A $P\left( \phi \right)$ quantum field theory

Quantum Field Theory Course

Part I. Classical Mechanics 9 0. Intro 9 0.1. Mechanical systems 9 0.2. Lagrangian and Hamiltonian formulation 9 1. Lagrangian approach 10 1.1. Manifolds 10 1.2. Differentiation 11 1.3. Calculus of Variations on an interval 11 1.4. Lagrangian reformulation of Newton‘s equation 13 2. Hamiltonian approach 14 2.1. Metrics: linear algebra 14 2.2. The passage to the cotangent vector bundle via the k...

Relativistic Quantum Field Theory

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...

Quantum Field Theory

closed curve C ). This implies F = −∇V for some potential function V . (Think of V as potential energy.) The total energy is E = T + V with T the kinetic energy T = 1 2 ∑ mi |vi| . The total energy is conserved because of the second law, because dE dt = mv · dv dt +∇V · dx dt = (ma− F ) · v = 0. In Hamiltonian mechanics, momentum p = mv is used instead of v as a primary object. The Hamiltonian ...

Topological Quantum Field Theory

A twisted version of four dimensional supersymmetric gauge theory is formulated. The model, which refines a nonrelativistic treatment by Atiyah, appears to underlie many recent developments in topology of low dimensional manifolds; the Donaldson polynomial invariants of four manifolds and the Floer groups of three manifolds appear naturally. The model may also be interesting from a physical vie...