We present new classes of time operators of a Hamiltonian H (a self-adjoint operator) with discrete eigenvalues which may be degenerate. Moreover we formulate necessary and sufficient conditions for...
Time Operators of a Hamiltonian with Purely Discrete Spectrum (2008)
Arai, Asao, Matsuzawa, Yasumichi
We develop a mathematical theory of time operators of a Hamiltonian with purely discrete spectrum. The main results include boundedness, unboundedness and spectral properties of them. In addition,...
On the Uniqueness of Weak Weyl Representations of the Canonical Commutation Relation (2008)
Let (T,H) be a weak Weyl representation of the canonical commutation relation (CCR) with one degree of freedom. Namely T is a symmetric operator and H is a self-adjoint operator on a complex Hilbert...
A class of Hilbert space representations of the quantum plane and the quantum algebra Uq(sl2) (2008)
A class of representations on the Hilbert space L^2(R^d) (d≧2) of the quantum plane C^2_q and the quantum algebra U_q(sl_2) is presented. The boundedness and the unboundedness of the...
Arai, Asao, Matsuzawa, Yasumichi
Weak Weyl representations of the canonical commutation relation (CCR) with one degree of freedom are considered in relation to the theory of time operator in quantum mechanics. It is proven that...
Arai, Asao, Matsuzawa, Yasumichi
Weak Weyl representations of the canonical commutation relation (CCR) with one degree of freedom are considered in relation to the theory of time operator in quantum mechanics. It is proven that...
Arai, Asao, Matsuzawa, Yasumichi
Weak Weyl representations of the canonical commutation relation (CCR) with one degree of freedom are considered in relation to the theory of time operator in quantum mechanics. It is proven that...
Arai, Asao, Matsuzawa, Yasumichi
Weak Weyl representations of the canonical commutation relation (CCR) with one degree of freedom are considered in relation to the theory of time operator in quantum mechanics. It is proven that...
Time Operators of a Hamiltonian with Purely Discrete Spectrum (2008)
Arai, Asao, Matsuzawa, Yasumichi
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Enhanced Binding in a General Class of Quantum Field Models (2007)
We consider, in an abstract form, a system of "quantum particles " coupled to a Bose field. It is shown that, under suitable hypotheses, the composed system can
Non-relativistic Limit of a Dirac-Maxwell Operator in Relativistic Quantum (2007)
The non-relativistic (scaling) limit of a particle-eld Hamiltonian H, called a Dirac-Maxwell operator, in relativistic quantum electrodynamics is considered. It is proven that the non-relativistic...
REGULARITIES OF GROUND STATES OF QUANTUM FIELD MODELS (2007)
Arai, Asao, Hirokawa, Masao, Hiroshima, Fumio, 新井, 朝雄, 広川, 真男, 廣島, 文生
Regularities and higher order regularities of ground states of quantum field models are investigated through the fact that asymptotic annihilation operators vanish ground states. Moreover, a...
Regularities of ground states of quantum field models (2007)
Arai, Asao, Hirokawa, Masao, Hiroshima, Fumio
Regularities and higher order regularities of ground states of quantum field models are investigated through the fact that asymptotic annihilation operators vanish ground states. Moreover a...
A class of representations on the Hilbert space $L^2(\R^d)$ ($d\geq 2$) of the quantum plane $\C_q^2$ and the quantum algebra $U_q({\rm sl}_2)$ is presented. The boundedness and the unboundedness of...
Spectrum of Time Operators (2007)
Let H be a self-adjoint operator on a complex Hilbert space H. A symmetric operator T on H is called a time operator of H if, for all t ∈ R, e^{-itH}D(T) ⊂ D(T) (D(T) denotes the domain of T) and...
HEISENBERG OPERATORS, INVARIANT DOMAINS AND HEISENBERG EQUATIONS OF MOTION (2007)
An abstract operator theory is developed on operators of the form A_{H}(t) := e^{itH}Ae^{-itH}, t ∈ R, with H a self-adjoint operator and A a linear operator on a Hilbert space (in the context of...
A class of representations on the Hilbert space $L^2(\R^d)$ ($d\geq 2$) of the quantum plane $\C_q^2$ and the quantum algebra $U_q({\rm sl}_2)$ is presented. The boundedness and the unboundedness of...
