Related papers: Higher-Derivative Wess-Zumino Model in Three Dimen…
It is known that local operators in quantum field theory transform in representations of ordinary global symmetry groups. The purpose of this paper is to generalise this statement to extended operators such as line and surface defects. We…
Several years ago, we proposed a modification of the Standard Model, in which the Higgs sector was stabilized by the addition of higher derivative operators, similar to Lee-Wick Electrodynamics. We studied this theory extensively, both…
In this paper we consider the problem of the existence of higher derivatives of the function $t\mapsto\f(A+tK)$, where $\f$ is a function on the real line, $A$ is a self-adjoint operator, and $K$ is a bounded self-adjoint operator. We…
We study the geometry and partial differential equations arising from the consideration of group-determinants, and representation theory. The simplest and most striking such example is undoubtedly that of the Humbert operator, associated…
Two-dimensional superintegrable systems with one third order and one lower order integral of motion are reviewed. The fact that Hamiltonian systems with higher order integrals of motion are not the same in classical and quantum mechanics is…
The effective dimension-5 operators can be induced by quantum gravity or inspired by string and M theories. They have important impacts on grand unified theories. We investigate the group theoretic nature of them for the well known E(6)…
We consider the Wess-Zumino-Witten theory to obtain the functional integral bosonization of the Thirring-Wess model with an arbitrary regularization parameter. Proceeding a systematic of decomposing the Bose field algebra into…
We present calculations of the leading and O(1/N) terms in a large-N expansion of the \beta-functions for various supersymmetric theories: a Wess-Zumino model, supersymmetric QED and a non-abelian supersymmetric gauge theory. In all cases N…
We introduce a method in differential geometry to study the derivative operators of Siegel modular forms. By determining the coefficients of the invariant Levi-Civita connection on a Siegel upper half plane, and further by calculating the…
For a large class of variational quantum circuits, we show how arbitrary-order derivatives can be analytically evaluated in terms of simple parameter-shift rules, i.e., by running the same circuit with different shifts of the parameters. As…
A new set of projection operators for three-dimensional models are constructed. Using these operators, an uncomplicated and easily handling algorithm for analysing the unitarity of the aforementioned systems is built up. Interestingly…
The calculation of higher twist (or dimension) corrections to physical quantities using operator product expansions is delicate. If dimensional regularization is used to regulate the ultra-violet divergences then there are ambiguities in…
A model operator $H_\mu,$ $\mu>0$ associated to a system of three particles on the three-dimensional lattice $ \mathbb{Z}^3$ that interact via nonlocal pair potentials is considered. We study the case where the parameter function $w$ has a…
We propose a finite-dimensional control-based method to approximate solution operators for evolutional partial differential equations (PDEs), particularly in high-dimensions. By employing a general reduced-order model, such as a deep neural…
We express the discrete 1+1-dimensional $O(3)$ non-linear sigma model (NL$\sigma$M) in a form well-suited for the continuous variable approach to quantum computing. Within the Schwinger boson formulation, we need two qumodes…
The derivative expansion of the effective action is considered in the model with two interacting real scalar fields in curved spacetime. Using the functional approach and local momentum representation, the coefficient of the derivative term…
A general formulation of noncommutative or quantum derivatives for operators in a Banach space is given on the basis of the Leibniz rule, irrespective of their explicit representations such as the G\^ateaux derivative or commutators. This…
We consider a (2+1)-dimensional modified electrodynamics endowed with terms that are either Lorentz-invariant or Lorentz-violating and involve an ever increasing number of derivatives. Our construction relies on U(1) gauge invariance and…
A simple systematic method for calculating derivative expansions of the one-loop effective action is presented. This method is based on using symbols of operators and well known deformation quantization theory. To demonstrate its advantages…
Effective Lagrangians can be used to parametrize the effects of physics beyond the standard model. Assuming the complete theory is a gauge theory, we determine which effective operators may be generated at tree level, and which are only…