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Nonstandard analysis is an area of modern mathematics that studies abstract number systems containing both infinitesimal and infinite numbers. This article applies nonstandard analysis to derive jump conditions for one-dimensional, converging shock waves in a compressible, inviscid, perfect gas....
Narasimhan and Ramadas Commun. Math. Phys. 67 , 121 ( 1979 ) showed that the restricted holonomy group of the Coulomb connection is dense in the connected component of the identity of the gauge group when one considers the product principal bundle S 3 × S U (2)→ S 3 S 3 × S U ( 2 ) → S 3 ....
The non-imprisonment conditions on spacetimes are studied. It is proved that the non-partial imprisonment property implies the distinction property. Moreover, it is proven that feeble distinction, a property which stays between weak distinction and causality, implies non-total imprisonment. As a...
Given a unitary representation U U of a compact group G G and a transitive G G -space Ω Ω , we characterize the extremal elements of the convex set of all U U -covariant positive operator valued measures.
A single master equation is given describing spin s ≤ 2 s ≤ 2 test fields that are gauge- and tetrad-invariant perturbations of the spinning C C metric space-time representing a source with mass M M , uniformly rotating with angular momentum per unit mass a a , and uniformly accelerated with...
Any matrix self-dual-type S S -integrable partial differential equation (PDE) possesses a family of lower-dimensional reductions represented by the matrix quasilinear first order PDEs solvable by the method of characteristics. These PDEs admit two types of particular solutions: (a) explicit...
The Schrödinger equation with point interaction in one dimension is revisited in a simple framework where the “singular” potential is defined as a symmetric operator in a natural way. The main tool is a scalar product of the elementary distributions constructed after a commutative (and...
We consider a conformal field theory for bosons on the Riemann sphere. Correlation functions are defined as singular limits of functional integrals. The main result is that these amplitudes define transition amplitudes, that is multilinear Hilbert–Schmidt functionals on a fixed Hilbert space.
By analytic continuation from a SU(2) SU ( 2 ) gauge field solution, Wu and Yang Phys. Rev. 13 , 3233 ( 1976 ) obtained a static and sourceless solution of gauge theory for the group SL(2, C ) SL ( 2 , C ) also for SO(3,1) SO ( 3 , 1 ) . This field configuration resembles a dyon that carries an...
We present a unified geometric framework for describing both the Lagrangian and Hamiltonian formalisms of regular and nonregular time-dependent mechanical systems, which is based on the approach of Skinner and Rusk “Generalized Hamiltonian dynamics I. Formulation on T * Q ⊗ T Q T * Q ⊗ T Q...
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