2 research outputs found
Photon topology
The topology of photons in vacuum is interesting because there are no photons
with , creating a hole in momentum space. We show that while
the set of all photons forms a trivial vector bundle over this
momentum space, the - and -photons form topologically nontrivial
subbundles with first Chern numbers . In contrast,
has no linearly polarized subbundles, and there is no Chern number associated
with linear polarizations. It is a known difficulty that the standard version
of Wigner's little group method produces singular representations of the
Poincar\'{e} group for massless particles. By considering representations of
the Poincar\'{e} group on vector bundles we obtain a version of Wigner's little
group method for massless particles which avoids these singularities. We show
that any massless bundle representation of the Poincar\'{e} group can be
canonically decomposed into irreducible bundle representations labeled by
helicity. This proves that the - and -photons are globally well-defined
as particles and that the photon wave function can be uniquely split into -
and -components. This formalism offers a method of quantizing the EM field
without invoking discontinuous polarization vectors as in the traditional
scheme. We also demonstrate that the spin-Chern number of photons is not a
purely topological quantity. Lastly, there has been an extended debate on
whether photon angular momentum can be split into spin and orbital parts. Our
work explains the precise issues that prevent this splitting. Photons, as
massless irreducible bundle representations of the Poincar\'{e} group, do not
admit a spin operator. Instead, the angular momentum associated with photons'
internal degree of freedom is described by a helicity-induced subalgebra, which
is 3D and commuting, corresponding to the translational symmetry of .Comment: 54 pages, 2 figure
26th Annual Computational Neuroscience Meeting (CNS*2017): Part 3 - Meeting Abstracts - Antwerp, Belgium. 15–20 July 2017
This work was produced as part of the activities of FAPESP Research,\ud
Disseminations and Innovation Center for Neuromathematics (grant\ud
2013/07699-0, S. Paulo Research Foundation). NLK is supported by a\ud
FAPESP postdoctoral fellowship (grant 2016/03855-5). ACR is partially\ud
supported by a CNPq fellowship (grant 306251/2014-0)