2/13/2023 0 Comments Flat space curved spaceWe will apply the techniques developed in the first part of the course to simplified models capturing the main aspects of the inflationary dynamic. Inflation is nowadays a well established paradigm fully consistent with observations and able to explain the generation of an almost scale invariant spectrum of primordial perturbations giving rise to structure formation. Ambiguity of the vacuum state and correlation functions.ġ.3 The Schwinger effect. Quantization of a scalar field with a time dependent mass.ġ.2. We will start by discussing the quantization of a scalar field with a time dependent mass.ġ.1. Introduction to QFT in non-trivial backgrounds The course will be divided in 3+1 parts: 1. Most of the topics and examples will be simplified to the barest possible minimum that still contains the relevant physical information (free scalar fields only, conformally flat metrics, reduced dimensions, etc…). The emphasis of the seminar will be on physical concepts rather than on an axiomatic formulation of QFT in CST. Familiarity with some concepts from quantum optics (coherent states, squeezed states,…) could be also helpful but not necessary. A basic knowledge of General Relativity (fields in arbitrary coordinate systems, concepts of proper distance and proper time, Schwarzschild and FRW metrics,… ) is highly recommended, specially in the last part. The relevant aspects of canonical quantization (mode expansion, creation and annihilation operators, vacuum definition, Fock space construction, etc…) will be covered during the course. Although a previous exposure to this topic in certainly positive, it is not necessary to have taken a course on Quantum Field Theory. The seminar is intended to be self-consistent regarding basic QFT concepts. The theory makes spectacular predictions such as the generation of primordial perturbations during inflation and the Hawking radiation of black holes. The material considered in this seminar is not only of academical interest. In particular, we will discover that familiar concepts like the vacuum state or the number of particles become ambiguous and observer-dependent on spaces without any particular symmetry. This extension will allow us to disentangle the important structures and concepts of QFT from the simplifications emerging in the flat spacetime approximation. In this seminar, we will extend the canonical quantization in Minkowski spacetime to curved spacetimes (Lorentzian manifolds). QFT in CST is expected to provide an accurate description of quantum phenomena in a regime in which the spacetime cannot be longer described by a Minkowski metric but quantum gravity itself can be neglected. This approximation is however not applicable to extreme astrophysical and cosmological environments. Particle physics experiments are performed in a background that can be very well approximated by a Minkowski spacetime. Master-Pflichtseminar : QFT in curved spacetimes SCHEDULE & NOTES Basic bibliography What all this is about
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