Ferromagnetic ordering of linearly coordinated Co ions in LiSr2_2[CoN2_2]

LiSr$_2$[CoN$_2$] single crystals were successfully grown out of Li-rich flux. Temperature- and field-dependent measurements of the magnetization in the range of $T = 2 - 300$ K and up to $\mu_{0}\textit{H} = 7$ T as well as measurements of the heat capacity are presented. Ferromagnetic ordering emerges below $T_C = 44$ K and comparatively large coercivity fields of $\mu_0H = 0.3$ T as well as pronounced anisotropy are observed upon cooling. Polycrystalline samples of the Ca analog LiCa$_2$[CoN$_2$] were obtained and investigated in a similar way. In both compounds Co manifests orbital contributions to the magnetic moment and large single-ion anisotropy that is caused by second-order Spin-orbit coupling. Quantum chemistry calculations reveal a magnetic anisotropy energy of 7 meV, twice as large as the values reported for similar Co $d^{8}$ systems.Comment: 21 pages, 6 figures, 5 table

From 'nothing' to inflation and back again

A procedure for solving Wheeler-DeWitt equation in Euclidean region, following step by step the construction of tunneling wave function in nonrelativistic quantum mechanics by Banks, Bender and Wu, is proposed. Solutions for a universe satisfying no-boundary condition and a universe created from 'nothing' are compared to the corresponding solutions for a particle in a two-dimensional potential well, and effects of indefiniteness of metric and zero energy in Wheeler-DeWitt equation are discussed.Comment: 8 pages, presented at the conference Relativity and Gravitation, 100 years after Einstein in Prague (Prague 2012

Effective relational dynamics

We provide a synopsis of an effective approach to the problem of time in the semiclassical regime. The essential features of this new approach to evaluating relational quantum dynamics in constrained systems are illustrated by means of a simple toy model.Comment: 4 pages, based on a talk given at Loops '11 in Madrid, to appear in Journal of Physics: Conference Series (JPCS

Effective approach to the problem of time: general features and examples

The effective approach to quantum dynamics allows a reformulation of the Dirac quantization procedure for constrained systems in terms of an infinite-dimensional constrained system of classical type. For semiclassical approximations, the quantum constrained system can be truncated to finite size and solved by the reduced phase space or gauge-fixing methods. In particular, the classical feasibility of local internal times is directly generalized to quantum systems, overcoming the main difficulties associated with the general problem of time in the semiclassical realm. The key features of local internal times and the procedure of patching global solutions using overlapping intervals of local internal times are described and illustrated by two quantum mechanical examples. Relational evolution in a given choice of internal time is most conveniently described and interpreted in a corresponding choice of gauge at the effective level and changing the internal clock is, therefore, essentially achieved by a gauge transformation. This article complements the conceptual discussion in arXiv:1009.5953.Comment: 42 pages, 9 figures; v2: streamlined discussions, more compact manuscrip

On Exceptional Vertex Operator (Super) Algebras

We consider exceptional vertex operator algebras and vertex operator superalgebras with the property that particular Casimir vectors constructed from the primary vectors of lowest conformal weight are Virasoro descendents of the vacuum. We show that the genus one partition function and characters for simple ordinary modules must satisfy modular linear differential equations. We show the rationality of the central charge and module lowest weights, modularity of solutions, the dimension of each graded space is a rational function of the central charge and that the lowest weight primaries generate the algebra. We also discuss conditions on the reducibility of the lowest weight primary vectors as a module for the automorphism group. Finally we analyse solutions for exceptional vertex operator algebras with primary vectors of lowest weight up to 9 and for vertex operator superalgebras with primary vectors of lowest weight up to 17/2. Most solutions can be identified with simple ordinary modules for known algebras but there are also four conjectured algebras generated by weight two primaries and three conjectured extremal vertex operator algebras generated by primaries of weight 3, 4 and 6 respectively.Comment: 37 page

Equivalence of Approaches to Relational Quantum Dynamics in Relativistic Settings

We have previously shown that three approaches to relational quantum dynamics—relational Dirac observables, the Page-Wootters formalism and quantum deparametrizations—are equivalent. Here we show that this “trinity” of relational quantum dynamics holds in relativistic settings per frequency superselection sector. Time according to a clock subsystem is defined via a positive operator-valued measure (POVM) that is covariant with respect to the group generated by its (quadratic) Hamiltonian. This differs from the usual choice of a self-adjoint clock observable conjugate to the clock momentum. It also resolves Kuchař's criticism that the Page-Wootters formalism yields incorrect localization probabilities for the relativistic particle when conditioning on a Minkowski time operator. We show that conditioning instead on the covariant clock POVM results in a Newton-Wigner type localization probability commonly used in relativistic quantum mechanics. By establishing the equivalence mentioned above, we also assign a consistent conditional-probability interpretation to relational observables and deparametrizations. Finally, we expand a recent method of changing temporal reference frames, and show how to transform states and observables frequency-sector-wise. We use this method to discuss an indirect clock self-reference effect and explore the state and temporal frame-dependence of the task of comparing and synchronizing different quantum clocks

(Broken) Gauge Symmetries and Constraints in Regge Calculus

We will examine the issue of diffeomorphism symmetry in simplicial models of (quantum) gravity, in particular for Regge calculus. We find that for a solution with curvature there do not exist exact gauge symmetries on the discrete level. Furthermore we derive a canonical formulation that exactly matches the dynamics and hence symmetries of the covariant picture. In this canonical formulation broken symmetries lead to the replacements of constraints by so--called pseudo constraints. These considerations should be taken into account in attempts to connect spin foam models, based on the Regge action, with canonical loop quantum gravity, which aims at implementing proper constraints. We will argue that the long standing problem of finding a consistent constraint algebra for discretized gravity theories is equivalent to the problem of finding an action with exact diffeomorphism symmetries. Finally we will analyze different limits in which the pseudo constraints might turn into proper constraints. This could be helpful to infer alternative discretization schemes in which the symmetries are not broken.Comment: 32 pages, 15 figure