A class of representations on the Hilbert space $L^2(\R^d)$ ($d\geq 2$) of the quantum plane $\C_q^2$ and the quantum algebra $U_q({\rm sl}_2)$ is presented. The boundedness and the unboundedness of...
Representations of the Quantum Plane and the Quantum Algebra Uq(sl2) on L 2 (R d) (2007)
The Erwin, Schrödinger International Boltzmanngasse, Asao Arai, Asao Arai
A class of representations on the Hilbert space L 2 (R d) (d ≥ 2) of the quantum plane C 2 q and the quantum algebra Uq(sl2) is presented. The boundedness and the unboundedness of the...
Mathematical Analysis of a Generalized Chiral Quark Soliton Model (2006)
A generalized version of the so-called chiral quark soliton model (CQSM) in nuclear physics is introduced. The Hamiltonian of the generalized CQSM is given by a Dirac type operator with a mass term...
Mathematical Analysis of a Generalized Chiral Quark Soliton Model (2006)
A generalized version of the so-called chiral quark soliton model (CQSM) in nuclear physics is introduced. The Hamiltonian of the generalized CQSM is given by a Dirac type operator with a mass term...
Non-relativistic Limit of a Dirac Polaron in Relativistic Quantum Electrodynamics (2006)
A quantum system of a Dirac particle interacting with the quantum radiation field is considered in the case where no external potentials exist. Then the total momentum of the system is conserved and...
Non-relativistic Limit of a Dirac Polaron in Relativistic Quantum Electrodynamics (2006)
A quantum system of a Dirac particle interacting with the quantum radiation field is considered in the case where no external potentials exist. Then the total momentum of the system is conserved and...
Non-relativistic Limit of a Dirac Polaron in Relativistic Quantum Electrodynamics (2006)
A quantum system of a Dirac particle interacting with the quantum radiation field is considered in the case where no external potentials exist. Then the total momentum of the system is conserved and...
Fundamental symmetry principles in quantum mechanics and its philosophical phases (2006)
A fundamental symmetry principle in quantum mechanics is formulated in the framework of the standard axiomatic quantum mechanics and a new philosophical interpretation for quantum mechanics, which...
Spectral Analysis of a Dirac Operator with a Meromorphic Potential (2005)
Arai, Asao, Hayashi, Kunimitsu
We consider an operator Q(V) of Dirac type with a meromorphic potential given in terms of a function V of the form V(z) = λV1(z) + μV2(z), z ∈ C ＼ {0}, where V1 is a complex polynomial of 1/z,...
Spectral properties of a Dirac operator in the chiral quark soliton model (2005)
Arai, Asao, Hayashi, Kunimitsu, Sasaki, Itaru, 新井, 朝雄
We consider a Dirac operator H acting in the Hilbert space L2(R3;C4)(x)C2, which describes a Hamiltonian of the chiral quark soliton model in nuclear physics. The mass term of H is a matrix-valued...
Spectral properties of a Dirac operator in the chiral quark soliton model (2005)
Arai, Asao, Hayashi, Kunimitsu, Sasaki, Itaru
We consider a Dirac operator H acting in the Hilbert space L2(R3;C4)(x)C2, which describes a Hamiltonian of the chiral quark soliton model in nuclear physics. The mass term of H is a matrix-valued...
Spectral properties of a Dirac operator in the chiral quark soliton model (2005)
Arai, Asao, Hayashi, Kunimitsu, Sasaki, Itaru
We consider a Dirac operator H acting in the Hilbert space L2(R3;C4)(x)C2, which describes a Hamiltonian of the chiral quark soliton model in nuclear physics. The mass term of H is a matrix-valued...
Generalized Weak Weyl Relation and Decay of Quantum Dynamics (2005)
Let $H$ be a self-adjoint operator on a Hilbert space ${\cal H}$, $T$ be a symmetric operator on ${\cal H}$ and $K(t)$ ($t\in \R$) be a bounded self-adjoint operator on ${\cal H}$. We say that...
