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Foundations of Physics (00159018)55(3)
The polarization,magnetization and conductivity features of a conductor polarizable and magnetizable medium are described by a continuum collection of the antisymmetric tensor fields and a continuum collection of the vector fields in the Minkowski’s space-time. The conservation principle of the energy-momentum four-vector of the total system is provided in a fully canonical approach. The conservation principle of the energy-momentum four-vector of the total system gives the force four-vector on the free external charges moving in the conductor magneto-dielectric medium. The total classical relativistic Cherenkov’s radiation power emerged by a charged particle uniformly moving inside the medium is calculated. The quantum relativistic Cherenkov’s radiation power of a charged particle moving inside a homogeneous conductor magneto-dielectric medium is calculated by two methods. In the first method the motion of the charged particle is described by the relativistic quantum mechanics. The quantum relativistic Cherenkov’s radiation power of the charged particle moving in the medium is calculated in the initial state that the charged particle is in a very sharp normalized distribution in the momentum space and the quantum relativistic fields describing the medium are in the vacuum states. In the second approach the motion of an electron moving in the medium is described by the quantum relativistic Dirac’s field. The quantum relativistic Cherenkov’s radiation power of the electron moving in the medium is computed in the initial state that the quantum relativistic Dirac’s field is contained an electron with a definite spin and a very sharp normalized distribution in the momentum space and the quantum relativistic dynamical fields modeling the medium are in the vacuum states. The two methods of the calculation of the quantum relativistic Cherenkov’s radiation power of the electron moving inside the conductor magneto-dielectric medium are compared. © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2025.
Physica Scripta (00318949)98(3)
A canonical quantization of electromagnetic field in the presence of a bi-anisotropic absorbing magneto-dielectric slab is provided. The quantized Maxwell’s equations in the presence of the slab are exactly solved and the time-space dependence of the quantized electric and magnetic fields are obtained. The Fock space of the total system is introduced. The scattering matrix of the bi-anisotropic magneto-dielectric slab is obtained in terms of the susceptibility tensors of the slab. The scattering matrix relates the annihilation operators of the outgoing quantized electromagnetic waves from the slab to the annihilation operators of the incoming quantized electromagnetic waves to the slab. The Fresnel’s coefficients of the bi-anisotropic magneto-dielectric slab are obtained in terms of the susceptibility tensors of the slab. The Fresnel’s coefficients relate the powers radiated by the outgoing quantized electromagnetic waves from the slab to the powers radiated by the incoming quantized electromagnetic waves to the slab. The radiated powers by the outgoing quantized electromagnetic waves are calculated in the special cases that the slab is in the thermal state and the incoming quantized electromagnetic waves to the slab are in the vacuum state and the coherent state. © 2023 IOP Publishing Ltd.
Modern Physics Letters A (02177323)34(30)
A canonical relativistic formulation to calculate the Casimir force four-vector exerted on anisotropic conductor polarizable and magnetizable media is provided. The anisotropic conductor polarizable and magnetizable medium is modeled by a continuum collection of the antisymmetric tensor fields of the second rank and a continuum collection of the vector fields in Minkowski spacetime. The collection of the antisymmetric tensor fields describes the polarization and the magnetization properties of the medium. The collection of the vector fields describes the conductivity property of the medium. The quantum relativistic wave equation of the four-vector potential of the electromagnetic field is solved using an iteration method. According to the conservation principle of the energy-momentum four-vector and using of the energy-momentum tensors of the relativistic dynamical fields, contained in the theory, the Casimir force four-vector on the anisotropic conductor polarizable and magnetizable medium is obtained. The Casimir force four-vector is obtained in terms of the relativistic dynamical fields, contained in the theory and the coupling tensors that couple the electromagnetic field to the anisotropic conductor polarizable and magnetizable medium. The Casimir force four-vector exerted on the medium is calculated in the vacuum state of the total system. As a special case, the formulation is applied to a multilayer medium. The tangential component of the Casimir force exerted on a multilayer medium vanish when the anisotropic conductor polarizable and magnetizable medium is converted to an isotropic one. © 2019 World Scientific Publishing Company.
