scholarly journals On first-order generalized Maxwell equations

2008 ◽  
Vol 86 (8) ◽  
pp. 995-1000 ◽  
Author(s):  
S I Kruglov
Keyword(s):  
Scalar Field ◽  
Gauge Invariance ◽  
Maxwell Equations ◽  
Canonical Quantization ◽  
Hamiltonian Form ◽  
First Order ◽  
The Matrix

The generalized Maxwell equations including an additional scalar field are considered in the first-order formalism. The gauge invariance of the Lagrangian and the equations is broken resulting in the appearance of a scalar field. We find the canonical and symmetrical Belinfante energy-momentum tensors. It is shown that the traces of the energy-momentum tensors are not equal to zero and the dilatation symmetry is broken in the theory considered. The matrix Hamiltonian form of equations is obtained after the exclusion of the nondynamical components. The canonical quantization is performed and the propagator of the fields is found in the first-order formalism.PACS Nos.: 03.65.Pm, 03.70.+k, 04.20.Fy

scholarly journals FIELD THEORY OF MASSIVE AND MASSLESS VECTOR PARTICLES IN THE DUFFIN–KEMMER–PETIAU FORMALISM

2011 ◽  
Vol 26 (15) ◽  
pp. 2487-2501 ◽  
Author(s):  
S. I. KRUGLOV
Keyword(s):  
Field Theory ◽  
Canonical Quantization ◽  
Hamiltonian Form ◽  
Massless Case ◽  
First Order ◽  
Dilatation Current ◽  
Vector Particles ◽  
Massive Fields

Field theory of massive and massless vector particles is considered in the first-order formalism. The Hamiltonian form of equations is obtained after the exclusion of nondynamical components. We obtain the canonical and symmetrical Belinfante energy–momentum tensors and their nonzero traces. We note that the dilatation symmetry is broken in the massive case but in the massless case the modified dilatation current is conserved. The canonical quantization is performed and the propagator of the massive fields is found in the Duffin–Kemmer–Petiau formalism.

Kinetic theory

2018 ◽  
Author(s):  
Nathalie Deruelle ◽  
Jean-Philippe Uzan
Keyword(s):  
Distribution Function ◽  
Kinetic Theory ◽  
Liouville Equation ◽  
Vlasov Equation ◽  
Particle Distribution ◽  
Equations Of Motion ◽  
Poisson Brackets ◽  
Hamiltonian Form ◽  
First Order ◽  
Number Of Particles

This chapter covers the equations governing the evolution of particle distribution and relates the macroscopic thermodynamical quantities to the distribution function. The motion of N particles is governed by 6N equations of motion of first order in time, written in either Hamiltonian form or in terms of Poisson brackets. Thus, as this chapter shows, as the number of particles grows it becomes necessary to resort to a statistical description. The chapter first introduces the Liouville equation, which states the conservation of the probability density, before turning to the Boltzmann–Vlasov equation. Finally, it discusses the Jeans equations, which are the equations obtained by taking various averages over velocities.

scholarly journals Scale Invariance, Horizons, and Inflation

2021 ◽  
Author(s):  
Andre Maeder ◽  
Vesselin G Gueorguiev
Keyword(s):  
Scalar Field ◽  
Scale Invariance ◽  
Maxwell Equations ◽  
High Redshift ◽  
Empty Space ◽  
Causal Connection ◽  
Cosmological Constant Problem ◽  
Scale Invariant ◽  
Starting Point ◽  
Final Answer

Abstract Maxwell equations and the equations of General Relativity are scale invariant in empty space. The presence of charge or currents in electromagnetism or the presence of matter in cosmology are preventing scale invariance. The question arises on how much matter within the horizon is necessary to kill scale invariance. The scale invariant field equation, first written by Dirac in 1973 and then revisited by Canuto et al. in 1977, provides the starting point to address this question. The resulting cosmological models show that, as soon as matter is present, the effects of scale invariance rapidly decline from ϱ = 0 to ϱc, and are forbidden for densities above ϱc. The absence of scale invariance in this case is consistent with considerations about causal connection. Below ϱc, scale invariance appears as an open possibility, which also depends on the occurrence of in the scale invariant context. In the present approach, we identify the scalar field of the empty space in the Scale Invariant Vacuum (SIV) context to the scalar field ϕ in the energy density $\varrho = \frac{1}{2} \dot{\varphi }^2 + V(\varphi )$ of the vacuum at inflation. This leads to some constraints on the potential. This identification also solves the so-called “cosmological constant problem”. In the framework of scale invariance, an inflation with a large number of e-foldings is also predicted. We conclude that scale invariance for models with densities below ϱc is an open possibility; the final answer may come from high redshift observations, where differences from the ΛCDM models appear.

