In this paper we define invariants of Hamiltonian group actions for central regular values of the moment map. The key hypotheses are that the moment map is proper and that the ambient manifold is symplectically aspherical. The invariants are based on the symplectic vortex equations. Applications include an existence theorem for relative periodic orbits, a computation for circle actions on a com...

The Schrödinger equation with a two-dimensional δ-function potential is a simple example of an asymptotically free theory that undergoes dimensional transmutation. Renormalization requires the introduction of a mass scale, which can be lowered perturbatively until an infrared cutoff produced by non-perturbative effects such as bound state formation is encountered. We outline the effective field...

Using the local potential approximation of the exact renormalization group (RG) equation , we show the various domains of values of the parameters of the O(1)-symmetric scalar Hamiltonian. In three dimensions, in addition to the usual critical surface S c (attraction domain of the Wilson-Fisher fixed point), we explicitly show the existence of a first-order phase transition domain S f separated...

A perturbative renormalization group (RG) scheme for light-front Hamiltonian is formulated on the basis of the Bloch-Horowitz effective Hamiltonian, and applied to the simplest φ4 model with spontaneous breaking of the Z2 symmetry. RG equations are derived at one-loop order for both symmetric and broken phases. The equations are consistent with those calculated in the covariant perturbation the...

We apply the renormalization group theory to the dynamical systems with the simplest example of basic biological motifs. This includes the interpretation of complex networks as the perturbation to simple network. This is the first step to build our original framework to infer the properties of biological networks, and the basis work to see its effectiveness to actual complex systems.

The AdS/CFT correspondence is developed from classical solutions on AdS5 with two boundaries. The corresponding limits and the reduction of degrees of freedom are discussed, as well as the required renormalization on the field theory side. The Hamiltonian first-order approach towards the solution of coupled gravitational/matter equations of motion is introduced, and the RG interpretation is exp...

Keywords-Hami l ton ian systems, Symmetry groups, Classification. 1. I N T R O D U C T I O N In [1], the Lie point symmet ry groups of a Hamiltonian system with two degrees of freedom were completely classified. In tha t case, a maximum dimension of 15 was obtained for a free particle and all dimensions between 1 and 7. We should clarify tha t we are dealing only with point t ransformations. In...

It is argued that renormalisation group flow can be interpreted as being a Hamiltonian vector flow on a phase space which consists of the couplings of the theory and their conjugate “momenta”, which are the vacuum expectation values of the corresponding composite operators. The Hamiltonian is linear in the conjugate variables and can be identified with the vacuum expectation value of the trace ...

A perturbative renormalization group is formulated for the study of Hamiltonian light-front field theory near a critical Gaussian fixed point. The only light-front renormalization group transformations found here that can be approximated by dropping irrelevant operators and using perturbation theory near Gaussian fixed volumes, employ invariant-mass cutoffs. These cutoffs violate covariance and...

Based on the Renormalization Group method, a reduction of non integrable multi-dimensional hamiltonian systems has been performed. The evolution equations for the slowly varying part of the angle-averaged phase space density, and for the amplitudes of the angular modes have been derived. It has been shown that these equations are precisely the Renormalization Group equations. As an application ...