International Journal of Modern Physics A (0217751X)34(26)
A fully canonical quantization of electromagnetic field in the presence of a bi-anisotropic absorbing magneto-dielectric cylindrical shell is provided. The mode expansions of the dynamical quantum fields, contained in the theory, is achieved and the ladder operators of the system are introduced. Using the Frobenius's series technique, the Maxwell's equations in the presence of the bi-anisotropic absorbing magneto-dielectric cylindrical shell are solved and the space-time dependence of the quantized electromagnetic field is obtained. Applying the conservation principle of the angular momentum, the net quantum vacuum torque exerted on the bi-anisotropic absorbing magneto-dielectric cylindrical shell is calculated. The net quantum vacuum torque exerted on the cylindrical shell is calculated in the vacuum state and the thermal state of the system. The quantum vacuum torque on the cylindrical shell identically vanishes when the bi-anisotropic absorbing magneto-dielectric cylindrical shell is converted to an isotropic one. © 2019 World Scientific Publishing Company.
Modern Physics Letters A (02177323)33(14)
A fully canonical quantization of electromagnetic field in the presence of a bi-anisotropic absorbing magneto-dielectric slab is demonstrated. The electric and the magnetic polarization densities of the magneto-dielectric slab are defined in terms of the dynamical variables modeling the slab and the coupling tensors that couple the electromagnetic field to the slab. The four susceptibility tensors of the bi-anisotropic magneto-dielectric slab are expressed in terms of the coupling tensors that couple an electromagnetic field to the slab. It is shown that the four susceptibility tensors of the bi-anisotropic magneto-dielectric slab satisfy Kramers-Kronig relations. The Maxwell's equations are exactly solved in the presence of the bi-anisotropic magneto-dielectric slab. The tangential and the normal components of the Casimir forces exerted on the bi-anisotropic magnet-dielectric slab exactly are calculated in the vacuum state and thermal state of the total system. It is shown that the tangential components of the Casimir forces vanish when the bi-anisotropic slab is converted to an isotropic slab. © 2018 World Scientific Publishing Company.
International Journal of Modern Physics A (0217751X)32(35)
A canonical relativistic quantization of the electromagnetic field is introduced in the presence of an anisotropic conductor magneto-dielectric medium in a standard way in the Gupta-Bleuler framework. The medium is modeled by a continuum collection of the vector fields and a continuum collection of the antisymmetric tensor fields of the second rank in Minkowski space-time. The collection of vector fields describes the conductivity property of the medium and the collection of antisymmetric tensor fields describes the polarization and the magnetization properties of the medium. The conservation law of the total electric charges, induced in the anisotropic conductor magneto-dielectric medium, is deduced using the antisymmetry conditions imposed on the coupling tensors that couple the electromagnetic field to the medium. Two relativistic covariant constitutive relations for the anisotropic conductor magneto-dielectric medium are obtained. The constitutive relations relate the antisymmetric electric-magnetic polarization tensor field of the medium and the free electric current density four-vector, induced in the medium, to the strength tensor of the electromagnetic field, separately. It is shown that for a homogeneous anisotropic medium the susceptibility tensor of the medium satisfies the Kramers-Kronig relations. Also it is shown that for a homogeneous anisotropic medium the real and imaginary parts of the conductivity tensor of the medium satisfy the Kramers-Kronig relations and a relation other than the Kramers-Kronig relations. © 2017 The Author(s).
International Journal of Theoretical Physics (00207748)55(8)pp. 3761-3776
Modeling a nonlinear anisotropic magnetodielectric medium with spatial-temporal dispersion by two continuum collections of three dimensional harmonic oscillators, a fully canonical quantization of the electromagnetic field is demonstrated in the presence of such a medium. Some coupling tensors of various ranks are introduced that couple the magnetodielectric medium with the electromagnetic field. The polarization and magnetization fields of the medium are defined in terms of the coupling tensors and the oscillators modeling the medium. The electric and magnetic susceptibility tensors of the medium are obtained in terms of the coupling tensors. It is shown that the electric field satisfy an integral equation in frequency domain. The integral equation is solved by an iteration method and the electric field is found up to an arbitrary accuracy. © 2016, Springer Science+Business Media New York.
European Physical Journal D (14346060)69(3)
A bi-anisotropic magnetodielectric medium is modeled by two independent set of three dimensional harmonic oscillators. A fully canonical quantization of electromagnetic field is demonstrated in the presence of a bi-anisotropic magnetodielectric medium. The electric and magnetic polarization fields of the medium are obtained in terms of the dynamical variable modeling the medium. The Heisenberg equations of the system are solved for a multilayer bi-anisotropic magnetodielectric medium. © 2015 EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg.
