Related papers: Fock space methods and large N
Recent progress in mathematical theory of random processes provides us with non-Fock product systems (continuous tensor products of Hilbert spaces) used here for constructing a toy model for fermions. Some state vectors describe infinitely…
The concept of a "space of quantum field theories" or "theory space" was set out in the 1970's in work of Wilson, Friedan and others. This structure should play an important role in organizing and classifying QFTs, and in the study of the…
The study of topological quantum field theories increasingly relies upon concepts from higher-dimensional algebra such as n-categories and n-vector spaces. We review progress towards a definition of n-category suited for this purpose, and…
We show how to construct general probabilistic theories that contain an energy observable dependent on position and momentum. The construction is in accordance with classical and quantum theory and allows for physical predictions, such as…
Non-Fock representations of the canonical commutation relations modeled over an infinite-dimensional nuclear space are constructed in an explicit form. The example of the nuclear space of smooth real functions of rapid decrease results in…
Classical objects have been excluded as subjects of the observed quantum properties, and the related problem of the nature of quantum objects has been suspended since the early days of Quantum Theory. Recent experiments show that the…
Quantum field theory has been shown recently renormalizable on flat Moyal space and better behaved than on ordinary space-time. Some models at least should be completely finite, even beyond perturbation theory. In this paper a first step is…
For decades, a lot of work has been devoted to the problem of constructing a non-trivial quantum field theory in four-dimensional space time. This letter addresses the attempts to construct an algebraic quantum field theory in the framework…
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…
Recently it was shown that an asymptotic behaviour of $SU(N)$ gauge theory for large $N$ is described by q-deformed quantum field. The master fields for large N theories satisfy to standard equations of relativistic field theory but fields…
We propose a formulation of quantum mechanics in an extended Fock space in which a tensor product structure is applied to time. Subspaces of histories consistent with the dynamics of a particular theory are defined by a direct quantum…
A representation of the conformal Newton-Hooke algebra on a phase space of n particles in arbitrary dimension which interact with one another via a generic conformal potential and experience a universal cosmological repulsion or attraction…
Conventional transport theory is not really applicable to non-equilibrium systems which exhibit strong quantum effects. We present two different approaches to overcome this problem. Firstly we point out how transport equations may be…
We adopt a geometric perspective on Fock space to provide two complementary insights into the eigenstates in many-body-localized fermionic systems. On the one hand, individual many-bodylocalized eigenstates are well approximated by a Slater…
A harmonic oscillator is an indefinite-frequency one if the parameter $\omega$ is replaced by an operator. An ensemble of $N$ such oscillators may be regarded as a toy model of a bosonic quantum field. All the possible frequencies…
Relational particle models are useful toy models for quantum cosmology and the problem of time in quantum general relativity. This paper shows how to extend existing work on concrete examples of relational particle models in 1-d to include…
Motivated by recent discussions of the string-theory landscape, we propose field-theoretic realizations of models with large numbers of vacua. These models contain multiple U(1) gauge groups, and can be interpreted as deconstructed versions…
Collective operators that describe interaction of generic quantum system with discrete spectrum with a quantum field are investigated. These operators, considered as operators in the entangled Fock space (space generated by action of…
A previously proposed algebra of asymptotic fields in quantum electrodynamics is formulated as a net of algebras localized in regions which in general have unbounded spacelike extension. Electromagnetic fields may be localized in…
The pseudospherical functions on one-sheet, two-dimensional hyperboloid are discussed. The simplest method of construction of these functions is introduced using the Fock space structure of the representation space of the su(1,1) algebra.…