相关论文: Zero modes, gauge fixing, monodromies, $\zeta$-fun…

The gauge dependence in the anomalous dimension of the gauge-invariant-canonical-energy-momentum tensor for proton is studied by the background field method. The naive calculation shows the problem, the absence of the counter term in the…

This paper is devoted to the analysis of linear second order discrete-time descriptor systems (or singular difference equations (SiDEs) with control). Following the algebraic approach proposed by Kunkel and Mehrmann for pencils of matrix…

Taking the two-dimensional $\phi^4$ theory as an example, we numerically solve the deterministic equations of motion with random initial states. Short-time behavior of the solutions is systematically investigated. Assuming that the…

Central issues of the Dirac constraint formalism are discussed in relation to the algorithmic methods of commutative algebra based on the Groebner basis techniques. For a wide class of finite dimensional polynomial degenerate Lagrangian…

We discuss conformally covariant differential operators, which under local rescalings of the metric, \delta_\sigma g^{\mu\nu} = 2 \sigma g^{\mu\nu}, transform according to \delta_\sigma \Delta = r \Delta \sigma + (s-r) \sigma \Delta for…

We study the problem of critical slowing-down for gauge-fixing algorithms (Landau gauge) in $SU(2)$ lattice gauge theory on $2$ and $4$ dimensional lattices, both numerically and analytically. We consider five such algorithms, and we…

We formulate the quantum mechanics of the solutions of a Klein-Gordon-type field equation: (\partial_t^2+D)\psi(t)=0, where D is a positive-definite operator acting in a Hilbert space \tilde H. We determine all the positive-definite inner…

This paper focuses on the analysis of a free energy functional, that models a dilute suspension of magnetic nanoparticles in a two-dimensional nematic well. The {\it first part} of the article is devoted to the asymptotic analysis of global…

We consider the factorization problem of matrix symbols relative to a closed contour, i.e., a Riemann-Hilbert problem, where the symbol depends analytically on parameters. We show how to define a function $\tau$ which is locally analytic on…

We study conformal symmetry breaking differential operators which map differential forms on $\mathbb{R}^n$ to differential forms on a codimension one subspace $\mathbb{R}^{n-1}$. These operators are equivariant with respect to the conformal…

Discrete Differential Equations (DDEs) are functional equations that relate polynomially a power series $F(t,u)$ in $t$ with polynomial coefficients in a "catalytic" variable $u$ and the specializations, say at $u=1$, of $F(t,u)$ and of…

In $L_2({\mathbb R}^d;{\mathbb C}^n)$, we consider a selfadjoint operator ${\mathcal B}_\varepsilon$, $0< \varepsilon \leqslant 1$, given by the differential expression $b({\mathbf D})^* g({\mathbf x}/\varepsilon)b({\mathbf D}) +…

The variational inclusion of spin-orbit coupling in self-consistent field (SCF) calculations requires a generalised two-component framework, which permits the single-determinant wave function to completely break spin symmetry. The…

The aim of this work is to study, from an intrinsic and geometric point of view, second-order constrained variational problems on Lie algebroids, that is, optimization problems defined by a cost functional which depends on higher-order…

Some aspects of the multiplicative anomaly of zeta determinants are investigated. A rather simple approach is adopted and, in particular, the question of zeta function factorization, together with its possible relation with the…

The concept of dimensional reduction in the high temperature regime is generalized to static Green's functions of composite operators that contain fermionic fields. The recognition of a natural kinematic region where the lowest Matsubara…

The work is dedicated to the derivation of the 'functional' integral representation of the disorder parameter. This derivation resolves the problem of the choice of the so called modifed action as well as the problem of the choice of the…

We consider the trigonometric Felderhof model, of free fermions in an external field, on a finite lattice with domain wall boundary conditions. The vertex weights are functions of rapidities and external fields. We obtain a determinant…

Second order linear non-autonomous differential equations with negative stiffness are considered. Using Chetaev-like (Lyapunov-like) functions, necessary (sufficient) conditions are found for the solutions to be bounded for all initial…

A finite difference numerical method is investigated for fractional order diffusion problems in one space dimension. For this, a mathematical model is developed to incorporate homogeneous Dirichlet and Neumann type boundary conditions. The…