scholarly journals THE CHARGE QUANTUM NUMBERS OF GAUGE INVARIANT QUASI-FREE ENDOMORPHISMS

2000 ◽  
Vol 12 (11) ◽  
pp. 1531-1549
Author(s):  
CARSTEN BINNENHEI
Keyword(s):  
Hilbert Spaces ◽  
Fock Space ◽  
Space Structure ◽  
Two Dimensions ◽  
Dirac Field ◽  
Quantum Field ◽  
Basic Representation ◽  
Quantum Numbers ◽  
Local Quantum ◽  
Tensor Powers

The representations of a group of gauge automorphisms of the canonical commutation or anticommutation relations which appear on the Hilbert spaces of isometries Hϱ implementing quasi-free endomorphisms ϱ on Fock space are studied. Such a representation, which characterizes the "charge" of ϱ in local quantum field theory, is determined by the Fock space structure of Hϱ itself: Together with a "basic" representation of the group, all higher symmetric or antisymmetric tensor powers thereof also appear. Hence ϱ is reducible unless it is an automorphism. It is further shown by the example of the massless Dirac field in two dimensions that localization and implementability of quasi-free endomorphisms are compatible with each other.

RAINBOW STATISTICS

2009 ◽  
Vol 24 (25n26) ◽  
pp. 4623-4641 ◽  
Author(s):  
MICHELE ARZANO ◽  
DARIO BENEDETTI
Keyword(s):  
Quantum Group ◽  
Hilbert Spaces ◽  
Group Symmetry ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Additional Structure ◽  
Local Quantum ◽  
Group Symmetries ◽  
Noncommutative Quantum

Noncommutative quantum field theories and their global quantum group symmetries provide an intriguing attempt to go beyond the realm of standard local quantum field theory. A common feature of these models is that the quantum group symmetry of their Hilbert spaces induces additional structure in the multiparticle states which reflects a nontrivial momentum-dependent statistics. We investigate the properties of this "rainbow statistics" in the particular context of κ-quantum fields and discuss the analogies/differences with models with twisted statistics.

scholarly journals Essential spectrum of a fermionic quantum field model

2014 ◽  
Vol 17 (04) ◽  
pp. 1450024 ◽  
Author(s):  
Toshimitsu Takaesu
Keyword(s):  
State Space ◽  
Essential Spectrum ◽  
Fock Space ◽  
Adjoint Operator ◽  
The State ◽  
Dirac Field ◽  
Quantum Field ◽  
Interaction System ◽  
Tensor Product Space ◽  
Klein Gordon

An interaction system of a fermionic quantum field is considered. The state space is defined by a tensor product space of a fermion Fock space and a Hilbert space. It is assumed that the total Hamiltonian is a self-adjoint operator on the state space and bounded from below. Then it is proven that a subset of real numbers is the essential spectrum of the total Hamiltonian. It is applied to a Yukawa interaction system, which is a system of a Dirac field coupled to a Klein–Gordon, and the HVZ theorem is obtained.

scholarly journals On the interacting Free Fock space and the deformed Wigner law

1997 ◽  
Vol 145 ◽  
pp. 1-28 ◽  
Author(s):  
Y. G. Lu
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Hilbert Spaces ◽  
Fock Space ◽  
Basic Structure ◽  
Stochastic Calculus ◽  
Quantum Field ◽  
Complex Field ◽  
Quantum Stochastic Calculus ◽  
Direct Sum

The Fock space is a basic structure for the quantum field theory and quantum stochastic calculus. In all the cases, a Fock space can be described as a direct sum of a sequence of some Hilbert spaces, i.e. a Fock space has the form of , where, is the complex field and is a given Hilbert space.

QUANTUM FIELD THEORIES OF STRONG INTERACTIONS

2010 ◽  
Vol 25 (17) ◽  
pp. 1403-1405
Author(s):  
YOSHIO YAMAGUCHI
Keyword(s):  
Fock Space ◽  
Bound State ◽  
Strong Interactions ◽  
Particle State ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Quantum Numbers ◽  
Physical Particle ◽  
Space State ◽  
The One

Strong interactions are described by the Quantum Field Theory due to Heisenberg–Pauli. We postulate that the one particle physical states with appropriate quantum numbers (fermions and bosons) must be expressed by the normalized Fock space state vectors, which can conveniently be (and approximately) calculated in their rest frame, using Tamm–Dancoff variational method. Interactions between two physical particles can be analyzed by the same Hamiltonian as for each physical particle state, similar to analyzing nucleus–nucleus collisions. Our theories are free from any ultraviolet divergency. Our one physical particle state is similar to bound state in quantum mechanics.

