SUMMARY
The Minkowski vacuum is definitively characterized as both Poincare invariant and a quasi-free state. The discussion raises the question of whether these two conditions fully define the Minkowski vacuum or if additional states exist that meet these criteria. It is established that in advanced Quantum Field Theory (QFT), the vacuum is defined as the lowest-energy eigenstate of the full interacting Hamiltonian, which may differ from the lowest-energy eigenstate of the free Hamiltonian. The conditions specified involve the invariance of the two-point function under the Poincare group and the expressibility of all n-point functions in terms of the two-point function.
PREREQUISITES
- Understanding of Quantum Field Theory (QFT)
- Familiarity with Poincare group representations
- Knowledge of Hamiltonian mechanics in quantum systems
- Concept of quasi-free states in quantum physics
NEXT STEPS
- Study Weinberg's "Quantum Theory of Fields, Volume 1" for insights on interacting representations of the Poincare group
- Explore the mathematical formulation of two-point functions in QFT
- Research the implications of quasi-free states on quantum correlations
- Investigate the differences between free and interacting Hamiltonians in QFT
USEFUL FOR
This discussion is beneficial for theoretical physicists, quantum field theorists, and advanced students in physics who are exploring the properties of the Minkowski vacuum and its implications in quantum mechanics.