Notes in Master::Quantum many body physics

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Status	Last Update	Fields
Published	11/29/2023	What general Symmetrie property leads to a phase transition? How is a phase transition connected to the free Energy F?
Published	11/29/2023	What does a Z2 symmetry mean?
Published	11/29/2023	In the Ising model with no Magnetic field present, how do temerature influence the symmetry of the magntisation under a global spin flip?
Published	11/29/2023	What is a quantum phase transition?
Published	11/29/2023	How are the wave functions in positional space of two particles (fermion or boson)?
Published	11/29/2023	How would you describe three particles in ground state in first and second quantisation? Why is second quantisation better?
Published	11/29/2023	What are relevant commutators in second quantisation?
Published	11/29/2023	Can operators from first quantisation be transformed in second quantisation? What do the new operators always contain?
Published	11/29/2023	How can scattering be thought of in second quantisation?
Published	11/29/2023	What is a correlation function?
Published	11/29/2023	What are pair correlation functions? What results do they show?
Published	11/29/2023	What are one body operators?
Published	11/29/2023	How ist the first Madlung rule derived from pair correlation funcitons?
Published	11/29/2023	What are the main goals of functional field integrals?
Published	11/29/2023	What is the basic idea of the path integral formalism? Why is it generally difficult?
Published	11/29/2023	What was Feynmans generall idea to simplify the calculation of the transition amplitude (zsmh. time evolution) in the path integral formalism
Published	11/29/2023	What is the Hamiltonian formulation of the Feynman path integral?
Published	11/29/2023	How is a D-dimensional quantum system related to a classical system?
Published	11/29/2023	How is the quantum partition function related to the transition amplitude of a QM state?
Published	11/29/2023	What is the saddle point approxmiation?
Published	11/29/2023	What is a coherent state? How does such a state look like in Fock space? Why do we need them? (Bosonic)
Published	11/29/2023	What must be fulfiled in the grassmann algebra?
Published	11/29/2023	How is a fermionic coherent state defined? Is it in the fock space? Why do we need it?
Published	11/29/2023	What is the concept of a functional field integral in the context of field theory? What is the goal and why?
Published	11/29/2023	What is the Matsubara frequency representation?
Published	11/29/2023	Simple sketch: How do you express the transition amplitude (time evolution) from arbitrary states \(\ket\phi\) with the help of path integra…
Published	11/29/2023	What are Matsubara summations? Wh do we need them? How do we perform them?
Published	11/29/2023	What is one of the most relevant time-ordered correlation functions? What does it tells you? What does a wick rotation do to the function?
Published	11/29/2023	What is the only known case of a phase transition in absence of any interactions?
Published	11/29/2023	What changes by introducing weak interaction compared to no interactions in the Weakly Bose system?
Published	11/29/2023	What is important so that the saddle point approximation holds?
Published	12/01/2023	What are offdiagnal long-range order?
Published	12/01/2023	What does a phase gradient generall mean?
Published	12/01/2023	What does the Landau Criterium state?
Status	Last Update	Fields