scholarly journals ANALYTIC INVARIANT CHARGE IN QCD

2003 ◽  
Vol 18 (30) ◽  
pp. 5475-5519 ◽  
Author(s):  
A. V. NESTERENKO
Keyword(s):  
Perturbative Expansion ◽  
Quantum Field ◽  
Perturbative Approach ◽  
Interaction Processes ◽  
Running Coupling ◽  
Wide Range ◽  
Local Quantum ◽  
Concrete Realization ◽  
Β Function ◽  
Analytic Invariant

This paper gives an overview of recently developed model for the QCD analytic invariant charge. Its underlying idea is to bring the analyticity condition, which follows from the general principles of local Quantum Field Theory, in perturbative approach to renormalization group (RG) method. The concrete realization of the latter consists in explicit imposition of analyticity requirement on the perturbative expansion of β function for the strong running coupling, with subsequent solution of the corresponding RG equation. In turn, this allows one to avoid the known difficulties originated in perturbative approximation of the RG functions. Ultimately, the proposed approach results in qualitatively new properties of the QCD invariant charge. The latter enables one to describe a wide range of the strong interaction processes both of perturbative and intrinsically nonperturbative nature.

Variational formulation of relativistic four-body systems in quantum field theory: scalar quadronium

2002 ◽  
Vol 80 (5) ◽  
pp. 605-612
Author(s):  
B Ding ◽  
J W Darewych
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Fock Space ◽  
Hamiltonian Formalism ◽  
Massless Scalar ◽  
Massless Scalar Field ◽  
Quantum Field ◽  
Scalar Particles ◽  
Pairwise Interactions ◽  
Approximate Wave

We discuss a variational method for describing relativistic four-body systems within the Hamiltonian formalism of quantum field theory. The scalar Yukawa (or Wick–Cutkosky) model, in which scalar particles and antiparticles interact via a massive or massless scalar field, is used to illustrate the method. A Fock-space variational trial state is used to describe the stationary states of scalar quadronium (two particles and two antiparticles) interacting via one-quantum exchange and virtual annihilation pairwise interactions. Numerical results for the ground-state mass and approximate wave functions of quadronium are presented for various strengths of the coupling, for the massive and massless quantum exchange cases. PACS Nos.: 11.10Ef, 11.10St, 03.70+k, 03.65Pm

scholarly journals THE LOCALLY COVARIANT DIRAC FIELD

2010 ◽  
Vol 22 (04) ◽  
pp. 381-430 ◽  
Author(s):  
KO SANDERS
Keyword(s):  
Energy Momentum Tensor ◽  
Momentum Tensor ◽  
Dirac Field ◽  
Quantum Field ◽  
Geometric Constructions ◽  
Covariant Quantum ◽  
Dimensional Spacetime ◽  
Stress Energy ◽  
Hadamard States ◽  
Stress Energy Momentum Tensor

We describe the free Dirac field in a four-dimensional spacetime as a locally covariant quantum field theory in the sense of Brunetti, Fredenhagen and Verch, using a representation independent construction. The freedom in the geometric constructions involved can be encoded in terms of the cohomology of the category of spin spacetimes. If we restrict ourselves to the observable algebra, the cohomological obstructions vanish and the theory is unique. We establish some basic properties of the theory and discuss the class of Hadamard states, filling some technical gaps in the literature. Finally, we show that the relative Cauchy evolution yields commutators with the stress-energy-momentum tensor, as in the scalar field case.

scholarly journals A thermodynamic origin for the Cohen-Kaplan-Nelson bound

2021 ◽  
Author(s):  
Satish Ramakrishna
Keyword(s):  
General Relativity ◽  
Free Energy ◽  
Equation Of State ◽  
Density Of States ◽  
Canonical Ensemble ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Local Quantum ◽  
The Universe

Abstract The Cohen-Kaplan-Nelson bound is imposed on the grounds of logical consistency (with classical General Relativity) upon local quantum field theories. This paper puts the bound into the context of a thermodynamic principle applicable to a field with a particular equation of state in an expanding universe. This is achieved without overtly appealing to either a decreasing density of states or a minimum coupling requirement, though they might still be consistent with the results described. The paper establishes that the holographic principle applied to cosmology is consistent with minimizing the free energy of the universe in the canonical ensemble, upon the assumption that the ultraviolet cutoff is a function of the causal horizon scale.

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