相关论文: A New Identity in Minkowski Space and Some Applica…
A new class of identities for Feynman graph amplitudes, dubbed Schouten identities, valid at fixed integer value of the dimension d is proposed. The identities are then used in the case of the two loop sunrise graph with arbitrary masses…
Gamma matrices for quantum Minkowski spaces are found. The invariance of the corresponding Dirac operator is proven. We introduce momenta for spin 1/2 particles and get (in certain cases) formal solutions of the Dirac equation.
Postulates which lead to Minkowski spacetime are amended in a subtle way, and used to construct a consistent flat spacetime geometry with intrinsic quantum character. Events in the new quantum geometry are described by labels of the form…
Corresponding to a certain Wronskian identity, we present two types of new Casoratian identities. We apply these identities to the Darboux transformations of quantum mechanical systems. The Wronskian identity is applied to the ordinary…
We give a new proof of the generalized Minkowski identities relating the higher degree mean curvatures of orientable closed hypersurfaces immersed in a given constant sectional curvature manifold. Our methods rely on a fundamental…
In this paper we study McShane's identity in real and complex hyperbolic spaces and obtain various generalizations of the identity for representations of surface groups into the isometry groups of rank one symmetric spaces. Our methods…
We discover a new version of the celebrated Montgomery identity via quantum integral operators and establish certain quantum integral inequalities of Ostrowski type by using this identity. Relevant connections of the results obtained in…
Scattering from a scale invariant potential in two spatial dimensions leads to a class of novel identities involving the sinc function.
This paper first introduces a new generalized inverse in Minkowski space, called the m-DMP inverse, and discusses its algebraic and geometrical properties. The second objective is to characterize the m-DMP inverse equivalently by ranges,…
New identities on traces of representations of the Hecke algebra on the spaces of paths on graphs are presented. These identities are relevant in the computation of partition functions with fixed boundary conditions and of two-point…
A second-order differential identity for the Riemann tensor is obtained, on a manifold with symmetric connection. Several old and some new differential identities for the Riemann and Ricci tensors descend from it. Applications to manifolds…
It was shown by the author [International Journal of Theoretical Physics 36 (1997), 1099-1131] in synthetic differential geometry that what is called the general Jacobi identity obtaining in microcubes underlies the Jacobi identity of…
New integral identities satisfied by topological solitons in a range of classical field theories are presented. They are derived by considering independent length rescalings in orthogonal directions, or equivalently, from the conservation…
Multisummation provides a transparent description of Stokes matrices which is reviewed here together with some applications. Examples of moduli spaces for Stokes matrices are computed and discussed. A moduli space for a third Painlev\'e…
Zonotopes are becoming an increasingly popular set representation for formal verification techniques. This is mainly due to their efficient representation and their favorable computational complexity of important operations in…
Minkowski functionals have recently been introduced into cosmology as novel tools for studying the large-scale distribution of matter in the Universe. We present a brief overview of the method, including its mathematical foundations as well…
For redundant second-class constraints the Dirac brackets cannot be defined and new brackets must be introduced. We prove here that the Jacobi identity for the new brackets must hold on the surface of the second-class constraints. In order…
We study implications of unitarity for pseudo-orbit expansions of the spectral determinants of quantum maps and quantum graphs. In particular, we advocate to group pseudo-orbits into sub-determinants. We show explicitly that the…
In this work, we introduce a new generalized integral transform involving many potentially known or new transforms as special cases. Basic properties of the new integral transform, that investigated in this work, include the existence…
We find the first three most general Minkowski or Hsiung-Minkowski identities relating the total mean curvatures $H_i$, of degrees $i=1,2,3$, of a closed hypersurface $N$ immersed in a given orientable Riemannian manifold $M$ endowed with…