Zobrazeno 1 - 10
of 83
pro vyhledávání: '"Libine, Matvei"'
Autor:
Liang, Chen, Libine, Matvei
We extend constructions of classical Clifford analysis to the case of indefinite non-degenerate quadratic forms. Clifford analogues of complex holomorphic functions - called monogenic functions - are defined by means of the Dirac operators that facto
Externí odkaz:
http://arxiv.org/abs/2404.01398
Autor:
Frenkel, Igor, Libine, Matvei
We study a new class of functions that arise naturally in quaternionic analysis, we call them "quasi regular functions". Like the well-known quaternionic regular functions, these functions provide representations of the quaternionic conformal group.
Externí odkaz:
http://arxiv.org/abs/2402.07073
Autor:
Frenkel, Igor, Libine, Matvei
In this paper we study left and right n-regular functions that originally were introduced in [FL4]. When n=1, these functions are the usual quaternionic left and right regular functions. We show that n-regular functions satisfy most of the properties
Externí odkaz:
http://arxiv.org/abs/2011.14188
Autor:
Libine, Matvei, Sandine, Ely
We extend constructions of classical Clifford analysis to the case of indefinite non-degenerate quadratic forms. We define (p,q)-left- and right-monogenic functions by means of Dirac operators that factor a certain wave operator. We prove two differe
Externí odkaz:
http://arxiv.org/abs/2011.08289
Autor:
Libine, Matvei
The original "magic identities" are due to J.M.Drummond, J.Henn, V.A.Smirnov and E.Sokatchev; they assert that all n-loop box integrals for four scalar massless particles are equal to each other [DHSS]. The authors give a proof of the magic identitie
Externí odkaz:
http://arxiv.org/abs/1911.04966
Autor:
Frenkel, Igor, Libine, Matvei
We develop further quaternionic analysis introducing left and right doubly regular functions. We derive Cauchy-Fueter type formulas for these doubly regular functions that can be regarded as another counterpart of Cauchy's integral formula for the se
Externí odkaz:
http://arxiv.org/abs/1907.01594
Autor:
Libine, Matvei, Raghavendran, Surya
We show that conformal transformations on the generalized Minkowski space $\mathbb{R}^{p,q}$ map hyperboloids and affine hyperplanes into hyperboloids and affine hyperplanes. We also show that this action on hyperboloids and affine hyperplanes is tra
Externí odkaz:
http://arxiv.org/abs/1503.00520
Autor:
Libine, Matvei
This is an addition to a series of papers [FL1, FL2, FL3, FL4], where we develop quaternionic analysis from the point of view of representation theory of the conformal Lie group and its Lie algebra. In this paper we develop split quaternionic analogu
Externí odkaz:
http://arxiv.org/abs/1411.4015
Autor:
Libine, Matvei
In [FL1, FL3] we found mathematical interpretations of the one-loop conformal four-point Feynman integral as well as the vacuum polarization Feynman integral in the context of representations of a Lie group U(2,2) and quaternionic analysis. Then we r
Externí odkaz:
http://arxiv.org/abs/1407.2507