Generalized Weak Weyl Relation and Decay of Quantum Dynamics (2005)
Reprinted from Publication, Reviews in Mathematical Physics, Vol 17-9, Arai, A, Generalized Weak Weyl Relation and Decay of Quantum Dynamics, p.1071-1109, c2005,with permission from World Scientific...
Generalized Weak Weyl Relation and Decay of Quantum Dynamics (2005)
Let H be a self-adjoint operator on a Hilbert space H, T be a symmetric operator
Generalized Weak Weyl Relation and Decay of Quantum Dynamics (2005)
Let H be a self-adjoint operator on a Hilbert space H, T be a symmetric operator
Generalized Weak Weyl Relation and Decay of Quantum Dynamics (2005)
Let $H$ be a self-adjoint operator on a Hilbert space ${\cal H}$, $T$ be a symmetric operator on ${\cal H}$ and $K(t)$ ($t\in \R$) be a bounded self-adjoint operator on ${\cal H}$. We say that...
Generalized Weak Weyl Relation and Decay of Quantum Dynamics (2005)
Let $H$ be a self-adjoint operator on a Hilbert space ${\cal H}$, $T$ be a symmetric operator on ${\cal H}$ and $K(t)$ ($t\in \R$) be a bounded self-adjoint operator on ${\cal H}$. We say that...
Spectral Properties of a Dirac Operator in the Chiral Quark Soliton Model (2004)
Arai, Asao, Hayashi, Kunimitsu, Sasaki, Itaru
We consider a Dirac operator $H$ acting in the Hilbert space $L^2(\BbbR^3;\BbbC^4)\otimes \BbbC^2$, which describes a Hamiltonian of the chiral quark soliton model in nuclear physics. The mass term...
Regularities of ground states of quantum field models (2004)
Arai, Asao, Hirokawa, Masao, Hiroshima, Fumio
Regularities and higher order regularities of ground states of quantum field models are investigated through the fact that asymptotic annihilation operators vanish ground states. Moreover a...
Spectral analysis of a Dirac operator with a meromorphic potential (2004)
Arai, Asao, Hayashi, Kunimitsu
We consider an operator $Q(V)$ of Dirac type with a meromorphic potential given in terms of a function $V$ of the form $V(z)=\lambda V_1(z)+\mu V_2(z), \ z\in \BbbC\setminus\{0\}$, where $V_1$ is a...
Spectral analysis of a Dirac operator with a meromorphic potential (2004)
Arai, Asao, Hayashi, Kunimitsu
We consider an operator $Q(V)$ of Dirac type with a meromorphic potential given in terms of a function $V$ of the form $V(z)=\lambda V_1(z)+\mu V_2(z), \ z\in \BbbC\setminus\{0\}$, where $V_1$ is a...
Spectral Properties of a Dirac Operator in the Chiral Quark Soliton Model (2004)
Arai, Asao, Hayashi, Kunimitsu, Sasaki, Itaru
We consider a Dirac operator $H$ acting in the Hilbert space $L^2(\BbbR^3;\BbbC^4)\otimes \BbbC^2$, which describes a Hamiltonian of the chiral quark soliton model in nuclear physics. The mass term...
Spectral analysis of a Dirac operator with a meromorphic potential (2004)
Arai, Asao, Hayashi, Kunimitsu
We consider an operator $Q(V)$ of Dirac type with a meromorphic potential given in terms of a function $V$ of the form $V(z)=\lambda V_1(z)+\mu V_2(z), \ z\in \BbbC\setminus\{0\}$, where $V_1$ is a...
Spectral Properties of a Dirac Operator in the Chiral Quark Soliton Model (2004)
Arai, Asao, Hayashi, Kunimitsu, Sasaki, Itaru
We consider a Dirac operator $H$ acting in the Hilbert space $L^2(\BbbR^3;\BbbC^4)\otimes \BbbC^2$, which describes a Hamiltonian of the chiral quark soliton model in nuclear physics. The mass term...
Enhanced Binding in a General Class of Quantum Field Models (2003)
We consider, in an abstract form, a system of "quantum particles" coupled to a Bose field. It is shown that, under suitable hypotheses, the composed system can have a ground state even if the...
