Titlebook: Statistical Approach to Quantum Field Theory; An Introduction Andreas Wipf Book 2021Latest edition The Editor(s) (if applicable) and The Au

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Path Integrals in Quantum and Statistical Mechanics,There exist three apparently different formulations of quantum mechanics: Heisenberg’s matrix mechanics, Schrödinger’s wave mechanics, and Feynman’s path integral approach. In contrast to matrix and wave mechanics, which are based on the Hamiltonian approach, the latter is based on the Lagrangian approach.

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Mean Field Approximation,Since only a few lattice models can be solved explicitly, one is interested in efficient approximation schemes. A simple and universally applicable approximation is the mean field approximation (MFA) which yields qualitatively correct results for many lattice systems.

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Renormalization Group on the Lattice,Previously we considered a variety of equilibrium systems which undergo second-order phase transitions. In this chapter we will show how the idea of scaling leads to a universal theory of critical phenomena, and we will derive some exact results for order-disorder transitions.

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Lattice Gauge Theories,According to present-day knowledge, . in nature are described by .. The best known example is electrodynamics with Abelian symmetry group U(1). In contrast, the electroweak and the strong interactions are modeled by gauge theories with the non-Abelian symmetry groups SU(2)×U(1) and SU(3), respectively.

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Interacting Fermions,In this chapter we study interacting four-Fermi theories in two and three spacetime dimension. Their Lagrangian density contains—besides the ubiquitous Dirac term .—a Lorentz invariant interaction term with four powers of the Fermi field.

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Scalar Fields at Zero and Finite Temperature,in quantum field theory. Even more important than their educational value is their role in the electroweak theory, where a scalar field interacts with the fields of leptons, quarks, and gauge bosons. The scalar field is needed for the Higgs mechanism which is essential to explain the mass generation for fermions and electroweak gauge bosons.