Related papers: Normal form theory for reversible equivariant vect…
In this work we develop a re-formulation of quantum field theory through the more general weighted Lorentz invariant measures that the definition of quantum fields allows; this approach provides finite answers for the long-live problems of…
We study the ultraviolet problem for models of a finite-dimensional quantum mechanical system linearly coupled to a bosonic quantum field, such as the (many-)spin boson model or its rotating-wave approximation. If the state change of the…
An imitation of 2d field theory is formulated by means of a model on the hierarchic tree (with branching number close to one) with the same potential and the free correlators identical to those of 2d ones. Such a model possesses some…
We obtain an equivariant class formula for z-deformation of t-modules. Under mild conditions, it allows us to get an equivariant class formula for t-modules.
A general form factor formula for the scaling Z(N)-Ising model is constructed. Exact expressions for matrix elements are obtained for several local operators. In addition, the commutation rules for order, disorder parameters and para-Fermi…
We derive two methods for simultaneously controlling the resonance frequency, linewidth and multipolar nature of the resonances of radially symmetric structures. Firstly, we formulate an eigenvalue problem for a global shift in the…
We introduce the notion of a field of covariances, a contravariant functor from non-commutative probability spaces to Hilbert spaces, as the natural categorical analogue of statistical covariance. In the case of finite-dimensional…
We pose and solve an inverse problem for the classical field equations that arise in the Standard Model of particle physics. Our main result describes natural conditions on the representations, so that it is possible to recover all the…
A formal series transformation to Birkhoff-Gustavson normal form is obtained for toroidal magnetic field configurations in the neighborhood of a magnetic axis. Bishop's rotation-minimizing coordinates are used to obtain a local orthogonal…
Non equilibrium effective field theory is presented as an inhomogeneous field theory, using a formulation which is analogous to that of a gauge theory. This formulation underlines the importance of structural aspects of non-equilibrium,…
This paper introduces a generative model equivariant to Euclidean symmetries: E(n) Equivariant Normalizing Flows (E-NFs). To construct E-NFs, we take the discriminative E(n) graph neural networks and integrate them as a differential…
We introduce and study covariance fields of distributions on a Riemannian manifold. At each point on the manifold, covariance is defined to be a symmetric and positive definite (2,0)-tensor. Its product with the metric tensor specifies a…
New solutions for second-order intertwining relations in two-dimensional SUSY QM are found via the repeated use of the first order supersymmetrical transformations with intermediate constant unitary rotation. Potentials obtained by this…
Based on the covariant background field method, we calculate the ultraviolet counter\-terms up to two-loop order and discuss the renormalizability of the three-dimensional non-linear sigma models with arbitrary Riemannian manifolds as…
This paper presents algebraic methods for the study of polynomial relative invariants, when the group G formed by the symmetries and relative symmetries is a compact Lie group. We deal with the case when the subgroup H of symmetries is…
A class of non-selfadjoint, $\PT$-symmetric operators is identified similar to a self-adjoint one, thus entailing the reality of the spectrum. The similarity transformation is explicitly constructed through the method of the quantum normal…
We study normal forms for families of area-preserving maps which have a fixed point with neutral multipliers -1 or +1 at epsilon=0. Our study covers both the orientation-preserving and orientation-reversing cases. In these cases Birkhoff…
As applied to quantum theories, the program of renormalization is successful for `renormalizable models' but fails for `nonrenormalizable models'. After some conceptual discussion and analysis, an enhanced program of renormalization is…
We describe a procedure for constructing formal normal forms of holomorphic maps with a hypersurface of fixed points, and we apply it to obtain a complete list of formal normal forms for 2-dimensional holomorphic maps tangential to a curve…
A novel inhomogeneous gauge transformation law is proposed for a non-Abelian adjoint two-form in four dimensions. Rules for constructing actions invariant under this are given. The auxiliary vector field which appears in some of these…