Electromagnetic external

In addition, there could be a mechanical or electromagnetic interaction of a system with an external entity which may do work on an otherwise isolated system. Such a contact with a work source can be represented by the Hamiltonian U p, q, x) where x is the coordinate (for example, the position of a piston in a box containing a gas, or the magnetic moment if an external magnetic field is present, or the electric dipole moment in the presence of an external electric field) describing the interaction between the system and the external work source. Then the force, canonically conjugate to x, which the system exerts on the outside world is... 

In die presence of an electromagnetic field of energy of about our systems can undergo absorjDtive transitions from to E2, extracting a photon from die electric field. In addition, as described by Einstein, die field can induce emission of photons from 2 lo E (given E2 is occupied). Let die energy density of die external field be E(v) dren. 

Now the Lagrangean associated with the nuclear motion is not invariant under a local gauge transformation. Eor this to be the case, the Lagrangean needs to include also an interaction field. This field can be represented either as a vector field (actually a four-vector, familiar from electromagnetism), or as a tensorial, YM type field. Whatever the form of the field, there are always two parts to it. First, the field induced by the nuclear motion itself and second, an externally induced field, actually produced by some other particles E, R, which are not part of the original formalism. (At our convenience, we could include these and then these would be part of the extended coordinates r, R. The procedure would then result in the appearance of a potential interaction, but not having the field. ) At a first glance, the field (whether induced internally... 

Two states /a and /b that are eigenfunctions of a Hamiltonian Hq in the absence of some external perturbation (e.g., electromagnetic field or static electric field or potential due to surrounding ligands) can be "coupled" by the perturbation V only if the symmetries of V and of the two wavefunctions obey a so-called selection rule. In particular, only if the coupling integral (see Appendix D which deals with time independent perturbation theory)... 

In a plasma, the constituent atoms, ions, and electrons are made to move faster by an electromagnetic field and not by application of heat externally or through combustion processes. Nevertheless, the result is the same as if the plasma had been heated externally the constituent atoms, ions, and electrons are made to move faster and faster, eventually reaching a distribution of kinetic energies that would be characteristic of the Boltzmann equation applied to a gas that had been... 

A discharge ignited in argon and coupled inductively to an external high-frequency electromagnetic field produces a plasma of ions, neutrals, and electrons with a temperature of about 7000 to 10,000°C. Samples introduced into the plasma under these extremely energetic conditions are fragmented into atoms and ions of their constituent elements. These ions are examined by a mass analyzer, frequently a quadrupole instrument. 

The composite conductor is typically wound in the form of a cable, which can be cooled either internally by a forced belium flow or externally by immersion in a pool of belium. Large electromagnetic body forces, up to 500 t/m, are experienced by the conductor during operation. These are contained by a massive external stmcture, although designs have been proposed in which the conductor itself serves as its own force containment stmcture (126). 

Opening the suc tion valves by some external force (oil from the lubricating system, discharge gas, electromagnets. . . ). 

Various electromagnetic and mechanical measuring methods are used to investigate the old well casings to determine whether there is external or internal corrosion. 

In the presence of an external magnetic induction B this dipole Pm has a potential energy given by the laws of classical electromagnetism as... 

Instruments with a balanced input circuit are available for measurements where both input terminals are normally at a potential other than earth. Further problems arise due to common-mode interference arising from the presence of multiple earth loops in the circuits. In these cases the instrument may need to be isolated from the mains earth. Finally, high-frequency instruments, unless properly screened, may be subject to radiated electromagnetic interference arising from strong external fields. 

Before embarking on the problem of the interaction of the negaton-positon field with the quantized electromagnetic field, we shall first consider the case of the negaton-positon field interacting with an external, classical (prescribed) electromagnetic field. We shall also outline in the present chapter those aspects of the theory of the S-matrix that will be required for the treatment of quantum electrodynamics. Section 10.4 presents a treatment of the Dirac equation in an external field. 

Heisenberg picture, the operators describing the negaton-positon field in the presence of an external (classically prescribed) electromagnetic field, Al(x), satisfy the following equations of motion... 

The relation between the external potential and the external current, which is the source of the external electromagnetic field, is... 

For a discussion of the quantized electromagnetic field interacting with a given (prescribed) external current, see ... 

Although the previous development was based on the assumption that H(t) = 27(0), it can readily be verified that the formulae (10-148)-(10-152) are valid more generally. In particular for the negaton-positon field interacting with an external electromagnetic field, we have... 

In other words, due to its interaction with the radiation field, a negaton interacts with a slowly varying external electromagnetic field magnetic moment were (approximately to order a) equal to... 

Navier-Stokes equations, 24 Negative criterion of Bendixon, 333 Negaton-positon field in an external field, 580 interacting with electromagnetic field, Hamiltonian for, 645 interaction with radiation field, 642 Negaton-positon system, 540 Negaton scattering by an external field, 613... 

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