Canonical relativistic formulation to calculate the Casimir force four-vector on anisotropic conductor polarizable and magnetizable media

2019 ◽  
Vol 34 (30) ◽  
pp. 1950247
Author(s):  
Majid Amooshahi
Keyword(s):  
Electromagnetic Field ◽  
Vector Fields ◽  
Casimir Force ◽  
Tangential Component ◽  
Antisymmetric Tensor ◽  
Relativistic Wave Equation ◽  
Total System ◽  
Tensor Fields ◽  
Relativistic Formulation ◽  
Multilayer Medium

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.

scholarly journals Canonical relativistic quantization of electromagnetic field in the presence of an anisotropic conductor magneto-dielectric medium

2017 ◽  
Vol 32 (35) ◽  
pp. 1750209 ◽  
Author(s):  
Majid Amooshahi
Keyword(s):  
Electromagnetic Field ◽  
Anisotropic Medium ◽  
Vector Fields ◽  
Constitutive Relations ◽  
Dielectric Medium ◽  
Antisymmetric Tensor ◽  
Tensor Fields ◽  
Conductivity Property ◽  
Strength Tensor ◽  
Homogeneous Anisotropic Medium

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.

Stueckelberg mechanism for antisymmetric tensor fields

2002 ◽  
Vol 80 (7) ◽  
pp. 767-779 ◽  
Author(s):  
S V Kuzmin ◽  
D.G.C. McKeon
Keyword(s):  
Gauge Invariance ◽  
Tensor Field ◽  
Vector Fields ◽  
Antisymmetric Tensor ◽  
Tensor Fields ◽  
Antisymmetric Tensor Field ◽  
Mass Terms

It is shown how vector Stueckelberg fields can be introduced to ensure gauge invariance for mass terms for an antisymmetric tensor field. Scalar Stueckelberg fields allow one to have gauge invariance for these vector fields. Both the Abelian and non-Abelian cases are considered. Fully antisymmetric rank-three tensor fields and symmetric rank-two tensor fields are also discussed. PACS No.: 11.15-1

THE RESOLUTION OF FOUR-DIMENSIONAL VECTOR FIELD AND TENSOR FIELDS, AND ITS APPLICATION TO ELECTRODYNAMICS

1955 ◽  
Vol 33 (5) ◽  
pp. 235-240
Author(s):  
N. L. Balazs
Keyword(s):  
Electromagnetic Field ◽  
Potential Field ◽  
Vector Fields ◽  
Dimensional Vector ◽  
Field Tensor ◽  
Algebraic Condition ◽  
Tensor Fields ◽  
Lorentz Condition ◽  
Electromagnetic Field Tensor ◽  
Magnetic Poles

We generalize Helmholtz's theorem and apply it to four-dimensional vector fields and tensor fields. For vector fields the generalization is straightforward. Antisymmetric tensor fields of rank two exhibit a beautiful symmetry between the irrotational part of the tensor and the dual of the solenoidal component. The physical applications show that in Maxwell's theory the irrotational part of the four-potential field has no physical meaning and the Lorentz condition makes it identically zero. In Dirac's new electrodynamics an algebraic condition is imposed on the four-potential. Hence in this theory the irrotational part is not zero, and the algebraic condition establishes a relation between the sources and vortices of the four-potential field. If we apply the resolution to the electromagnetic field tensor we can see that the free charges are responsible for the sources, and the magnetic poles, if they exist, for the vortices, provided we use the customary association between the components of the electromagnetic field tensor and the components of the electric and magnetic fields.

Spacetime symmetries

2018 ◽  
Author(s):  
Michael Kachelriess
Keyword(s):  
Riemannian Manifold ◽  
Conservation Laws ◽  
Vector Fields ◽  
Killing Vector ◽  
Geodesic Equation ◽  
Spacetime Symmetries ◽  
Tensor Fields ◽  
Killing Vector Fields ◽  
Covariant Derivatives ◽  
Killing Equation

This chapter introduces tensor fields, covariant derivatives and the geodesic equation on a (pseudo-) Riemannian manifold. It discusses how symmetries of a general space-time can be found from the Killing equation, and how the existence of Killing vector fields is connected to global conservation laws.

Massive totally antisymmetric tensor fields, a systematic study

1987 ◽  
Vol 97 (2) ◽  
pp. 141-169
Author(s):  
A. Z. Capri ◽  
M. Kobatashi
Keyword(s):  
Systematic Study ◽  
Antisymmetric Tensor ◽  
Tensor Fields

scholarly journals Antisymmetric tensor fields in Randall–Sundrum thick branes

2010 ◽  
Vol 693 (4) ◽  
pp. 503-508 ◽  
Author(s):  
G. Alencar ◽  
R.R. Landim ◽  
M.O. Tahim ◽  
C.R. Muniz ◽  
R.N. Costa Filho
Keyword(s):  
Antisymmetric Tensor ◽  
Tensor Fields ◽  
Thick Branes

scholarly journals Gauge theory approach to branes and spontaneous symmetry breaking

2017 ◽  
Vol 29 (03) ◽  
pp. 1750009 ◽  
Author(s):  
A. A. Zheltukhin
Keyword(s):  
Gauge Theory ◽  
Symmetry Breaking ◽  
Spontaneous Symmetry Breaking ◽  
Vector Fields ◽  
Theory Approach ◽  
Tensor Fields ◽  
Broken Symmetries ◽  
Goldstone Bosons ◽  
Dimensional Minkowski Space ◽  
Poincaré Symmetry

We discuss the gauge theory approach to consideration of the Nambu–Goldstone bosons as gauge and vector fields represented by the Cartan forms of spontaneously broken symmetries. The approach is generalized to describe the fundamental branes in terms of [Formula: see text]-dimensional worldvolume gauge and massless tensor fields consisting of the Nambu–Goldstone bosons associated with the spontaneously broken Poincaré symmetry of the [Formula: see text]-dimensional Minkowski space.

Strings and Antisymmetric Tensor Fields

1989 ◽  
Vol 501 (6) ◽  
pp. 439-444 ◽  
Author(s):  
S. N. Solodukhin
Keyword(s):  
Antisymmetric Tensor ◽  
Tensor Fields

Field models

2021 ◽  
pp. 42-69
Author(s):  
Iosif L. Buchbinder ◽  
Ilya L. Shapiro
Keyword(s):  
Electromagnetic Field ◽  
Scalar Field ◽  
Spinor Field ◽  
Vector Fields ◽  
Sigma Model ◽  
Complex Scalar ◽  
Yang Mills ◽  
Scalar Field Models ◽  
Complex Scalar Field ◽  
Mills Field

This chapter provides constructions of Lagrangians for various field models and discusses the basic properties of these models. Concrete examples of field models are constructed, including real and complex scalar field models, the sigma model, spinor field models and models of massless and massive free vector fields. In addition, the chapter discusses various interactions between fields, including the interactions of scalars and spinors with the electromagnetic field. A detailed discussion of the Yang-Mills field is given as well.

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