Related papers: Quantum field theory on affine bundles
We introduce the notion of locally trivial quantum principal bundles. The base space and total space are compact quantum spaces (unital $C^{\star}$-algebras), the structure group is a compact matrix quantum group. We prove that a quantum…
This paper proposes a refinement of the usual concept of algebraic quantum field theories (AQFTs) to theories that are smooth in the sense that they assign to every smooth family of spacetimes a smooth family of observable algebras. Using…
In this paper we develop the theory of reduction of quantum principal bundles over projective bases. We show how the sheaf theoretic approach can be effectively applied to certain relevant examples as the Klein model for the projective…
Realizing bosonic field v(x) as current of massless (chiral) fermions we derive hierarchy of quantum polynomial interactions of the field v(x) that are completely integrable and lead to linear evolutions for the fermionic field. It is…
A geometric framework for describing quantum particles on a possibly curved background is proposed. Natural constructions on certain distributional bundles (`quantum bundles') over the spacetime manifold yield a quantum ``formalism'' along…
Electromagnetism is the paradigm case of a theory that satisfies relativistic locality. This can be proven by demonstrating that, once the theory's laws are imposed, what is happening within a region fixes what will happen in the…
A method of constructing a canonical gauge invariant quantum formulation for a non-gauge classical theory depending on a set of parameters is advanced and then applied to the theory of closed bosonic string interacting with massive…
It is shown how to map the quantum states of a system of free scalar particles one-to-one onto the states of a completely deterministic model. It is a classical field theory with a large (global) gauge group. The mapping is now also applied…
Affine coherent states are generated by affine kinematical variables much like canonical coherent states are generated by canonical kinematical variables. Although all classical and quantum formalisms normally entail canonical variables, it…
A realistic axiomatic formulation of Galilean Quantum Field Theories is presented, from which the most important theorems of the theory can be deduced. In comparison with others formulations, the formal aspect has been improved by the use…
In this article a non--technical survey is given of the present status of Axiomatic Quantum Field Theory and interesting future directions of this approach are outlined. The topics covered are the universal structure of the local algebras…
We develop a reformulation of the functional integral for bosons in terms of bilocal fields. Correlation functions correspond to quantum probabilities instead of probability amplitudes. Discrete and continuous global symmetries can be…
The requirement of general covariance of quantum field theory (QFT) naturally leads to quantization based on the manifestly covariant De Donder-Weyl formalism. To recover the standard noncovariant formalism without violating covariance,…
An effective formalism for white noise analysis, conceptually equivalent to Wilsonian renormalization theory, is introduced. Space-time gets represented by a boolean lattice of coarse regions, energy scales become space-time partitions by…
Goal of this review is to introduce the algebraic approach to quantum field theory on curved backgrounds. Based on a set of axioms, first written down by Haag and Kastler, this method consists of a two-step procedure. In the first one, a…
We extend the recently developed kinematical framework for diffeomorphism invariant theories of connections for compact gauge groups to the case of a diffeomorphism invariant quantum field theory which includes besides connections also…
We propose a geometric setting of the axiomatic mathematical formalism of quantum theory. Guided by the idea that understanding the mathematical structures of these axioms is of similar importance as was historically the process of…
We introduce a higher dimensional generalization of the affine Kac-Moody algebra using the language of factorization algebras. In particular, on any complex manifold there is a factorization algebra of "currents" associated to any Lie…
A generalization of the Heisenberg algebra has been recently constructed. This generalized algebra has a characteristic function which depends on one of its generators. When this function is linear, $qJ_0+s$, it is possible to construct a…
We implement in the formal language of homotopy type theory a new set of axioms called cohesion. Then we indicate how the resulting cohesive homotopy type theory naturally serves as a formal foundation for central concepts in quantum gauge…