Related papers: Higher Operations in Perturbation Theory
The spectral analysis of a non-Hermitian unbounded operator appearing in quantum physics is our main concern. The properties of such an operator are essentially different from those of Hermitian Hamiltonians, namely due to spectral…
It was recently argued that quantum field theories possess one-form and higher-form symmetries, labelled `generalized global symmetries.' In this paper, we describe how those higher-form symmetries can be understood mathematically as…
We perform conformal perturbation theory by marginal operators to first order. A suitable renormalization method is needed that makes the conformal invariance of the deformed correlation functions manifest. Combining the embedding space…
A class of unitary operations generated by idealized, semiclassical fields is studied. The operations implemented by sharp potential kicks are revisited and the possibility of performing them by softly varying external fields is examined.…
A central theme in current work in quantum information and quantum foundations is to see quantum mechanics as occupying one point in a space of possible theories, and to use this perspective to understand the special features and properties…
L-infinity morphisms are studied from the point of view of perturbative quantum field theory, as generalizations of Feynman expansions. The connection with the Hopf algebra approach to renormalization is exploited. Using the coalgebra…
We formulate $\lambda$-deformed $\sigma$-models as QFTs in the upper-half plane. For different boundary conditions we compute correlation functions of currents and primary operators, exactly in the deformation parameter $\lambda$ and for…
We report lowest-order series expansions for primary matrix functions of quantum states based on a perturbation theory for functions of linear operators. Our theory enables efficient computation of functions of perturbed quantum states that…
The unrivaled robustness of topologically ordered states of matter against perturbations has immediate applications in quantum computing and quantum metrology, yet their very existence poses a challenge to our understanding of phase…
The paper is devoted to the study of BRST charge in perturbed two dimensional conformal field theory. The main goal is to write the operator equation expressing the conservation law of BRST charge in perturbed theory in terms of purely…
This chapter provides a non-technical overview and motivation for the recent interactions between algebraic quantum field theory (AQFT) and rather abstract mathematical disciplines such as operads, model categories and higher categories.
Based on some results on reparmetrisation of time in Hamiltonian path integral formalism, a pseudo time formulation of operator formalism of quantum mechanics is presented. Relation of reparametrisation of time in quantum with super…
We study perturbative renormalization of the composite operators in the $T\bar T$-deformed two-dimensional free field theories. The pattern of renormalization for the stress-energy tensor is different in the massive and massless cases.…
We present a new characterization of quantum theory in terms of simple physical principles that is different from previous ones in two important respects: first, it only refers to properties of single systems without any assumptions on the…
A deformation of Heisenberg algebra induces among other consequences a loss of Hermiticity of some operators that generate this algebra. Therefore, these operators are not Hermitian, nor is the Hamiltonian operator built from them. In the…
This paper studies a particular class of higher order conformally invariant dif- ferential operators and related integral operators acting on functions taking values in particular finite dimensional irreducible representations of the Spin…
In the q-deformed theory the perturbation approach can be expressed in terms of two pairs of undeformed position and momentum operators. There are two configuration spaces. Correspondingly there are two q-perturbation Hamiltonians, one…
In this work, we present a logical formalism for reasoning about quantum systems in finite dimension. Contrary to the usual approach in quantum logic, our formalism is based classical first-order logic, which allows us to use the tools of…
A new totally algebraic formalism based on general, abstract ladder operators has been proposed. This approach heavily grounds in the superoperator formalism of Primas. However it is necessary to introduce many improvements in his…
In this paper a theory of Hecke operators for higher order modular forms is established. The definition of cusp forms and attached L-functions is extended beyond the realm of parabolic invariants. The role of representation theoretic…