The quantum stress-energy tensor

• Applicant: Dr. Daniela Cadamuro
• Subject Area: Nuclear and Elementary Particle Physics, Quantum Mechanics, Relativity, Fields ; Mathematics
• Term: since 2018
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 396692871

The project concerns the theory describing the physics of elementary particles (Quantum Field Theory). Examples of these elementary particles are electrons, protons, photons, among other subatomic constituents of matter. These particles can travel with velocities near (or at) the speed of light, and can possess very high energy. Further, they can interact by scattering with other particles and/or interacting with external influences (for example with a magnetic or a gravitational force), in this way modifying their direction of propagation or producing new particles. Quantum field theory provides a mathematical description of these fundamental interactions. It successfully predicts results of experiments, e.g., in particle accelerators like the Large Hadron Collider (LHC). There, two high-energy particle beams travel almost at the speed of light before colliding inside particle detectors. The detectors measure quantities like the particle's speed, mass, and energy – from which physicists can determine a particle's identity. Therefore, measurements of energy play an essential role in particle physics. The energy density (energy per volume) also plays a crucial role in Einstein’s theory of General Relativity, which is fundamental to our present understanding of the geometric properties of space and time, or “spacetime”. It links the curvature of spacetime (and thus the gravitational force) to the energy density of the matter. The energy density therefore influences the structure of space and time. In particular, certain conditions on the energy density (“energy inequalities”) guarantee the absence of exotic spacetime geometries, like time machines, wormholes and warp drives. These energy inequalities are known to be fulfilled in macroscopic physics. Unfortunately, they cannot hold in the world of elementary particle physics. Instead, one hopes that so called “quantum energy inequalities” (QEIs) hold, which would suggest that the above-mentioned results - such as absence of wormholes - can still hold for realistic matter. The goal of this project is to clarify whether, and under which conditions, QEIs can hold in Quantum Field Theory. So far, they have been obtained only in very simple situations, excluding any interaction between the particles involved. By contrast, we will investigate QEIs where interaction is present, and in theories where particles move in a thermal bath, rather than in the vacuum, where a generalized notion of energy inequality may be needed, as the usual one fails. Energy inequalities also appear to be related to statistical quantities, such as the relative entropy, and the latter to a mathematically intricate object called the modular Hamiltonian. This plays an important role in quantum field theory, but its explicit mathematical expression is generally unknown. Our aim is to investigate the structure of the modular Hamiltonian more in general, beyond very special situations.

• DFG Programme: Independent Junior Research Groups