Non-relativistic Limit of a Dirac-Maxwell Operator in Relativistic Quantum Electrodynamics (2003)
The non-relativistic (scaling) limit of a particle-field Hamiltonian H, called a Dirac-Maxwell operator, in relativistic quantum electrodynamics is considered. It is proven that the non-relativistic...
The Erwin, Schrödinger International Boltzmanngasse, Asao Arai, Hiroyuki Kawano, Asao Arai, Hiroyuki Kawano
We consider, in an abstract form, a system of “quantum particles ” coupled to a Bose field. It is shown that, under suitable hypotheses, the composed system can have a ground state even if the...
We consider a model of quantum particles coupled to a massless quantum scalar field, called the massless Nelson model, in a non-Fock representation of the timezero fields which satisfy the canonical...
Stability of Ground States in Sectors and Its Application to the Wigner-Weisskopf Model (2001)
We consider two kinds of stability (under a perturbation) of the ground state of a self-adjoint operator, being concerned with (i) the sector to which the ground state belongs and (ii) the uniqueness...
We consider a model of quantum particles coupled to a massless quantum scalar field, called the massless Nelson model, in a non-Fock representation of the timezero fields which satisfy the canonical...
Ground States of a General Class of Quantum Field Hamiltonians (2000)
We consider a model of a quantum mechanical system coupled to a (massless) Bose field, called the generalized spin-boson model (A. Arai and M. Hirokawa, J. Funct. Anal. 151 (1997), 455-503), without...
A particle-field Hamiltonian in relativistic quantum electrodynamics (2000)
We mathematically analyze a Hamiltonian Hτ(V,g) of a Dirac particle—a relativistic charged particle with spin 1/2—minimally coupled to the quantized radiation field, acting in the Hilbert space...
A particle-field Hamiltonian in relativistic quantum electrodynamics (2000)
We mathematically analyze a Hamiltonian Hτ(V,g) of a Dirac particle—a relativistic charged particle with spin 1/2—minimally coupled to the quantized radiation field, acting in the Hilbert space...
A particle-field Hamiltonian in relativistic quantum electrodynamics (2000)
We mathematically analyze a Hamiltonian Hτ(V,g) of a Dirac particle—a relativistic charged particle with spin 1/2—minimally coupled to the quantized radiation field, acting in the Hilbert space...
Stability of Ground States in Sectors and Its Application to the Wigner-Weisskopf Model (1999)
We consider two kinds of stability (under a perturbation) of the ground state of a self-adjoint operator, being concerned with (i) the sector to which the ground state belongs and (ii) the uniqueness...
Some representation-theoretic aspects of a two-dimensional quantum system of a charged particle in a vector potential A, which may be singular on an infinite discrete subset D of R^2 are...
Some representation-theoretic aspects of a two-dimensional quantum system of a charged particle in a vector potential A, which may be singular on an infinite discrete subset D of R^2 are...
Some representation-theoretic aspects of a two-dimensional quantum system of a charged particle in a vector potential A, which may be singular on an infinite discrete subset D of R^2 are...
A two-dimensional quantum system of a charged particle interacting with a vector potential determined by the Weierstrass Zeta function is considered. The position and the physical momentum operators...
A two-dimensional quantum system of a charged particle interacting with a vector potential determined by the Weierstrass Zeta function is considered. The position and the physical momentum operators...
A two-dimensional quantum system of a charged particle interacting with a vector potential determined by the Weierstrass Zeta function is considered. The position and the physical momentum operators...
A quantum system of a particle interacting with a (non-Abelian) gauge field on the non-simply connected domain M=R^2\{an}Nn=1 is considered, where an, n=1,...,N, are fixed isolated points in R^2. The...
A quantum system of a particle interacting with a (non-Abelian) gauge field on the non-simply connected domain M=R^2\{an}Nn=1 is considered, where an, n=1,...,N, are fixed isolated points in R^2. The...
A quantum system of a particle interacting with a (non-Abelian) gauge field on the non-simply connected domain M=R^2\{an}Nn=1 is considered, where an, n=1,...,N, are fixed isolated points in R^2. The...
