ﻻ يوجد ملخص باللغة العربية
Motivated by the universal knot polynomials in the gauge Chern-Simons theory, we show that the values of the second Casimir operator on an arbitrary power of Cartan product of $X_2$ and adjoint representations of simple Lie algebras can be represented in a universal form. We show that it complies with $Nlongrightarrow -N$ duality of the same operator for $SO(2n)$ and $Sp(2n)$ algebras (the part of $Nleftrightarrow-N$ duality of gauge $SO(2n)$ and $Sp(2n)$ theories). We discuss the phenomena of non-zero universal values of Casimir operator on zero representations.
We construct characteristic identities for the split (polarized) Casimir operators of the simple Lie algebras in defining (minimal fundamental) and adjoint representations. By means of these characteristic identities, for all simple Lie algebras we d
We construct spectral zeta functions for the Dirac operator on metric graphs. We start with the case of a rose graph, a graph with a single vertex where every edge is a loop. The technique is then developed to cover any finite graph with general ener
The Casimir energy for a massless, neutral scalar field in presence of a point interaction is analyzed using a general zeta-regularization approach developed in earlier works. In addition to a regular bulk contribution, there arises an anomalous boun
This is the first one of a series of papers about zeta regularization of the divergences appearing in the vacuum expectation value (VEV) of several local and global observables in quantum field theory. More precisely we consider a quantized, neutral
In this work we study the Casimir effect for massless scalar fields propagating in a piston geometry of the type $Itimes N$ where $I$ is an interval of the real line and $N$ is a smooth compact Riemannian manifold. Our analysis represents a generaliz