Related papers: Spaces of Quantum Field Theories
A pedagogical introduction to the theory of a gaussian scalar field which shows firstly, how the whole theory is encapsulated in the Wightman function $W(x,y)=\langle\phi(x)\phi(y)\rangle$ regarded abstractly as a two-index tensor on the…
It is generally taken for granted that two-dimensional critical phenomena can be fully classified by the well known two-dimensional (rational) conformal quantum field theories (CQFTs). In particular it is believed that in models with a…
Till now, the foundation of quantum physics is still mysterious. To explore the mysteries in the foundation of quantum physics, people always take it for granted that quantum processes must be some types of fields/objects on a rigid space.…
In the present article we display a new constructive quantum field theory approach to quantum gauge field theory, utilizing the recent progress in the integration theory on the moduli space of generalized connections modulo gauge…
The worldline approach to Quantum Field Theory (QFT) allows to efficiently compute several quantities, such as one-loop effective actions, scattering amplitudes and anomalies, which are linked to particle path integrals on the circle. A…
The functorial mathematical definition of conformal field theory was first formulated approximately 30 years ago. The underlying geometric category is based on the moduli space of Riemann surfaces with parametrized boundary components and…
For a quantum field living on a non - static spacetime no instantaneous Hamiltonian is definable, for this generically necessitates a choice of inequivalent representation of the canonical commutation relations at each instant of time. This…
Mostly self-contained script on functorial topological quantum field theories. These notes give a slow introduction to the basic notions of category theory which serve a closer investigation of cobordisms and (commutative) Frobenius…
This paper is a programmatic article presenting an outline of a new view of the foundations of quantum mechanics and quantum field theory. In short, the proposed foundations are given by the following statements: * Coherent quantum physics…
Talk presented at the conference ``Historical and Philosophical Reflections on the Foundations of Quantum Field Theory,'' at Boston University, March 1996. It will be published in the proceedings of this conference.
We comment on the present status, the concepts and their limitations, and the successes and open problems of the various approaches to a relativistic quantum theory of elementary particles, with a hindsight to questions concerning quantum…
Quantum-matter theory (QMT), based on the Schr\"odinger or Dirac equations, is firmly established for both intra- and intermolecular interactions. However, there are two key issues with QMT. First, its applicability to large molecular…
A new application of quantum field theory is developed that gives a description of the internal dynamics of dressed elementary particles and predicts their masses. The fermionic and bosonic quantum fields are treated as interdependent…
Topological qauntum field theory(TQFT) is a very powerful theoretical tool to study topological phases and phase transitions. In $2+1$D, it is well known that the Chern-Simons theory captures all the universal topological data of…
The space of continuous states of perturbative interacting quantum field theories in globally hyperbolic curved spacetimes is determined. Following Brunetti and Fredenhagen, we first define an abstract algebra of observables which contains…
In order to better understand quantum field theory we present some toy models on finite dimensional Hilbert spaces. We discuss how these models converge to a discrete spacetime version of quantum field theory. We first define toy fermion,…
The rather unintuitive nature of quantum theory has led numerous people to develop sets of (physically motivated) principles that can be used to derive quantum mechanics from the ground up, in order to better understand where the structure…
This work has a methodological nature and is a set of lecture notes for undergraduate students. It is devoted to the study of the basic tools of quantum field theory on the example of the simplest cubic "toy" model. We introduce such…
Two singularity theorems can be proven if one attempts to let a Lorentzian cobordism interpolate between two topologically distinct manifolds. On the other hand, Cartier and DeWitt-Morette have given a rigorous definition for quantum field…
Parametrized field theories, which are generally covariant versions of ordinary field theories, are studied from the point of view of the covariant phase space: the space of solutions of the field equations equipped with a canonical…