Quantum field theory for discrepancies

Quantum field theory for discrepancies

The concept of discrepancy plays an important rôle in the study of uniformity properties of point sets. For sets of random points, the discrepancy is a random variable. We apply techniques from quantum field theory to translate the problem of calculating the probability density of (quadratic) discrepancies into that of evaluating certain path integrals. Both their perturbative and non-perturbat...

Quantum field theory for discrepancies II: 1/N corrections using fermions

We calculate the 1/N corrections to the probability distributions of quadratic discrepancies for sets of N random points. This is achieved by the introduction of fermionic variables. We give the diagrammatic expansion up to and including the second order in 1/N . For some discrepancies, we give the explicit expansion to first order. [email protected] [email protected] [email protected]...

Field beables for quantum field theory

The deBroglie-Bohm pilot-wave theory is an interpretation of quantum theory in which the observer plays no fundamental role. In a pilot-wave theory, quantum systems are not only described by the state vector, but also by some additional variables. These additional variables, also called beables, can be particle positions, field configurations, strings, etc. In this paper we focus our attention ...

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