We consider the motion of a particle described by an action that is a functional of the Frenet-Serret [FS] curvatures associated with the embedding of its worldline in Minkowski space. We develop a theory of deformations tailored to the FS frame. Both the Euler-Lagrange equations and the physical invariants of the motion associated with the Poincaré symmetry of Minkowski space, the mass and the...

We consider the motion of a particle described by an action that is a functional of the Frenet-Serret [FS] curvatures associated with the embedding of its worldline in Minkowski space. We develop a theory of deformations tailored to the FS frame. Both the Euler-Lagrange equations and the physical invariants of the motion associated with the Poincaré symmetry of Minkowski space, the mass and the...

We present the main results of our microcanonical simulation of the Wess Zumino Witten action functional. This action, being highly nontrivial and capable of exhibiting many different phase transitions, is chosen to be representative of general complex actions. We verify the applicability of microcanonical simulation by successfully obtaining two of the many critical points of the Wess ZuminoWi...

Algebraic properties of the Becchi-Rouet-Stora-Tyutin (BRST) symmetry associated to twisted gauge occurring in $\ensuremath{\kappa}$-Poincar\'e invariant theories on $\ensuremath{\kappa}$-Minkowski space are investigated. We find that BRST operation invariance action functional can be continuously deformed together with its corresponding Leibniz rule, into a nilpotent operation, leading algebra...

We study the Minkowski length L(P ) of a lattice polytope P , which is defined to be the largest number of non-trivial primitive segments whose Minkowski sum lies in P . The Minkowski length represents the largest possible number of factors in a factorization of polynomials with exponent vectors in P , and shows up in lower bounds for the minimum distance of toric codes. In this paper we give a...

Minkowski Pythagorean hodograph curves are polynomial curves with polynomial speed, measured with respect to Minkowski norm. Curves of this special class are particularly well suited for representing medial axis transforms of planar domains. In the present paper we generalize this polynomial class to a rational class of curves in Minkowski 3-space. We show that any rational Minkowski Pythagorea...

Abstract The Minkowski functionals, including the Euler characteristic statistics, are standard tools for morphological analysis in cosmology. Motivated by cosmic research, we examine functional of excursion set an isotropic central limit random field, whose k -point correlation functions ( th-order cumulants) have same structure as that assumed research. Using 3- and 4-point functions, derive ...

The functional renormalization group flow of a scalar field theory with quartic couplings and sharp spatial momentum cutoff is presented in four-dimensional Minkowski space-time for the bare action by retaining entanglement IR UV particle modes. It argued that open interaction channels have to be taken into account quantum defined help cutoff, non-perturbative UV-IR found closed or almost models.

We explore the morphological and dynamical evolution of galaxy clusters in simulations using scalar and vector-valued Minkowski valuations and the concept of fundamental plane relations. In this context, three questions are of fundamental interest: 1. How does the average cluster morphology depend on the cosmological background model? 2. Is it possible to discriminate between different cosmolog...

A multidimensional-scaling approach is used to analyze frequently used medical-topic terms in queries submitted to aWeb-based consumer health information system. Based on a year-long transaction log file, five medical focus keywords (stomach, hip, stroke, depression, and cholesterol ) and their co-occurring query terms are analyzed. An overlap-coefficient similarity measure and a conversion mea...