Supergeometry and Quantum Field Theory, or: What is a Classical Configuration?

What Is a Quantum Field Theory ?

Introduction. Quantum field theory began in 1927 with a paper by Dirac [1] in which he sought a framework that would unite the classical electromagnetism of Maxwell with quantum mechanics. Ever since then it has been under continuous scrutiny by physicists, which illustrates the fact that in some ways, physics is more highly focused than mathematics. A mathematician is not forced to work on the...

Classical or Quantum ? What is Reality ?

ar X iv : h ep - t h / 96 07 13 2 v 1 1 6 Ju l 1 99 6 SUPERGEOMETRY AND QUANTUM FIELD THEORY , OR : WHAT IS A CLASSICAL CONFIGURATION ?

We discuss of the conceptual difficulties connected with the anticommutativity of classical fermion fields, and we argue that the ”space” of all classical configurations of a model with such fields should be described as an infinite-dimensional supermanifold M . We discuss the two main approaches to supermanifolds, and we examine the reasons why many physicists tend to prefer the Rogers approac...

What is the Simplest Quantum Field Theory?

Conventional wisdom says that the simpler the Lagrangian of a theory the simpler its perturbation theory. An ever-increasing understanding of the structure of scattering amplitudes has however been pointing to the opposite conclusion. At tree level, the BCFW recursion relations that completely determine the S-matrix are valid not for scalar theories but for gauge theories and gravity, with grav...

Classical and Quantum Causality in Quantum Field Theory

Based on a number of experimentally verified physical observations, it is argued that the standard principles of quantum mechanics should be applied to the Universe as a whole. Thus, a paradigm is proposed in which the entire Universe is represented by a pure state wavefunction contained in a factorisable Hilbert space of enormous dimension, and where this statevector is developed by successive...