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...

Let G be a compact Lie group, and let LG denote the corresponding loop group. Let (X,ω) be a weakly symplectic Banach manifold. Consider a Hamiltonian action of LG on (X,ω), and assume that the moment map μ : X −→ Lg∗ is proper. We consider the function |μ|2 : X −→ R, and use a version of Morse theory to show that the inclusion map j : μ(0) −→ X induces a surjection j∗ : H∗ G(X) −→ H∗ G(μ−1(0))...

A method of Hamiltonian diagonalization is suitable for calculating physical quantities associated with wavefunctions, such as structure functions and form factors. However, we cannot diagonalize Hamiltonian directly in quantum field theories because dimension of Hilbert space is generally infinite. To create effective Hamiltonian, we extend a technique of NRG (numerical renormalization group) ...

Let M be a G-covering of a nilpotent orbit in 0 where G isa complex semisimple Lie group and g = Lie(G). We prove that under Poisson bracket the space R[2] of homogeneous functions on M of degree 2 is the unique maximal semisimple Lie subalgebra of R = R{M) containing g . The action of g' ~ R[2] exponentiates to an action of the corresponding Lie group G' on a G'-cover M' of a nilpotent orbit i...

Bentea and Tu{a}rnu{a}uceanu~(An. c{S}tiinc{t}. Univ. Al. I.Cuza Iac{s}, Ser. Nouv{a}, Mat., {bf 54(1)} (2008), 209-220)proposed the following problem: Find an explicit formula for thenumber of fuzzy subgroups of a finite hamiltonian group of type$Q_8times mathbb{Z}_n$ where $Q_8$ is the quaternion group oforder $8$ and $n$ is an arbitrary odd integer. In this paper weconsider more general grou...

We prove a nonlinear Poisson type formula for the Schrödinger group. Such a formula had been derived in a previous paper by the authors, as a consequence of the study of the asymptotic behavior of nonlinear wave operators for small data. In this note, we propose a direct proof, and extend the range allowed for the power of the nonlinearity to the set of all short range nonlinearities. Moreover,...

Suppose that a compact and connected Lie group G acts on complex Hodge manifold M in holomorphic Hamiltonian manner, the action linearizes to positive line bundle A M. Then there is an induced unitary representation associated Hardy space and, if moment map of nowhere vanishing, corresponding isotypical components are all finite dimensional. We study asymptotic concentration behavior equivarian...