50 research outputs found
New order parameters in the Potts model on a Cayley tree
For the state Potts model new order parameters projecting on a group of
spins instead of a single spin are introduced. On a Cayley tree this allows the
physical interpretation of the Potts model at noninteger values q of the number
of states. The model can be solved recursively. This recursion exhibits chaotic
behaviour changing qualitatively at critical values of . Using an
additional order parameter belonging to a group of zero extrapolated size the
additional ordering is related to a percolation problem. This percolation
distinguishes different phases and explains the critical indices of percolation
class occuring at the Peierls temperature.Comment: 16 pages TeX, 5 figures PostScrip
Random Tilings: Concepts and Examples
We introduce a concept for random tilings which, comprising the conventional
one, is also applicable to tiling ensembles without height representation. In
particular, we focus on the random tiling entropy as a function of the tile
densities. In this context, and under rather mild assumptions, we prove a
generalization of the first random tiling hypothesis which connects the maximum
of the entropy with the symmetry of the ensemble. Explicit examples are
obtained through the re-interpretation of several exactly solvable models. This
also leads to a counterexample to the analogue of the second random tiling
hypothesis about the form of the entropy function near its maximum.Comment: 32 pages, 42 eps-figures, Latex2e updated version, minor grammatical
change
Spectral action for torsion with and without boundaries
We derive a commutative spectral triple and study the spectral action for a
rather general geometric setting which includes the (skew-symmetric) torsion
and the chiral bag conditions on the boundary. The spectral action splits into
bulk and boundary parts. In the bulk, we clarify certain issues of the previous
calculations, show that many terms in fact cancel out, and demonstrate that
this cancellation is a result of the chiral symmetry of spectral action. On the
boundary, we calculate several leading terms in the expansion of spectral
action in four dimensions for vanishing chiral parameter of the
boundary conditions, and show that is a critical point of the action
in any dimension and at all orders of the expansion.Comment: 16 pages, references adde
Translational invariance of the Einstein-Cartan action in any dimension
We demonstrate that from the first order formulation of the Einstein-Cartan
action it is possible to derive the basic differential identity that leads to
translational invariance of the action in the tangent space. The
transformations of fields is written explicitly for both the first and second
order formulations and the group properties of transformations are studied.
This, combined with the preliminary results from the Hamiltonian formulation
(arXiv:0907.1553 [gr-qc]), allows us to conclude that without any modification,
the Einstein-Cartan action in any dimension higher than two possesses not only
rotational invariance but also a form of \textit{translational invariance in
the tangent space}. We argue that \textit{not} only a complete Hamiltonian
analysis can unambiguously give an answer to the question of what a gauge
symmetry is, but also the pure Lagrangian methods allow us to find the same
gauge symmetry from the \textit{basic} differential identities.Comment: 25 pages, new Section on group properties of transformations is
added, references are added. This version will appear in General Relativity
and Gravitatio
Hamiltonian formulation of tetrad gravity: three dimensional case
The Hamiltonian formulation of the tetrad gravity in any dimension higher
than two, using its first order form when tetrads and spin connections are
treated as independent variables, is discussed and the complete solution of the
three dimensional case is given. For the first time, applying the methods of
constrained dynamics, the Hamiltonian and constraints are explicitly derived
and the algebra of the Poisson brackets among all constraints is calculated.
The algebra of the Poisson brackets among first class secondary constraints
locally coincides with Lie algebra of the ISO(2,1) Poincare group. All the
first class constraints of this formulation, according to the Dirac conjecture
and using the Castellani procedure, allow us to unambiguously derive the
generator of gauge transformations and find the gauge transformations of the
tetrads and spin connections which turn out to be the same found by Witten
without recourse to the Hamiltonian methods [\textit{Nucl. Phys. B 311 (1988)
46}]. The gauge symmetry of the tetrad gravity generated by Lie algebra of
constraints is compared with another invariance, diffeomorphism. Some
conclusions about the Hamiltonian formulation in higher dimensions are briefly
discussed; in particular, that diffeomorphism invariance is \textit{not
derivable} as a \textit{gauge symmetry} from the Hamiltonian formulation of
tetrad gravity in any dimension when tetrads and spin connections are used as
independent variables.Comment: 31 pages, minor corrections, references are added, to appear in
Gravitation & Cosmolog
Poincare gauge invariance and gravitation in Minkowski spacetime
A formulation of Poincare symmetry as an inner symmetry of field theories
defined on a fixed Minkowski spacetime is given. Local P gauge transformations
and the corresponding covariant derivative with P gauge fields are introduced.
The renormalization properties of scalar, spinor and vector fields in P gauge
field backgrounds are determined. A minimal gauge field dynamics consistent
with the renormalization constraints is given.Comment: 36 pages, latex-fil
Energy Management of People in Organizations: A Review and Research Agenda
Although energy is a concept that is implied in many motivational theories, is hardly ever explicitly mentioned or researched. The current article first relates theories and research findings that were thus far not explicitly related to energy. We describe theories such as flow, subjective well-being, engagement and burn-out, and make the link with energy more explicit. Also, we make a first link between personality characteristics and energy, and describe the role of leadership in unleashing followers’ energy. Following, we identify how the topic of energy management can be profitably incorporated in research from a scientific as well as a practitioner viewpoint. Finally, we describe several interventions to enhance energy in individuals and organizations
Minimal coupling of electromagnetic field in Riemann-Cartan spacetime for perfect fluids
We minimally couple the electromagnetic field to gravity in Riemann-Cartan spacetime in the self-consistent formalism for perfect fluids by treating the internal energy of matter as a function of the electromagnetic field. The overall Lagrangian of the gravitational field, perfect fluid, and the electromagnetic field is constrained to be gauge invariant under gauge transformations of the vector potential. The theory preserves both charge conservation and particle number conservation, and gives the usual form of the free field equations.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/44578/1/10773_2004_Article_BF00673926.pd