International Journal of Theoretical Physics (00207748)54(10)pp. 3691-3698
The quantum dynamics of a localized spin−12$-\frac {1}{2} $ Particle interacting with an absorbing environment is investigated. The quantum Langevin-Schrödinger equation for spin−12$-\frac {1}{2} $ is obtained. The susceptibility function of the environment is calculated in terms of the coupling function of the spin and the environment. it is shown that the susceptibility function satisfies the Kramers-Kronig relations. Spontaneous emission and the shift frequency of the spin is obtained in terms of the imaginary part of the susceptibility function in frequency domain. Some transition probabilities between the spin states are calculated when the absorbing environment is in the thermal state. © 2015, Springer Science+Business Media New York.
Annals of Physics (1096035X)325(9)pp. 1976-1986
A canonical quantization scheme is represented for a quantum system interacting with a non-linear absorbing environment. The environment is taken anisotropic and the main system is coupled to its environment through some coupling tensors of various ranks. The non-linear response equation of the environment against the motion of the main system is obtained. The non-linear Langevin-Schrödinger equation is concluded as the macroscopic equation of motion of the dissipative system. The effect of non-linearity of the environment is investigated on the spontaneous emission of an initially excited two-level atom imbedded in such an environment. © 2010 Elsevier Inc.
Annals of Physics (1096035X)325(9)pp. 1913-1930
By introducing a suitable Lagrangian, a canonical quantization of the electromagnetic field in the presence of a non-dispersive bi-anisotropic inhomogeneous magnetodielectric medium is investigated. A tensor projection operator is defined and the commutation relation between the vector potential and its canonically conjugate variable is written in terms of the projection operator. The quantization method is generalized in the presence of the atomic systems. The spontaneous emission of a two-level atom located in a non-dispersive anisotropic megnetodielectric medium is studied. © 2010 Elsevier Inc.
Journal of Physics B: Atomic, Molecular and Optical Physics (13616455)42(7)
In this paper, by extending the Lagrangian of the Huttner-Barnett model an electromagnetic field in a nonhomogeneous and anisotropic magnetodielectric medium is quantized canonically. In this model, Maxwell equations in the medium are obtained and solved using the Green function technique. The noise operators are found and the results are compared with the phenomenological method. © 2009 IOP Publishing Ltd.
European Physical Journal D (14346060)54(1)pp. 115-118
A canonical relativistic formulation is introduced to quantize electromagnetic field in the presence of a polarizable and magnetizable moving medium. The medium is modeled by a continuum of the second rank antisymmetric tensors in a phenomenological way. The covariant wave equation for the vector potential and the covariant constitutive equation of the medium are obtained as the Euler-Lagrange equations using the Lagrangian of the total system. A fourth rank tensor which couples the electromagnetic field and the medium is introduced. The susceptibility tensor of the medium is obtained in terms of this coupling tensor. The noise polarization tensor is calculated in terms of both the coupling tensor and the ladder operators of the tensors modeling the medium. © EDP Sciences, Societá Italiana di Fisica, Springer-Verlag 2009.
Journal of Mathematical Physics (00222488)50(6)
A fully canonical quantization of electromagnetic field is introduced in the presence of an anisotropic polarizable and magnetizable medium. Two tensor fields which couple the electromagnetic field with the medium and have an important role in this quantization method are introduced. The electric and magnetic polarization fields of the medium naturally are concluded in terms of the coupling tensors and the dynamical variables modeling the magnetodielectric medium. In Heisenberg picture, the constitutive equations of the medium together with the Maxwell laws are obtained as the equations of motion of the total system and the susceptibility tensors of the medium are calculated in terms of the coupling tensors. Following a perturbation method the Green function related to the total system is found and the time dependence of electromagnetic field operators is derived. © 2009 American Institute of Physics.
AIP Conference Proceedings (15517616)1150pp. 416-419
The electromagnetic field in a nonlinear magnetodielectric medium is quantized by modeling the medium with two quantum fields, namely E and M. The vector potential, electric and magnetic polarization densities of the medium, Maxwell and constitutive equations of the medium are found. © 2009 American Institute of Physics.
AIP Conference Proceedings (0094243X)1079pp. 89-95
Quantum field theory of a damped vibrating string as the simplest dissipative scalar field theory is investigated by introducing a minimal coupling method. The rate of energy flowing between the system and its environment is obtained. © 2008 American Institute of Physics.
