Dr. Daniela Cadamuro
Daniela Cadamuro |
Zentrum Mathematik, M5
Technische Universität München
Forschung - Lehre - Publikationen
My area of expertise is in relativistic quantum field theory (QFT), namely the theory which describes the physics of elementary particles. This broad and topical area often combines ideas from various other mathematical disciplines such as Analysis, Algebra and Differential Geometry; and vice versa, these disciplines have been influenced by developments in QFT. Within the context of my research:
- I use a novel constructive approach based on techniques in Operator Algebra and Functional Analysis to construct interacting QFTs with bound states in 1+1 dimensional Minkowski space (e.g., the sine-Gordon model, the Thirring model and their possible deformations). This aspect of my work is not only a very challenging topic in mathematical physics, but also requires the development of novel techniques in mathematics, in particular, the study of self-adjoint extensions of certain symmetric operators which are not amenable to an application of the standard results in the literature.
- I study lower bounds to the smeared energy density (quantum energy inequalities) in self-interacting models of QFT, which is a topic of interest not only in physics (Cosmology, Astrophysics) since they exclude the existence of exotic spacetime geometries, such as wormholes, warp drives and time machines, but also with respect to the mathematical techniques applied: it requires very detailed estimates on lower bounds of certain integral operators, including integral kernels with singularities, and in that respect requires advanced techniques of Functional Analysis.
- I am working in some aspects of Quantum Mechanics that may be directly verified in experiments. It is the study of inequalities for the probability Backflow of a particle scattering onto a potential. This topic involves a certain knowledge of (estimates of) the solution of the interacting Schrödinger equation and of the expression of the Møller operator. In this respect, it is a hot topic in (non relativistic) scattering theory.
- I recently started working in mathematical aspects of Quantum information theory, in particular on the problem of data compression in quantum communication.
- I have substantial teaching experience in the UK higher education sector. I was a temporary Lecturer in Applied Mathematics from 2013 to 2015 at the University of Bristol, where I taught lectures at undergraduate and postgraduate level on topics such as Calculus (1st year, class of 260 students), courses at Foundation Year and service courses to students in other sciences, in particular Physics, Chemistry, Economics and Biology. I also lectured more advanced courses (4th year and doctoral level), e.g., my course Advanced Quantum Mechanics.
Conference and seminar organization, invited talks, additional activities
Informations about Conference and seminar organization, Invited talks and research visits, Additional activities can be found here