Operator-theoretical analysis of a representation of a supersymmetry algebra in Hilbert space (1995)
Operator-theoretical analysis is made on (unbounded) representations, in Hilbert spaces, of a supersymmetry (SUSY) algebra coming from a supersymmetric quantum field theory in two-dimensional...
Operator-theoretical analysis of a representation of a supersymmetry algebra in Hilbert space (1995)
Operator-theoretical analysis is made on (unbounded) representations, in Hilbert spaces, of a supersymmetry (SUSY) algebra coming from a supersymmetric quantum field theory in two-dimensional...
Operator-theoretical analysis of a representation of a supersymmetry algebra in Hilbert space (1995)
Operator-theoretical analysis is made on (unbounded) representations, in Hilbert spaces, of a supersymmetry (SUSY) algebra coming from a supersymmetric quantum field theory in two-dimensional...
Infinite Dimensional Analysis on an Exterior Bundle and Supersymmetric Quantum Field Theory (1994)
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Properties of the Dirac-Weyl operator with a strongly singular gauge potential (1993)
Considered is a quantum system of a charged particle moving in the plane R^2 under the influence of a perpendicular magnetic field concentrated on some fixed isolated points in R^2. Such a magnetic...
Properties of the Dirac-Weyl operator with a strongly singular gauge potential (1993)
Considered is a quantum system of a charged particle moving in the plane R^2 under the influence of a perpendicular magnetic field concentrated on some fixed isolated points in R^2. Such a magnetic...
Properties of the Dirac-Weyl operator with a strongly singular gauge potential (1993)
Considered is a quantum system of a charged particle moving in the plane R^2 under the influence of a perpendicular magnetic field concentrated on some fixed isolated points in R^2. Such a magnetic...
Commutation properties of two-dimensional momentum operators with gauge potentials are investigated. A notion of local quantization of magnetic flux is introduced to characterize physically the...
Commutation properties of two-dimensional momentum operators with gauge potentials are investigated. A notion of local quantization of magnetic flux is introduced to characterize physically the...
Commutation properties of two-dimensional momentum operators with gauge potentials are investigated. A notion of local quantization of magnetic flux is introduced to characterize physically the...
157
Meromorphic N=2 Wess-Zumino supersymmetric quantum mechanics (1991)
The ordinary (holomorphic) N=2 Wess–Zumino model in supersymmetric quantum mechanics is extended to the case where the superpotential V(z) is a meromorphic function on C■{∞}. The extended model...
Meromorphic N=2 Wess-Zumino supersymmetric quantum mechanics (1991)
The ordinary (holomorphic) N=2 Wess–Zumino model in supersymmetric quantum mechanics is extended to the case where the superpotential V(z) is a meromorphic function on C■{∞}. The extended model...
Meromorphic N=2 Wess-Zumino supersymmetric quantum mechanics (1991)
The ordinary (holomorphic) N=2 Wess–Zumino model in supersymmetric quantum mechanics is extended to the case where the superpotential V(z) is a meromorphic function on C■{∞}. The extended model...
Long-time behavior of an electron interacting with a quantized radiation field (1991)
The long-time behavior of an electron coupled to a quantized radiation field is discussed in the ground state and in equilibrium states at finite temperatures. The electron is not confined in an...
An abstract theorem is given on essential self-adjointness of operators in infinite direct sum of Hilbert spaces and is applied to a class of Hamiltonians in nonrelativistic quantum field theory to...
Long-time behavior of an electron interacting with a quantized radiation field (1991)
The long-time behavior of an electron coupled to a quantized radiation field is discussed in the ground state and in equilibrium states at finite temperatures. The electron is not confined in an...
An abstract theorem is given on essential self-adjointness of operators in infinite direct sum of Hilbert spaces and is applied to a class of Hamiltonians in nonrelativistic quantum field theory to...
Long-time behavior of an electron interacting with a quantized radiation field (1991)
The long-time behavior of an electron coupled to a quantized radiation field is discussed in the ground state and in equilibrium states at finite temperatures. The electron is not confined in an...
An abstract theorem is given on essential self-adjointness of operators in infinite direct sum of Hilbert spaces and is applied to a class of Hamiltonians in nonrelativistic quantum field theory to...
