Quantum mechanics of Klein–Gordon fields II: Relativistic coherent states

Mostafazadeh, Alí; Zamani, Farhad

doi:10.1016/j.aop.2006.02.008

Cited by 24 publications

(37 citation statements)

References 54 publications

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“…The metric operator associated with the CPT -inner product that is computed using the spectral method in [51] turns out to correspond to a particular choice for w ± in (180).…”

Section: Universal Field Equation For the Metricmentioning

confidence: 99%

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Pseudo-Hermitian Representation of Quantum Mechanics

Mostafazadeh

2010

Int. J. Geom. Methods Mod. Phys.

865

1,210

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A diagonalizable non-Hermitian Hamiltonian having a real spectrum may be used to define a unitary quantum system, if one modifies the inner product of the Hilbert space properly. We give a comprehensive and essentially self-contained review of the basic ideas and techniques responsible for the recent developments in this subject. We provide a critical assessment of the role of the geometry of the Hilbert space in conventional quantum mechanics to reveal the basic physical principle motivating our study. We then offer a survey of the necessary mathematical tools, present their utility in establishing a lucid and precise formulation of a unitary quantum theory based on a non-Hermitian Hamiltonian, and elaborate on a number of relevant issues of fundamental importance. In particular, we discuss the role of the antilinear symmetries such as PT , the true meaning and significance of the so-called charge operators C and the CPT -inner products, the nature of the physical observables, the equivalent description of such models using ordinary Hermitian quantum mechanics, the pertaining duality between localnon-Hermitian versus nonlocal-Hermitian descriptions of their dynamics, the corresponding classical systems, the pseudo-Hermitian canonical quantization scheme, various methods of calculating the (pseudo-) metric operators, subtleties of dealing with time-dependent quasi-Hermitian Hamiltonians and the path-integral formulation of the theory, and the structure of the state space and its ramifications for the quantum Brachistochrone problem. We also explore some concrete physical applications and manifestations of the abstract concepts and tools that have been developed in the course of this investigation. These include applications in nuclear physics, condensed matter physics, relativistic quantum mechanics and quantum field theory, quantum cosmology, electromagnetic wave propagation, open quantum systems, magnetohydrodynamics, quantum chaos, and biophysics.

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“…The metric operator associated with the CPT -inner product that is computed using the spectral method in [51] turns out to correspond to a particular choice for w ± in (180).…”

Section: Universal Field Equation For the Metricmentioning

confidence: 99%

“…A natural consequence of these developments is the construction of a set of genuine relativistic coherent states for Klein-Gordon fields interacting with a constant magnetic field [180].…”

mentioning

confidence: 99%

Pseudo-Hermitian Representation of Quantum Mechanics

Mostafazadeh

2010

Int. J. Geom. Methods Mod. Phys.

865

1,210

View full text Add to dashboard Cite

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“…(14) and (15) from the standpoint of the algebraic approach developed in works devoted to studying non Hermitian quantum theory [28][29][30][31][32][33]. Hamiltonians (14) and (15) are non Hermitian but ᏼsymmetric.…”

Section: Non Hermitian Relativisticmentioning

confidence: 99%

“…Additionally, an alternative formalism for regarding the systems defined by non Hermitian Hamiltonians [25][26][27][28][29][30][31][32][33] is also known, according to which the spec trum reality for a non Hermitian system occurs owing to the so called pseudo Hermitian properties of a Hamiltonian. A Hamiltonian is called η 0 pseudo Hermitian if it satisfies the condition (16) where η 0 is the linear Hermitian operator.…”

Section: Introductionmentioning

confidence: 99%

The algebraic and geometric approaches to PJ-symmetric non-Hermitian relativistic quantum mechanics with maximal mass

Rodionov

Kravtsova

2014

Moscow Univ. Phys.

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A non Hermitian fermion model containing a γ 5 matrix in the mass term m m 1 + γ 5 m 2 is con sidered. A new refined condition of the unbroken ᏼsymmetry of the theory is proposed that comprises an indication that the initial domain of unbroken ᏼsymmetry is divided into subdomains corresponding to the description of ordinary and exotic particles. A relationship is established between the theory under study and the quantum field theory with maximal mass M developed on the basis of the geometric approach. The operator Ꮿ is calculated explicitly, which is required for the construction of a new scalar product in the theory with a non Hermitian Hamiltonian.

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“…The discovery of such a new freedom of making the choice between alternative inner products can be perceived as belonging to the most important recent achievements in quantum physics, with impact ranging from the new flexibility of the interacting boson models in nuclear physics [17] and from formulations of several new theoretical ideas in quantum mechanics [42] up to the emergence of the new classes of phenomenological Lagrangians in quantum field theory [41] where, e.g., the presence of ghosts can successfully be eliminated in some cases [45] and where even the concept of integrability acquired an updated meaning [43]. The use of the varying non-Dirac metrics Θ = I also opened the way toward new challenges connected, e.g., with the description of bound states in time-dependent systems [46] or in the relativistic kinematical regime [47]. In some phenomenological models of scattering the variability of Θ has been suggested as a guarantee of the causality and/or unitarity of the process [33,34,37,39].…”

Section: The Proofs Of the Reality Of Energiesmentioning

confidence: 99%

Fundamental length in quantum theories withPT-symmetric Hamiltonians. II. The case of quantum graphs

Znojil

2009

Phys. Rev. D

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PT −symmetrization of quantum graphs is proposed as an innovation where an adjustable, tunable nonlocality is admitted. The proposal generalizes the PT −symmetric square-well models of Ref.[1] (with real spectrum and with a variable fundamental length θ) which are reclassified as the most elementary quantum q−pointed-star graphs with minimal q = 2. Their equilateral q = 3, 4, . . . generalizations are considered, with interactions attached to the vertices. Runge-Kutta discretization of coordinates simplifies the quantitative analysis by reducing our graphs to star-shaped lattices of N = qK + 1 points. The resulting bound-state spectra are found real in an N−independent interval of couplings λ ∈ (−1, 1). Inside this interval the set of closed-form metrics Θ (N ) j (λ) is constructed, defining independent eligible local (at j = 0) or increasingly nonlocal (at j = 1, 2, . . .) inner products in the respective physical Hilbert spaces of states H (N ) j (λ). In this way each graph is assigned a menu of non-equivalent, optional probabilistic quantum interpretations.

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Quantum mechanics of Klein–Gordon fields II: Relativistic coherent states

Cited by 24 publications

References 54 publications

Pseudo-Hermitian Representation of Quantum Mechanics

Pseudo-Hermitian Representation of Quantum Mechanics

The algebraic and geometric approaches to PJ-symmetric non-Hermitian relativistic quantum mechanics with maximal mass

Fundamental length in quantum theories withPT-symmetric Hamiltonians. II. The case of quantum graphs

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