Related papers: Reidemeister transformations of the potential func…
We revisit Newton's equation of motion in one dimension when the moving particle has a variable mass m(x,t) depending both on position (x) and time (t). Geometrically the mass function is identified with one of the metric function in a…
Given an oriented closed manifold $M$ of odd dimension and a unitary representation $\rho : \pi_1(M) \ra \GL_n(\F)$, we define a Reidemeister torsion, even if the cohomology associated with $\rho$ is not acyclic. As corollaries, we…
For a hyperbolic link complement with a triangulation, there are hyperbolicity equations of the triangulation, which guarantee the hyperbolic structure of the link complement. In this paper, we explain that the number of the essential…
A complete Reidemeister characterisation of welded links is a long-standing open problem. We present a Reidemeister Theorem for a related class of four-dimensional links, solid ribbon torus links: immersed solid tori in R4 with only ribbon…
Special relativity, the symmetry breakdown in the electroweak standard model, and the dichotomy of the spacetime related transformations with the Lorentz group, on the one side, and the chargelike transformations with the hypercharge and…
It is shown how nucleon-nucleon potentials can be defined in N dimensions, using dimensional regularization to continue amplitudes. This provides an easy way to separate out contact ($\delta$-function) terms arising from renormalization. An…
We investigate the interaction between two rubidium atoms in highly excited Rydberg states, and find that very long-range potential wells exist. These wells are shown to support many bound states. We calculate the properties of the wells…
We apply the functional renormalization group theory to the dynamics of first-order phase transitions and show that a potential with all odd-order terms can describe spinodal decomposition phenomena. We derive a momentum-dependent dynamic…
In this article we extend the test of Hamiltonian Renormalisation proposed in this series of articles to the D-dimensional case using a massive free scalar field. The concepts we introduce are explicitly computed for the D=2 case but…
We define eventually symmetric functions to be those power series of bounded degree in infinitely many variables that are invariant under interchanging all the variables with large enough indices. We show how this ring $\tilde{\Lambda}$ is…
On even-dimensional Euclidean space for integer powers of the Laplace operator greater than or equal to half the dimension, a fundamental solution of the polyharmonic equation has binomial and logarithmic behavior. Gegenbauer polynomial…
The feasibility of a perturbation expansion for Green's functions of the t-J model directly in terms of X-operators is demonstrated using the Baym- Kadanoff functional method. As an application we derive explicit expressions for the kernel…
The generalization of the factorization method performed by Mielnik [J. Math. Phys. {\bf 25}, 3387 (1984)] opened new ways to generate exactly solvable potentials in quantum mechanics. We present an application of Mielnik's method to…
We represent in this note the solutions of the electronic Schr\"odinger equation as traces of higher-dimensional functions. This allows to decouple the electron-electron interaction potential but comes at the price of a degenerate elliptic…
We propose a new class of transforms that we call {\it Lehmer Transform} which is motivated by the {\it Lehmer mean function}. The proposed {\it Lehmer transform} decomposes a function of a sample into their constituting statistical…
In this paper, a supersymmetric extension of a system of hydrodynamic type equations involving Riemann invariants is formulated in terms of a superspace and superfield formalism. The symmetry properties of both the classical and…
We reconsider some fundamental aspects of the fluid mechanics model, and the derivation of continuum flow equations from gas kinetic theory. Two topologies for fluid representation are presented, and a set of macroscopic equations are…
After a brief review of the definition and properties of the quantum effective Hamiltonian action we describe its renormalization flow by a functional RG equation. This equation can be used for a non-perturbative quantization and study also…
A class of elliptic-hyperbolic equations is placed in the context of a geometric variational theory, in which the change of type is viewed as a change in the character of an underlying metric. A fundamental example of a metric which changes…
We define an invariant of tangles and framed tangles given a finite crossed module and a pair of functions, called a Reidemeister pair, satisfying natural properties. We give several examples of Reidemeister pairs derived from racks,…