scholarly journals On the new field theory

1936 ◽  
Vol 155 (886) ◽  
pp. 597-613 ◽  
Keyword(s):  
Field Theory ◽  
Quantum Theory ◽  
Classical Mechanics ◽  
Total Force ◽  
Field Equations ◽  
Conservation Of Energy ◽  
Variation Equation ◽  
Energy And Momentum ◽  
Field Strengths

The purpose of this paper is to derive the dynamical conditions governing the motion of point charges in the New Field Theory from the variation equation δ ∫ H√- g dx 1 dx 2 dx 3 dx 4 = 0, of Born and infeld, where the coordinates of the charges, as well as the field strengths, are varied; also to develop the theory along lines parallel to classical mechanics, with a view to generalization to the quantum theory in a later paper. It was clear from the start of the New Field Theory (although not fully appreciated in I and II) that the motion of the charges was not governed by the field equations alone, and that some further condition had to be added. It was also clear from physical considerations of conservation of energy and momentum what this condition had to be; namely, that the total force ( see § 5) on each charge must vanish. But hitherto this has not been derived from the more basic variation equation.

The classical field theory of matter and electricity - An approach from first principles

1960 ◽  
Vol 253 (1025) ◽  
pp. 185-204 ◽  
Keyword(s):  
Field Theory ◽  
First Principles ◽  
Classical Field Theory ◽  
Classical Field ◽  
Field Equations ◽  
Additional Energy ◽  
Conservation Of Energy ◽  
Electromagnetic Field Theory ◽  
Energy And Momentum ◽  
Accepted Form

The most desirable classical field theory of the fundamental continuous substratum of matter, from which we can imagine particles are formed, would generally be considered to be the electromagnetic equations but for the fact that these are not consistent with the permanent existence of electrons. Instead of attempting (as has been usual) to modify the equations by special assumptions for the purpose, the problem is attacked here by deriving from first principles field equations which represent conserved matter; for the failure of the standard equations can be traced to the fact that they do not admit conservation of energy and momentum in general, but only in simple cases. The new equations are found to be identical with those of standard electromagnetic theory except that they contain two extra variables, which indicate the existence of additional energy, momentum and stress in the field. The two variables, however, come into the equations in a way which allows them to be included in the charge and current terms, so that they become there concealed and leave the form of the equations virtually unchanged. Consequently they do not affect the ordinary practical use which is made of the electromagnetic equations; they only come into open play in fundamental theory and in the presence of charge and current in the field, and there they remove the difficulties which the electromagnetic field theory in its accepted form presents.

Canonical quantization of free fields

2021 ◽  
pp. 70-98
Author(s):  
Iosif L. Buchbinder ◽  
Ilya L. Shapiro
Keyword(s):  
Field Theory ◽  
Quantum Theory ◽  
Electromagnetic Fields ◽  
Classical Theory ◽  
Canonical Quantization ◽  
Classical Mechanics ◽  
Scalar Fields ◽  
Complex Scalar ◽  
Spinor Fields ◽  
Free Fields

This chapter discusses canonical quantization in field theory and shows how the notion of a particle arises within the framework of the concept of a field. Canonical quantization is the process of constructing a quantum theory on the basis of a classical theory. The chapter briefly considers the main elements of this procedure, starting from its simplest version in classical mechanics. It first describes the general principles of canonical quantization and then provides concrete examples. The examples include the canonical quantization of free real scalar fields, free complex scalar fields, free spinor fields and free electromagnetic fields.

scholarly journals The scattering of hard gamma rays.—Part I

1930 ◽  
Vol 128 (808) ◽  
pp. 361-375 ◽  
Keyword(s):  
Quantum Theory ◽  
Free Electron ◽  
Scattered Radiation ◽  
Wave Length ◽  
Strong Support ◽  
Conservation Of Energy ◽  
Simple Quantum ◽  
Recent Developments ◽  
Series Of Experiments ◽  
Energy And Momentum

