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.

GROUND STATE OF THE YUKAWA MODEL WITH CUTOFFS

2011 ◽  
Vol 14 (02) ◽  
pp. 225-235 ◽  
Author(s):  
TOSHIMITSU TAKAESU
Keyword(s):  
Ground State ◽  
Spectral Gap ◽  
Fock Space ◽  
Adjoint Operator ◽  
Coupling Constants ◽  
Dirac Field ◽  
Yukawa Model ◽  
Klein Gordon

The ground state of the Yukawa model is considered. The Yukawa model describes the system of a Dirac field interacting with a Klein–Gordon field. By introducing ultraviolet cutoffs and spatial cutoffs, the total Hamiltonian is defined as a self-adjoint operator on a boson–fermion Fock space. It is shown that the total Hamiltonian has a positive spectral gap for all values of coupling constants. In particular, the existence of the ground state is proven.

IS THE MILNE COORDINATE SYSTEM A GOOD ONE?

1994 ◽  
Vol 09 (01) ◽  
pp. 19-27 ◽  
Author(s):  
R.C. ARCURI ◽  
B.F. SVAITER ◽  
N.F. SVAITER
Keyword(s):  
Field Theory ◽  
Coordinate System ◽  
Gordon Equation ◽  
Fock Space ◽  
Flat Space ◽  
The Other ◽  
Quantum Field ◽  
System A ◽  
Klein Gordon ◽  
Klein Gordon Equation

The upper and lower quadrants of flat space-time can be described using the Milne coordinate system. The Klein-Gordon equation of a scalar field in such a coordinate system admits at least two sets of solutions. Based on the Feynman propagator behavior it is shown that only one of the two sets gives the conventional interpretation of quantum field theory, based on a Fock space. Therefore, discarding the other set, one can still keep the Milne coordinate system.

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.

scholarly journals Self-adjoint time operator of a quantum field

2020 ◽  
Vol 18 (01) ◽  
pp. 1941016
Author(s):  
Hou Y. Yau
Keyword(s):  
Adjoint Operator ◽  
Dynamical Variable ◽  
Matter Field ◽  
Quantum Field ◽  
Time And Space ◽  
Bosonic Field ◽  
Pauli’S Theorem ◽  
Interesting Candidate ◽  
Klein Gordon ◽  
Temporal And Spatial

We study the properties of a quantum field with time as a dynamical variable. Temporal vibrations are introduced to restore the symmetry between time and space in a matter field. The system with vibrations of matter in time and space obeys the Klein–Gordon equation and Schrödinger equation. The energy observed is quantized under the constraint that a particle’s mass is on shell. This real scalar field has the same properties of a zero-spin bosonic field. Furthermore, the internal time of this system can be represented by a self-adjoint operator without contradicting the Pauli’s theorem. Neutrino can be an interesting candidate for investigating the effects of these temporal and spatial vibrations because of its extremely light weight.

GRAVITONS AS EMBROIDERY ON THE WEAVE

1992 ◽  
Vol 01 (03n04) ◽  
pp. 533-557 ◽  
Author(s):  
JUNICHI IWASAKI ◽  
CARLO ROVELLI
Keyword(s):  
Quantum Theory ◽  
State Space ◽  
Loop Space ◽  
Fock Space ◽  
Preliminary Investigation ◽  
Flat Space ◽  
The State ◽  
Low Energy ◽  
Linearized Theory ◽  
Nonperturbative Theory

We investigate the physical interpretation of the loop states that appear in the loop representation of quantum gravity. By utilizing the “weave” state, which has been recently introduced as a quantum description of the microstructure of flat space, we analyze the relation between loop states and graviton states. This relation determines a linear map M from the state-space of the nonperturbative theory (loop space) into the state-space of the linearized theory (Fock space). We present an explicit form of this map, and a preliminary investigation of its properties. The existence of such a map indicates that the full nonperturbative quantum theory includes a sector that describes the same physics as (the low energy regimes of) the linearized theory, namely gravitons on flat space.

Modeling of CCLP in koryo extract production

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Ji Chol ◽  
Ri Jun Il
Keyword(s):  
Process Control ◽  
Medical Care ◽  
State Space ◽  
State Space Model ◽  
The State ◽  
Space Model ◽  
Effective Components ◽  
Counter Current

Abstract The modeling of counter-current leaching plant (CCLP) in Koryo Extract Production is presented in this paper. Koryo medicine is a natural physic to be used for a diet and the medical care. The counter-current leaching method is mainly used for producing Koryo medicine. The purpose of the modeling in the previous works is to indicate the concentration distributions, and not to describe the model for the process control. In literature, there are no nearly the papers for modeling CCLP and especially not the presence of papers that have described the issue for extracting the effective components from the Koryo medicinal materials. First, this paper presents that CCLP can be shown like the equivalent process consisting of two tanks, where there is a shaking apparatus, respectively. It allows leachate to flow between two tanks. Then, this paper presents the principle model for CCLP and the state space model on based it. The accuracy of the model has been verified from experiments made at CCLP in the Koryo Extract Production at the Gang Gyi Koryo Manufacture Factory.

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