Classical Field Theories

Truesdell, C. and Toupin, R.A., The Classical Field Theories, in Encyclopedia of Physics, Vol. III/l (edited by Fliigge, S.), Springer-Verlag, Berlin, 1960. 

C. Truesdell and R.A. Toupin, The Classical Field Theories, Encyclopedia of Physics, Volume III/l, Springer-Verlag, New York, 1960. 

MSN. 180. T. Petrosky and I. Prigogine, Limits to causality and delocalization in classical field theory, in Evolution Equations and Their Applications in Physical and Life Sciences, G. Lumer and L. Weis, eds., Marcel Decker, New York, 2000. 

Truesdell, C., R. Toupin, The Classical Field Theories, Hand, der Physik, III/l, p. 700 et seq. Berlin-GOttingen-Heidelberg Springer 1960. 

From classical field theory we know that the force on a particle of mass m, charge e, and velocity v which is moving in an electromagnetic field is given by... 

The most unsatisfactory features of our derivation of the molecular Hamiltonian from the Dirac equation stem from the fact that the Dirac equation is, of course, a single particle equation. Hence all of the inter-electron terms have been introduced by including the effects of other electrons in the magnetic vector and electric scalar potentials. A particularly objectionable aspect is the inclusion of electron spin terms in the magnetic vector potential A, with the use of classical field theory to derive the results. It is therefore of interest to examine an alternative development and in this section we introduce the Breit Hamiltonian [16] as the starting point. We eventually arrive at the same molecular Hamiltonian as before, but the derivation is more satisfactory, although fundamental difficulties are still present. 

C Truesdell, R Toupin. The Classical Field Theories In S Fliige, ed. Handbuch der Physik, Berlin/Gottingen/Heildelbert Springer III/l. Vol. 3, Pt. 1. p 226 1960. 

B.T. Pickup, Classical field theory and second quantization, in Handbook of Molecular Physics and Quantum Chemistry, vol. 1 Fundamentals, ed. S. Wilson, P.F. Bernath and R. McWeeny, chapter 26, Wiley, Chichester, 2003. 

Toong TY (1983) Combustion Dynamics The Dynamics of Chemically Reacting Fluids. McGraw-Hill Book Company, New York Truesdell C, Toupin R (1960) The Classical Field Theories. In Handbuch der Physik, Vol. Ill, Pt. 1, Springer-Verlag, Berlin... 

It is a well known fact, that the PAB of stationary fields is one of the manifestations of nonclassical properties of light. PAB cannot be understood within the classical field theory describing light as a wave. But, on the other hand, it has a simple interpretation in particle (photon) models by the rise of the joint probability of two detected particles upon the increase of their time separation x close to zero. 

The connection of 1-d quantum field models and 2-d classical models is obvious because a quantum field theory in 1 space and 1 time dimension is equivalent to a Euclidean (or classical) field theory in 2 spatial dimensions. 

Our starting point is the classical field theory characterized by the Lagrangian... 

In the first step one has to quantize the classical field theory. The standard canonical quantization via equal-time commutation relations for the fermion field operator % yields... 

Truesdell, C., Toupin,R. The classical field theories. In Fliigge, S. (ed.)Handbuch der Physik, vol. III/l. Springer, Berlin (1960)... 

The BBB model is a means of macroscopic approximation to the system on an exclusively electrostatic basis it describes the solvation effects with the aid of classical field theories, primarily electrostatics and hydrodynamics. The nomenclature BBB, an abbreviation of the expression Brass Balls in a Bathtub , originates from Frank [Fr 65]. The more important classical theories included in this group have led to a result only for dilute solutions nevertheless, their refinement has continued up to the present [Ab 79, Be 78, Kr 79, Li 79]. 

TIO. C.Truesdell and R. A.Toupiti,The Classical Field Theories, in Handbuch der Physik, Vol. 

Truesdell C, Noll W (1965) The nonlinear field theories of mechanics. In FlOgge S (ed) Encyclopedia of physics, vol III/3. Springer, Heidelberg Truesdell C, Toupin RA (1960) The classical field theories. In Flugge S (ed) Encyclopedia of physics, vol III/l. Springer, Heidelberg... 

The year 1960 brought Transport Phenomena as perhaps predicted by Tom Chilton in 1939, and the The Classical Field Theories as perhaps ordained by Leonhard Euler in 1750. The wide-ranging treatment of heat, mass and momentum transfer by Bird, Stewzirt and lightfoot signalled a new era in chemical engineering research and teaching, but the basic concepts of kinematics, stress and constitutive relations still remained to be placed in their proper perspective. 

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