Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: From the Photon to Maxwell Equation. Ponderations on the Concept of
  Photon Localizability and Photon Trajectory in a de Broglie-Bohm
  Interpretation of Quantum Mechanics   In this paper using the Clifford bundle formalism we show how starting from
the photon concept and its relativistic Hamilton-Jacobi equation (HJE) we
immediately get (with a simple hypothesis concerning the form of the photon
canonical momentum) Maxwell equation (ME) satisfied by a null $2$-form field
$\boldsymbol{F}$ which is a plane wave solution (PWS) of ME. Moreover, we show
how introducing a potential $1$-form $\boldsymbol{A}$ such that
$\boldsymbol{F}=d\boldsymbol{A}$ we can see how a duality rotation changed in a
\ spatial rotation transformation besides showing how $\mathrm{i}=\sqrt{-1}$
enters Maxwell theory thus permitting the writing of a representative of ME as
Schr\"{o}dinger like equation which plays a key role in answering one of the
main questions addressed in this paper, namely: is there any sense in talking
about photon trajectories in de Broglie-Bohm like theories? To this end we
investigate first the nature of the energy-momentum \emph{extensor} field of
the Maxwell field $\mathbf{T}(n)$ in some special situations showing that for
some of those cases $\mathbf{T}_{0}=\mathbf{T}(\boldsymbol{\gamma}_{0})$ even
cannot describe the flow of energy. A proposed solution is offered. We also
prove that there exists a pulse reshaping phenomenon even in vacuum. Finally we
discuss the Schr\"{o}dinger equation for a photon that follows from quantum
field theory and investigate solutions that some authors think imply in photon
localization. We discuss if such an idea is meaningful. Moreover, we show that
for such solutions it is possible (once we accept that photon wave functions
are extended in the space and also in the time domains) to derive a generalized
HJE containing a quantum potential and which may lead to non lightlike photon
trajectories in free space. We briefly discuss our findings in relation to a
recent experiment.

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The categories of this paper are: nlin
26
The categories of this paper are: bayes-an
31
The categories of this paper are: ao-sci
32
The categories of this paper are: atom-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: adap-org
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The categories of this paper are: acc-phys
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The categories of this paper are: dg-ga
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The categories of this paper are: q-bio
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The categories of this paper are: stat
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The categories of this paper are: hep-th
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The categories of this paper are: chao-dyn
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The categories of this paper are: q-alg
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The categories of this paper are: nucl-th
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The categories of this paper are: q-fin