Noninvertible Bogoliubov transformations and instability of embedded eigenvalues (1991)
A class of noninvertible Bogoliubov transformations in an abstract Boson Fock space is used to construct in the Fock space a family of self-adjoint operators H which are quadratic in the annihilation...
Noninvertible Bogoliubov transformations and instability of embedded eigenvalues (1991)
A class of noninvertible Bogoliubov transformations in an abstract Boson Fock space is used to construct in the Fock space a family of self-adjoint operators H which are quadratic in the annihilation...
Noninvertible Bogoliubov transformations and instability of embedded eigenvalues (1991)
A class of noninvertible Bogoliubov transformations in an abstract Boson Fock space is used to construct in the Fock space a family of self-adjoint operators H which are quadratic in the annihilation...
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An abstract asymptotic theory of a family of self-adjoint operators {Hκ}κ>0 acting in the tensor product of two Hilbert spaces is presented and it is applied to the nonrelativistic limit of the...
An abstract asymptotic theory of a family of self-adjoint operators {Hκ}κ>0 acting in the tensor product of two Hilbert spaces is presented and it is applied to the nonrelativistic limit of the...
An abstract asymptotic theory of a family of self-adjoint operators {Hκ}κ>0 acting in the tensor product of two Hilbert spaces is presented and it is applied to the nonrelativistic limit of the...
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On the degeneracy in the ground state of the N=2 Wess–Zumino supersymmetric quantum mechanics (1989)
It is known that the N=2 Wess–Zumino supersymmetric quantum mechanical model has p–1 degenerate zero-energy ground states consisting of only bosonic states, where p>3 is the degree of the...
On the degeneracy in the ground state of the N=2 Wess–Zumino supersymmetric quantum mechanics (1989)
It is known that the N=2 Wess–Zumino supersymmetric quantum mechanical model has p–1 degenerate zero-energy ground states consisting of only bosonic states, where p>3 is the degree of the...
On the degeneracy in the ground state of the N=2 Wess–Zumino supersymmetric quantum mechanics (1989)
It is known that the N=2 Wess–Zumino supersymmetric quantum mechanical model has p–1 degenerate zero-energy ground states consisting of only bosonic states, where p>3 is the degree of the...
A class of exactly soluble models of a one-dimensional quantum harmonic oscillator interacting with bosons moving in the d-dimensional space R^d is considered and the long-time behavior of the...
A class of exactly soluble models of a one-dimensional quantum harmonic oscillator interacting with bosons moving in the d-dimensional space R^d is considered and the long-time behavior of the...
A class of exactly soluble models of a one-dimensional quantum harmonic oscillator interacting with bosons moving in the d-dimensional space R^d is considered and the long-time behavior of the...
The general framework of the N=2 Wess–Zumino holomorphic supersymmetric quantum mechanics with polynomial superpotentials is extended to the case of nonpolynomial superpotentials V(z) (z∈C) in a...
The general framework of the N=2 Wess–Zumino holomorphic supersymmetric quantum mechanics with polynomial superpotentials is extended to the case of nonpolynomial superpotentials V(z) (z∈C) in a...
The general framework of the N=2 Wess–Zumino holomorphic supersymmetric quantum mechanics with polynomial superpotentials is extended to the case of nonpolynomial superpotentials V(z) (z∈C) in a...
A mathematically rigorous analysis is given on supersymmetric embedding of a model of a one-dimensional quantum harmonic oscillator interacting with infinitely many bosons moving in the s-dimensional...
A mathematically rigorous analysis is given on supersymmetric embedding of a model of a one-dimensional quantum harmonic oscillator interacting with infinitely many bosons moving in the s-dimensional...
A mathematically rigorous analysis is given on supersymmetric embedding of a model of a one-dimensional quantum harmonic oscillator interacting with infinitely many bosons moving in the s-dimensional...
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Perturbation of Embedded Eigenvalues in Fock Spaces A General Class of Exactly Soluble Models (1988)
Perturbation of Embedded Eigenvalues in Fock Spaces A General Class of Exactly Soluble Models (1988)
Perturbation of Embedded Eigenvalues in Fock Spaces A General Class of Exactly Soluble Models (1988)
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