3 Non-Fock Representations

2008 ◽  
pp. 81-87
Author(s):  
Franco Strocchi
Keyword(s):  
Fock Representations

scholarly journals The kernel of Fock representations of Wick algebras with braided operator of coefficients

2001 ◽  
Vol 198 (1) ◽  
pp. 109-123 ◽  
Author(s):  
Palle E. T. Jørgensen ◽  
Daniil P. Proskurin ◽  
Yuriĭ S. Samoĭlenko
Keyword(s):  
Fock Representations

scholarly journals Boson fock representations of stochastic processes

2000 ◽  
Vol 67 (1) ◽  
pp. 3-11 ◽  
Author(s):  
L. Accardi ◽  
T. Hida ◽  
W. W. Htay
Keyword(s):  
Stochastic Processes ◽  
Fock Representations

scholarly journals Hamiltonian Renormalization V: Free Vector Bosons

2021 ◽  
Vol 7 ◽  
Author(s):  
K. Liegener ◽  
T. Thiemann
Keyword(s):  
Quantum Gravity ◽  
Coarse Graining ◽  
Scalar Fields ◽  
Recent Proposal ◽  
Fock Representation ◽  
Vector Bosons ◽  
Free Scalar ◽  
Fock Representations ◽  
Canonical Quantum Gravity ◽  
Canonical Quantum

In a recent proposal we applied methods from constructive QFT to derive a Hamiltonian Renormalization Group in order to employ it ultimately for canonical quantum gravity. The proposal was successfully tested for free scalar fields and thus a natural next step is to test it for free gauge theories. This can be done in the framework of reduced phase space quantization which allows using techniques developed earlier for scalar field theories. In addition, in canonical quantum gravity one works in representations that support holonomy operators which are ill defined in the Fock representation of say Maxwell or Proca theory. Thus, we consider toy models that have both features, i.e. which employ Fock representations in which holonomy operators are well-defined. We adapt the coarse graining maps considered for scalar fields to those theories for free vector bosons. It turns out that the corresponding fixed pointed theories can be found analytically.

scholarly journals Fock representations of multicomponent (particularly non-Abelian anyon) commutation relations

2019 ◽  
Vol 32 (05) ◽  
pp. 2030004
Author(s):  
Alexei Daletskii ◽  
Alexander Kalyuzhny ◽  
Eugene Lytvynov ◽  
Daniil Proskurin
Keyword(s):  
Linear Operator ◽  
Fock Space ◽  
Multicomponent System ◽  
Baxter Equation ◽  
Special Choice ◽  
Bounded Linear ◽  
Creation And Annihilation Operators ◽  
Commutation Relations ◽  
System A ◽  
Fock Representations

Let [Formula: see text] be a separable Hilbert space and [Formula: see text] be a self-adjoint bounded linear operator on [Formula: see text] with norm [Formula: see text], satisfying the Yang–Baxter equation. Bożejko and Speicher ([10]) proved that the operator [Formula: see text] determines a [Formula: see text]-deformed Fock space [Formula: see text]. We start with reviewing and extending the known results about the structure of the [Formula: see text]-particle spaces [Formula: see text] and the commutation relations satisfied by the corresponding creation and annihilation operators acting on [Formula: see text]. We then choose [Formula: see text], the [Formula: see text]-space of [Formula: see text]-valued functions on [Formula: see text]. Here [Formula: see text] and [Formula: see text] with [Formula: see text]. Furthermore, we assume that the operator [Formula: see text] acting on [Formula: see text] is given by [Formula: see text]. Here, for a.a. [Formula: see text], [Formula: see text] is a linear operator on [Formula: see text] with norm [Formula: see text] that satisfies [Formula: see text] and the spectral quantum Yang–Baxter equation. The corresponding creation and annihilation operators describe a multicomponent quantum system. A special choice of the operator-valued function [Formula: see text] in the case [Formula: see text] determines non-Abelian anyons (also called plektons). For a multicomponent system, we describe its [Formula: see text]-deformed Fock space and the available commutation relations satisfied by the corresponding creation and annihilation operators. Finally, we consider several examples of multicomponent quantum systems.

Sign in / Sign up

Export Citation Format

Share Document