CLASSICAL FIELD THEORY: ADVANCED MATHEMATICAL FORMULATION

Classical Field Theory

a) Energy-momentum Based on Noether’s theorem, construct the energy-momentum tensor for classical electromagnetism from the above Lagrangian. Note that the usual procedure does not result in a symmetric tensor. To remedy that, we can add to T μν a term of the form ∂λK λμν , where K is antisymmetric in its first two indices. Such an object is automatically divergenceless, so T̂ μν = T μν + ∂λK λμ...

Ostrogradski formulation of field theory

We present a method for the Hamiltonian formulation of field theories that are based on Lagrangians containing second derivatives. The new feature of our formalism is that all four partial derivatives of the field variables are initially considered as independent fields, in contrast to the conventional Ostrogradski method, where only the velocity is turned into an independent field variable. Th...

Classical mathematical structures within topological graph theory

Finite simple graphs are a playground for classical areas of mathematics. We illustrate this by looking at some results.

Advanced Quantum Field Theory

1 Basic formalism for interacting theories 4 1.1 Perturbative approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.2 Correlation functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.3 Diagrammatics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.4 Asymptotic states and S-matrix . . . . . . . . . . . . . . . . . . . . . . . . . 6...

A field theory formulation of polymer networks