Modern Physics Letters A (02177323)23(26)pp. 2163-2176
The electromagnetic field in an anisotropic and inhomogeneous magnetodielectric medium is quantized by modelling the medium with two independent quantum fields. Maxwell and constitutive equations of the medium are obtained using a minimal coupling scheme. The electric and magnetic susceptibility tensors of the medium are calculated. Finally the efficiency of the approach is elucidated by some examples. © 2008 World Scientific Publishing Company.
Journal of Physics A: Mathematical and Theoretical (17518121)41(27)
By modeling a linear, anisotropic and inhomogeneous magnetodielectric medium with two independent sets of harmonic oscillators, the electromagnetic field is quantized in such a medium. The electric and magnetic polarizations of the medium are expressed as linear combinations of the ladder operators of the harmonic oscillators modeling the magnetodielectric medium. Maxwell and the constitutive equations of the medium are obtained as the Heisenberg equations of the total system. The electric and magnetic susceptibility tensors of the medium are obtained in terms of the tensors coupling the medium with the electromagnetic field. The explicit forms of the electromagnetic field operators are obtained for a translationally invariant medium. © 2008 IOP Publishing Ltd.
Chinese Journal of Physics (05779073)46(6)pp. 723-732
The electromagnetic field in a linear absorptive dielectric medium is quantized in the framework of the damped polarization model by a new minimal coupling scheme. A Hamiltonian containing a reservoir with continuous degrees of freedom is proposed. The reservoir minimally couples to the dielectric polarization and the electromagnetic field. The Langevin equation is obtained as the equation of motion of the polarization field. Finally, the equations of motion are solved for homogeneous dielectrics. © 2008 THE PHYSICAL SOCIETY OF THE REPUBLIC OF CHINA.
Physical Review A - Atomic, Molecular, and Optical Physics (10941622)76(6)
The electromagnetic field inside a cubic cavity filled with a linear magnetodielectric medium and in the presence of external charges is quantized by modeling the magnetodielectric medium with two independent quantum fields. The electric and magnetic polarization densities of the medium are defined in terms of the ladder operators of the medium and eigenmodes of the cavity. The Maxwell and constitutive equations of the medium together with the equation of motion of the charged particles have been obtained from the Heisenberg equations using a minimal coupling scheme. The spontaneous emission of a two-level atom embedded in a magnetodielectric medium is calculated in terms of the electric and magnetic susceptibilities of the medium and the Green function of the cubic cavity, as an application of the model. © 2007 The American Physical Society.
Physical Review A - Atomic, Molecular, and Optical Physics (10941622)74(4)
By modeling a linear polarizable and magnetizable medium (magnetodielectric) with two quantum fields, namely E and M, the electromagnetic field is quantized in such a medium consistently and systematically. A Hamiltonian is proposed from which, using the Heisenberg equations, Maxwell and constitutive equations of the medium are obtained. For a homogeneous medium, the equation of motion of the quantum vector potential, A, is derived and solved analytically. Two coupling functions which describe the electromagnetic properties of the medium are introduced. Four examples are considered showing the features and the applicability of the model to both absorptive and nonabsorptive magnetodielectrics. © 2006 The American Physical Society.
International Journal of Theoretical Physics (15729575)45(1)pp. 33-46
Quantum field theory of a damped vibrating string as the simplest dissipative scalar field is investigated by it's coupling to an infinite number of Klein-Gordon fields as the environment by introducing a minimal coupling method. Heisenberg equation containing a dissipative term proportional to the velocity is obtained for a special choice of coupling function and quantum dynamics for such a dissipative system is investigated. Some kinematical relations is calculated by tracing out the environment degrees of freedom. The rate of energy flowing between the system and it's environment is obtained. © 2006 Springer Science+Business Media, Inc.
International Journal of Theoretical Physics (00207748)44(9)pp. 1573-1585
The classical and quantum dynamic of a non-linear charged vibrating string and its interaction with quantum vacuum field is investigated. Some probability amplitudes for transitions between vacuum field and quantum states of the string are obtained. The effect of non-linearity on some probability amplitudes is investigated and finally the correct equation for string containing the vacuum and radiation reaction field is obtained. © 2005 Springer Science+Business Media, Inc.
Modern Physics Letters A (02177323)20(39)pp. 3025-3034
By taking a Klein-Gordon field as the environment of a harmonic oscillator and using a new method for dealing with quantum dissipative systems (minimal coupling method), we find out the quantum dynamics and radiation reaction for a quantum damped harmonic oscillator. Applying perturbation method, we obtain some transition probabilities indicating the way energy flows between oscillator, reservoir and quantum vacuum. © World Scientific Publishing Company.
