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lorentz condition
We prove d' Alembert equation in gravitational field with gauge invariance under the Lorentz condition.
      
From this sole hypothesis, we deduce that such a quantization may only be performed using indefinite metrics and requiring the Lorentz condition (in the form given by Gupta and Bleuler) together with gauge invariance.
      
The Lorentz condition is satisfied without indefinite metric in Hilbert space.
      
It is shown that the well-known separation of the electromagnetic field of a classical point particle into velocity-dependent and pure-radiation fields can be obtained in a simple way for the potentials also, if the Lorentz condition is dropped.
      
The metric tensor is calculated exactly and shown to be a solution ofRμv=0 without the ?Lorentz condition? taken into account.
      
The expectation value of the subsidiary condition for the ghost state, corresponding to the Lorentz condition in the classical theory, vanishes.
      
They correspond to having the Lorentz condition or e se the Bianchi identity satisfied by the fields.
      
Current conservation, the Lorentz condition and weak gauge invariance in the description of massive and massless vector particle
      
The reasons against adopting the Lorentz condition as an operator equation are not serions enough to justify the usual devices for avoiding this.
      
Lorentz) condition lead to boson models with rather different properties.
      
Minimal sections are shown to correspond to a nonlinear modification of the Lorentz condition.
      
We study the Hamiltonian of the system and we discover that, after imposing the 'Lorentz condition', it reduces to an integral over a two-dimensional surface at spatial infinity.
      
It becomes subject to the wave equation and the Lorentz condition.
      
These conditions lead to the Lorentz condition and the wave equation for the vector potential.
      
A c-number four-vector potential and Lorentz condition are derived from the relativistic wave equation.
      
The gauge condition φvuv=0 (Lorentz condition) and conservation of energy and momentum Tvμv=0 are used.
      
In addition, it is found that the five-dimensional harmonic condition is reduced to the usual four-dimensional harmonic condition plus the Lorentz condition.
      
The method also gives subsidiary conditions which, in conjunction with the masslessness of the particle, yield the Lorentz condition and the correct values of photon polarization.
      
The quantization of an electromagnetic field is analyzed and problems associated with the longitudinal and scalar components of the vector potential and governed by the Lorentz condition are discussed.
      
It is shown that the evolutionary approach to the problem makes it possible to abandon the Lorentz condition as a postulate of the theory.
      
 

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