129 research outputs found
SU(2)-invariant reduction of the 3+1 dimensional Ashtekar's gravity
We consider a space-time with spatial sections isomorphic to the group
manifold of SU(2). Triad and connection fluctuations are assumed to be
SU(2)-invariant. Thus, they form a finite dimensional phase space. We perform
non-perturbative path integral quantization of the model. Contarary to previous
claims the path integral measure appeared to be non-singular near
configurations admitting additional Killing vectors. In this model we are able
to calculate the generating functional of Green functions of the reduced phase
space variables exactly.Comment: 12 page
The Role of Psychological Factors in Judo: A Systematic Review
(1) Background: Psychological parameters are relevant in the practice of judo. Previous studies have shown that parameters such as anxiety or motivation can have a negative or positive impact on the athlete\u2019s performance and general well-being, depending on the athlete\u2019s perception. This systematic review aimed to summarize the studies examining the influence of various psychological parameters on well-being and performance in judo athletes; (2) Methods: We followed preferred reporting elements for systematic reviews and meta-analyses. We searched the Web of Science database for studies that explained the role of these parameters in elite athletes. Of the 286 articles initially identified, 17 met our eligibility criteria and were included in the review. In total, we analyzed data from 721 judo athletes; (3) Results: The studies found have demonstrated the impact of various psychological parameters during high-level performance and how these parameters can influence and lead an athlete to win or lose a competition. The feelings of tension, anger, anxiety, and nervousness were significantly increased in athletes who were facing defeat, while a decrease in the same segments and an increase in motivation among athletes who were experiencing better performance was observed. Further research under standardized conditions is needed to better understand the effects of these parameters on judo athletes; (4) Conclusions: Considering the athlete\u2019s psychological state can affect performance, and it is therefore important to monitor and train these factors
Non-crystallographic reduction of generalized Calogero-Moser models
We apply a recently introduced reduction procedure based on the embedding of non-crystallographic Coxeter groups into crystallographic ones to Calogero–Moser systems. For rational potentials the familiar generalized Calogero Hamiltonian is recovered. For the Hamiltonians of trigonometric, hyperbolic and elliptic types, we obtain novel integrable dynamical systems with a second potential term which is rescaled by the golden ratio. We explicitly show for the simplest of these non-crystallographic models, how the corresponding classical equations of motion can be derived from a Lie algebraic Lax pair based on the larger, crystallographic Coxeter group
Asymptotic behaviour of cylindrical waves interacting with spinning strings
We consider a family of cylindrical spacetimes endowed with angular momentum
that are solutions to the vacuum Einstein equations outside the symmetry axis.
This family was recently obtained by performing a complete gauge fixing adapted
to cylindrical symmetry. In the present work, we find boundary conditions that
ensure that the metric arising from this gauge fixing is well defined and that
the resulting reduced system has a consistent Hamiltonian dynamics. These
boundary conditions must be imposed both on the symmetry axis and in the region
far from the axis at spacelike infinity. Employing such conditions, we
determine the asymptotic behaviour of the metric close to and far from the
axis. In each of these regions, the approximate metric describes a conical
geometry with a time dislocation. In particular, around the symmetry axis the
effect of the singularity consists in inducing a constant deficit angle and a
timelike helical structure. Based on these results and on the fact that the
degrees of freedom in our family of metrics coincide with those of cylindrical
vacuum gravity, we argue that the analysed set of spacetimes represent
cylindrical gravitational waves surrounding a spinning cosmic string. For any
of these spacetimes, a prediction of our analysis is that the wave content
increases the deficit angle at spatial infinity with respect to that detected
around the axis.Comment: 25 pages, accepted for publication in Classical and Quantum Gravit
Singularities of -fold integrals of the Ising class and the theory of elliptic curves
We introduce some multiple integrals that are expected to have the same
singularities as the singularities of the -particle contributions
to the susceptibility of the square lattice Ising model. We find
the Fuchsian linear differential equation satisfied by these multiple integrals
for and only modulo some primes for and , thus
providing a large set of (possible) new singularities of the . We
discuss the singularity structure for these multiple integrals by solving the
Landau conditions. We find that the singularities of the associated ODEs
identify (up to ) with the leading pinch Landau singularities. The second
remarkable obtained feature is that the singularities of the ODEs associated
with the multiple integrals reduce to the singularities of the ODEs associated
with a {\em finite number of one dimensional integrals}. Among the
singularities found, we underline the fact that the quadratic polynomial
condition , that occurs in the linear differential equation
of , actually corresponds to a remarkable property of selected
elliptic curves, namely the occurrence of complex multiplication. The
interpretation of complex multiplication for elliptic curves as complex fixed
points of the selected generators of the renormalization group, namely
isogenies of elliptic curves, is sketched. Most of the other singularities
occurring in our multiple integrals are not related to complex multiplication
situations, suggesting an interpretation in terms of (motivic) mathematical
structures beyond the theory of elliptic curves.Comment: 39 pages, 7 figure
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