xn is computed.

Recent developments in the index theory of discrete-time quantum walks allow us to assign a certain well-defined supersymmetric unitary time evolution U and $$\mathbb {Z}_2$$ -grading operator $$\varGamma $$ satisfying chiral symmetry condition, $$U^* = \varGamma .$$ In present article, we extend this encompass non-unitary evolutions U. The existing literature for assumes that is essentially ga...