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Lecture# Non-Perturbative Energy Splitting in Symmetric Potentials

Description

This lecture covers the derivation of the instanton pre-factor and the general formula for non-perturbative energy splitting in arbitrary symmetric potentials with degenerate minima, illustrated with examples. The discussion includes the concept of saddle points, the double well potential, dilute instanton gas approximation, and the twisted partition function. The lecture concludes with exercises demonstrating the simplification of expressions and the application of classical quantities to fully express energy splitting.

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In course

PHYS-426: Quantum physics IV

Introduction to the path integral formulation of quantum mechanics. Derivation of the perturbation expansion of Green's functions in terms of Feynman diagrams. Several applications will be presented,

Related concepts (25)

Representation theory of the symmetric group

In mathematics, the representation theory of the symmetric group is a particular case of the representation theory of finite groups, for which a concrete and detailed theory can be obtained. This has a large area of potential applications, from symmetric function theory to quantum chemistry studies of atoms, molecules and solids. The symmetric group Sn has order n!. Its conjugacy classes are labeled by partitions of n.

Symmetric group

In abstract algebra, the symmetric group defined over any set is the group whose elements are all the bijections from the set to itself, and whose group operation is the composition of functions. In particular, the finite symmetric group defined over a finite set of symbols consists of the permutations that can be performed on the symbols. Since there are ( factorial) such permutation operations, the order (number of elements) of the symmetric group is .

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