.... This chapter discusses the perturbative calculation of correlation or vertex functions expressed in terms of field (functional) integrals. The successive contributions to the perturbative expansion are Gaussian expectation values which can be calculated with the help, for example, of Wick′s theorem and which...

... functional fermionic theory perturbative expansion functional integral functional determinant In this chapter, we consider an alternative approach to the quantization of fields. This approach will be critically important to the development of quantum field theory in curved space, which is the subject...

...Random Tensors. Razvan Gheorghe Gurau. © Razvan Gheorghe Gurau 2017. Published 2017 by Oxford University Press. This chapter presents the perturbative expansion of invariant tensor measures in terms of Feynman graphs. It is shown that, assuming that the perturbation and the Gaussian part scale...

... of a loop-expansion parameter, are divergent series. anharmonic oscillator large degenerate minima Landau ghost renormalon fermion quantum perturbative expansion large orders instanton divergent series barrier penetration quantum mechanics (QM) quantum field theory (QFT) In quantum field theory...

... in Grassmann algebras, Gaussian integrals and perturbative expansion, partition function, and quantum Fermi gas. fermions Grassmann algebra Clifford algebra Wick's theorem Grassmann analytic function Grassmann δ function vacuum annihilation and creation operators fermion creation annihilation symmetry...

... space. Quantum evolution (that is, in real time) is introduced, after which a path integral representation of the scattering matrix is constructed. From this S matrix, the standard perturbative expansion in powers of the potential is recovered. Even the evolution of a free quantum...

...-expansion, but from the perturbative expansion of the non-critical field theory (but in the critical domain) directly in d = 3 (following a suggestion of Parisi (1973)), because the evaluation of the successive terms of the perturbative expansion is easier. For example, the functions...