scholarly journals Canonical Quantization of the Scalar Field: The Measure Theoretic Perspective

2015 ◽  
Vol 2015 ◽  
pp. 1-12 ◽  
Author(s):  
José Velhinho
Keyword(s):  
Scalar Field ◽  
Canonical Quantization ◽  
Field Theories ◽  
Quantum Fields ◽  
Theoretical Methods ◽  
Local Properties ◽  
Free Scalar ◽  
Free Fields ◽  
Field Behaviour

This review is devoted to measure theoretical methods in the canonical quantization of scalar field theories. We present in some detail the canonical quantization of the free scalar field. We study the measures associated with the free fields and present two characterizations of the support of these measures. The first characterization concerns local properties of the quantum fields, whereas for the second one we introduce a sequence of variables that test the field behaviour at large distances, thus allowing distinguishing between the typical quantum fields associated with different values of the mass.

scholarly journals ON SUPERLUMINAL FERMIONS WITHIN THE SECOND DERIVATIVE EQUATION

2012 ◽  
Vol 27 (14) ◽  
pp. 1250081 ◽  
Author(s):  
S. I. KRUGLOV
Keyword(s):  
Energy Momentum Tensor ◽  
Canonical Quantization ◽  
Vacuum Expectation ◽  
Momentum Tensor ◽  
Order Equation ◽  
Quantum Mechanical ◽  
Projection Operators ◽  
The Novel ◽  
First Order ◽  
Electromagnetic Interactions

We postulate the second-order derivative equation with four parameters for spin-1/2 fermions possessing two mass states. For some choice of parameters fermions propagate with the superluminal speed. Thus, the novel tachyonic equation is suggested. The relativistic 20-component first-order wave equation is formulated and projection operators extracting states with definite energy and spin projections are obtained. The Lagrangian formulation of the first-order equation is presented and the electric current and energy–momentum tensor are found. The minimal and nonminimal electromagnetic interactions of fermions are considered and Schrödinger's form of the equation and the quantum-mechanical Hamiltonian are obtained. The canonical quantization of the field in the first-order formalism is performed and we find the vacuum expectation of chronological pairing of operators.

FORC analysis of magnetically soft microparticles embedded in a polymeric elastic environment

2022 ◽  
Author(s):  
Dmitry Yu Borin ◽  
Mikhail V Vaganov
Keyword(s):  
Particle Concentration ◽  
Magnetic Hysteresis ◽  
Magnetic Response ◽  
Soft Matrix ◽  
First Order ◽  
Matrix Elasticity ◽  
Intrinsic Coercivity ◽  
The Matrix ◽  
Soft Particles ◽  
Elastomer Composites

Abstract First-order reversal curve (FORC) analysis allows one to investigate composite magnetic materials by decomposing the magnetic response of a whole sample into individual responses of the elementary objects comprising the sample. In this work, we apply this technique to analysing silicone elastomer composites reinforced with ferromagnetic microparticles possessing low intrinsic coercivity. Even though the material of such particles does not demonstrate significant magnetic hysteresis, the soft matrix of the elastomers allows for the translational mobility of the particles and enables their magnetomechanical hysteresis which renders into a wasp-waisted major magnetization loop of the whole sample. It is demonstrated that the FORC diagrams of the composites contain characteristic wing features arising from the collective hysteretic magnetization of the magnetically soft particles. The influence of the matrix elasticity and particle concentration on the shape of the wing feature is investigated, and an approach to interpreting experimental FORC diagrams of the magnetically soft magnetoactive elastomers is proposed. The experimental data are in qualitative agreement with the results of the simulation of the particle magnetization process obtained using a model comprised of two magnetically soft particles embedded in an elastic environment.

A reduction class containing formulas with one monadic predicate and one binary function symbol

1976 ◽  
Vol 41 (1) ◽  
pp. 45-49
Author(s):  
Charles E. Hughes
Keyword(s):  
Normal Form ◽  
Predicate Symbol ◽  
Conjunctive Normal Form ◽  
Function Symbol ◽  
Predicate Calculus ◽  
Binary Function ◽  
First Order ◽  
The Matrix ◽  
Reduction Class ◽  
Order Predicate Calculus

AbstractA new reduction class is presented for the satisfiability problem for well-formed formulas of the first-order predicate calculus. The members of this class are closed prenex formulas of the form ∀x∀yC. The matrix C is in conjunctive normal form and has no disjuncts with more than three literals, in fact all but one conjunct is unary. Furthermore C contains but one predicate symbol, that being unary, and one function symbol which symbol is binary.

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