Related papers: Quantum Field Theory on Fock Projective Space
In this article we propose a `second quantization' scheme especially suitable to deal with non-trivial, highly symmetric phase spaces, implemented within a more general Group Approach to Quantization, which recovers the standard Quantum…
We study a class of dynamical systems for which the motions can be described in terms of geodesics on a manifold (ordinary potential models can be cast into this form by means of a conformal map). It is rigorously proven that the geodesic…
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…
The basic ideas of second quantization and Fock space are extended to density operator states, used in treatments of open many-body systems. This can be done for fermions and bosons. While the former only requires the use of a…
Quantum theory of the free Maxwell field in Minkowski space is constructed using a representation in which the self dual connection is diagonal. Quantum states are now holomorphic functionals of self dual connections and a decomposition of…
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…
I construct lowest-energy representations of non-centrally extended algebras of Noether symmetries, including diffeomorphisms and reparametrizations of the observer's trajectory. This may be viewed as a new scheme for quantization. First…
Quantum theory of field (extended) objects without a priori space-time geometry has been represented. Intrinsic coordinates in the tangent fibre bundle over complex projective Hilbert state space $CP(N-1)$ are used instead of space-time…
Quantum physics on manifolds with boundary brings novel aspects due to boundary conditions. One important feature is the appearance of localised negative eigenmodes for the Laplacian on the boundary. These can potentially lead to…
The framework of locally covariant quantum field theory is discussed, motivated in part using "ignorance principles". It is shown how theories can be represented by suitable functors, so that physical equivalence of theories may be…
We further investigate postulates for realist versions of relativistic quantum theory and quantum field theory in Minkowski space and other background space-times. According to these postulates, quantum theory is supplemented by local…
A mathematically well-defined, manifestly covariant theory of classical and quantum field is given, based on Euclidean Poisson algebras and a generalization of the Ehrenfest equation, which implies the stationary action principle. The…
Quantum field theory (QFT) on non-stationary spacetimes is well understood from the side of the algebra of observables. The state space, however, is largely unexplored, due to the non-existence of distinguished states (vacuum, scattering…
The symmetrization postulate and the associated Bose/Fermi (anti)-commutators for field mode operators are among the pillars on which local quantum field theory lays its foundations. They ultimately determine the structure of Fock space and…
There exists a physically well motivated method for approximating manifolds by certain topological spaces with a finite or a countable set of points. These spaces, which are partially ordered sets (posets) have the power to effectively…
Nature allows one to explore a manifold of remarkable quantum effects. Most prominently, quantum entanglement can be observed in many-particle systems, between multiple quantized fields, and in hybrid combinations thereof. This diversity,…
It is shown that in the model [3,4] of quantum mechanics besides probability amplitudes, the Planck constant and the Fock space, the cosmological constant also appear in the natural way. The Poisson brackets are generalized for the case of…
We advocate that the dual picture of spacetime noncommutativity , i.e. the existence of a curved momentum space, could be a way out to solve some of the open conceptual problems in the field, such as the basis dependence of observables. In…
It is shown that quantization of the dynamical systems with second class constraints actually can be reduced to quantization of the systems with first class constraints. The motion of the non-relativistic particle along the plane curve and…
We present a simple geometric construction linking geometric to deformation quantization. Both theories depend on some apparently arbitrary parameters, most importantly a polarization and a symplectic connection, and for real polarizations…