As early as 1904 it was shown by Eve that the passage of γ -rays through matter was accompanied by the emission of secondary rays somewhat less penetrating than the primary radiation. Experiments by Kleeman, Madsen and Florance led to the conclusion that the secondary radiation was not a fluorescent radiation but a scattered radiation since its quality appeared to be independent of the nature of the radiator. These early investigations prepared the way for an admirable series of experiments by J. A. Gray which established the main features of the scattering process, showing in particular that the smaller penetrating power of the scattered radiation is due to a change in quality accompanying the act of scattering. As is well-known, a simple quantum explanation of the phenomenon has been given by Compton, the smaller penetrating power of the scattered radiation being ascribed to the smaller momentum, and therefore longer wave-lengths of the deflected quanta. Recent developments of the quantum theory leave unchanged Compton’s relation between the change in wave-length and angle of scattering, since this relation involves only the assumption of the conservation of energy and momentum during the interaction of a quantum and a free electron. Experimental research since 1913 has in the main been directed towards establishing the angular distribution of intensity of the scattered radiation, and the variation with wave-length of the probability of interaction between a quantum and an electron. The experimental results lend strong support to the theoretical formulæ recently proposed by Klein and Nishina ( loc. cit. ), in fact it now appears probable that over the whole range of wave-lengths investigated, the new quantum mechanics leads to an accurate description of the interaction between a quantum and a free electron. From the standpoint of the older quantum theory all electrons could be regarded as “free” since the binding energy of even the K electrons in lead could be neglected in comparison with the energy of the quantum, which for the γ -rays usually investigated was between 1 and 2 million volts. The scattering power per electron (the scattering coefficient divided by the number of electrons per unit volume) of all substances should therefore be the same. The early measurements of J. A. Gray referred to above showed that this was roughly true of carbon, iron and lead over a limited angular range.

The classical field theory of matter and electricity - The electromagnetic theory of particles

1960 ◽  
Vol 253 (1025) ◽  
pp. 205-226 ◽  
Keyword(s):  
Field Theory ◽  
Wave Equation ◽  
Classical Field Theory ◽  
Relativity Theory ◽  
Modern Theory ◽  
Field Equations ◽  
Electromagnetic Field Theory ◽  
Energy And Momentum ◽  
Static Form ◽  
Classical Particles

The electromagnetic field theory developed in the previous paper is here applied to the problem of devising systems which behave as classical particles. It is found that spherically symmetrical systems can exist which, when they are stationary: (1) satisfy the static form of the extended equations at every point of space; and (2) are characterized mechanically by being everywhere in equilibrium under the sole action of the Maxwellian stress of their own field—thus they are pure electromagnetic systems subsisting free of external constraint. (3) When they are transformed so as to be in motion, the energy and momentum they possess are exactly those required for material particles by relativity theory. A rather obvious restriction made on the generality of the conditions for particle existence brought to light the possibility of a solution denoting an ‘atomic’ system built up of successive shells, each of which must contain the same energy, and net charge, as the others. The reason for such a result is that, when their very great generality is restricted in the most straightforward way, the field equations reduce to the form of a wave equation. The relation of this to the wave equation of modern theory is briefly discussed. The transformation behaviour of the field equations when a Lorentz transformation is applied to the co-ordinates is dealt with in this paper; it is found that they remain invariant in form under wider transformations of the field variables than are permitted by the classical equations. The variables may be submitted to a certain transformation without the co-ordinates being transformed at all. The physical meaning of this is investigated and an explanation of it found.

scholarly journals SPACETIME SYMMETRIES IN NONCOMMUTATIVE GAUGE THEORY: A HAMILTONIAN ANALYSIS

2004 ◽  
Vol 19 (33) ◽  
pp. 2505-2517 ◽  
Author(s):  
SUBIR GHOSH
Keyword(s):  
Field Theory ◽  
Gauge Theory ◽  
Lorentz Invariance ◽  
Spacetime Symmetries ◽  
Translation Invariance ◽  
Conservation Of Energy ◽  
Invariance Violation ◽  
Poincaré Algebra ◽  
Noncommutative Gauge Theory ◽  
Energy And Momentum

We study spacetime symmetries in noncommutative (NC) gauge theory in the (constrained) Hamiltonian framework. The specific example of NC CP(1) model, posited in Ref. 9, has been considered. Subtle features of Lorentz invariance violation in NC field theory were pointed out in Ref. 13. Out of the two — observer and particle — distinct types of Lorentz transformations, symmetry under the former, (due to the translation invariance), is reflected in the conservation of energy and momentum in NC theory. The constant tensor θμν (the noncommutativity parameter) destroys invariance under the latter. In this paper we have constructed the Hamiltonian and momentum operators which are the generators of time and space translations respectively. This is related to the observer Lorentz invariance. We have also shown that the Schwinger condition and subsequently the Poincaré algebra is not obeyed and that one cannot derive a Lorentz covariant dynamical field equation. These features signal a loss of the Particle Lorentz symmetry. The basic observations in the present work will be relevant in the Hamiltonian study of a generic noncommutative field theory.

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