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Minkowski Space (minkowski + space)

Distribution by Scientific Domains
Mathematics and Statistics66%

Selected Abstracts

An ultraviolet-finite Hamiltonian approach on the noncommutative Minkowski space

FORTSCHRITTE DER PHYSIK/PROGRESS OF PHYSICS, Issue 6-7 2004
D. Bahns
This is an exposition of joint work with S. Doplicher, K. Fredenhagen, and G. Piacitelli on field theory on the noncommutative Minkowski space [1]. The limit of coinciding points is modified compared to ordinary field theory in a suitable way which allows for the definition of so-called regularized field monomials as interaction terms. Employing these in the Hamiltonian formalism results in an ultraviolet finite S -matrix. [source]

Complex-distance potential theory, wave equations, and physical wavelets

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 16-18 2002
Gerald Kaiser
Potential theory in ,n is extended to ,n by analytically continuing the Euclidean distance function. The extended Newtonian potential ,(z) is generated by a (non-holomorphic) source distribution ,,(z) extending the usual point source ,(x). With Minkowski space ,n, 1 embedded in ,n+1, the Laplacian ,n+1 restricts to the wave operator ,n,1 in ,n, 1. We show that ,,(z) acts as a propagator generating solutions of the wave equation from their initial values, where the Cauchy data need not be assumed analytic. This generalizes an old result by Garabedian, who established a connection between solutions of the boundary-value problem for ,n+1 and the initial-value problem for ,n,1 provided the boundary data extends holomorphically to the initial data. We relate these results to the physical avelets introduced previously. In the context of Clifford analysis, our methods can be used to extend the Borel,Pompeiu formula from ,n+1 to ,n+1, where its riction to Minkowski space ,n, 1 provides solutions for time-dependent Maxwell and Dirac equations. Copyright © 2002 John Wiley & Sons, Ltd. [source]

Continuum limits for classical sequential growth models

RANDOM STRUCTURES AND ALGORITHMS, Issue 2 2010
Graham Brightwell
Abstract A random graph order, also known as a transitive percolation process, is defined by taking a random graph on the vertex set {0,,,n , 1} and putting i below j if there is a path i = i1,ik = j in the graph with i1 < , < ik. Rideout and Sorkin Phys. Rev. D 63 (2001) 104011 provide computational evidence that suitably normalized sequences of random graph orders have a "continuum limit." We confirm that this is the case and show that the continuum limit is always a semiorder. Transitive percolation processes are a special case of a more general class called classical sequential growth models. We give a number of results describing the large-scale structure of a general classical sequential growth model. We show that for any sufficiently large n, and any classical sequential growth model, there is a semiorder S on {0,,,n - 1} such that the random partial order on {0,,,n - 1} generated according to the model differs from S on an arbitrarily small proportion of pairs. We also show that, if any sequence of classical sequential growth models has a continuum limit, then this limit is (essentially) a semiorder. We give some examples of continuum limits that can occur. Classical sequential growth models were introduced as the only models satisfying certain properties making them suitable as discrete models for spacetime. Our results indicate that this class of models does not contain any that are good approximations to Minkowski space in any dimension , 2. © 2009 Wiley Periodicals, Inc. Random Struct. Alg., 2010 [source]

On the existence of smooth self-similar blowup profiles for the wave map equation

COMMUNICATIONS ON PURE & APPLIED MATHEMATICS, Issue 5 2009
Pierre Germain
Consider the equivariant wave map equation from Minkowski space to a rotationally symmetric manifold N that has an equator (e.g., the sphere). In dimension 3, this paper presents a necessary and sufficient condition on N for the existence of a smooth self-similar blowup profile. More generally, we study the relation between the minimizing properties of the equator map for the Dirichlet energy corresponding to the (elliptic) harmonic map problem and the existence of a smooth blowup profile for the (hyperbolic) wave map problem. This has several applications to questions of regularity and uniqueness for the wave map equation. © 2008 Wiley Periodicals, Inc. [source]

Equivariant wave maps in two space dimensions,

COMMUNICATIONS ON PURE & APPLIED MATHEMATICS, Issue 7 2003
Michael Struwe
Singularities of corotational wave maps from (1 + 2)-dimensional Minkowski space into a surface N of revolution after a suitable rescaling give rise to nonconstant corotational harmonic maps from ,,2 into ,. In consequence, for noncompact target surfaces of revolution, the Cauchy problem for wave maps is globally well-posed. © 2003 Wiley Periodicals, Inc. [source]