1,830 research outputs found
Pascual Jordan, his contributions to quantum mechanics and his legacy in contemporary local quantum physics
After recalling episodes from Pascual Jordan's biography including his
pivotal role in the shaping of quantum field theory and his much criticized
conduct during the NS regime, I draw attention to his presentation of the first
phase of development of quantum field theory in a talk presented at the 1929
Kharkov conference. He starts by giving a comprehensive account of the
beginnings of quantum theory, emphasising that particle-like properties arise
as a consequence of treating wave-motions quantum-mechanically. He then goes on
to his recent discovery of quantization of ``wave fields'' and problems of
gauge invariance. The most surprising aspect of Jordan's presentation is
however his strong belief that his field quantization is a transitory not yet
optimal formulation of the principles underlying causal, local quantum physics.
The expectation of a future more radical change coming from the main architect
of field quantization already shortly after his discovery is certainly quite
startling. I try to answer the question to what extent Jordan's 1929
expectations have been vindicated. The larger part of the present essay
consists in arguing that Jordan's plea for a formulation without ``classical
correspondence crutches'', i.e. for an intrinsic approach (which avoids
classical fields altogether), is successfully addressed in past and recent
publications on local quantum physics.Comment: More biographical detail, expansion of the part referring to Jordan's
legacy in quantum field theory, 37 pages late
Quantum corrections in the Boltzmann conductivity of graphene and their sensitivity to the choice of formalism
Semiclassical spin-coherent kinetic equations can be derived from quantum
theory with many different approaches (Liouville equation based approaches,
nonequilibrium Green's functions techniques, etc.). The collision integrals
turn out to be formally different, but coincide in textbook examples as well as
for systems where the spin-orbit coupling is only a small part of the kinetic
energy like in related studies on the spin Hall effect. In Dirac cone physics
(graphene, surface states of topological insulators like Bi_{1-x}Sb_x, Bi_2Te_3
etc.), where this coupling constitutes the entire kinetic energy, the
difference manifests itself in the precise value of the electron-hole coherence
originated quantum correction to the Drude conductivity . The leading correction is derived analytically for single and multilayer
graphene with general scalar impurities. The often neglected principal value
terms in the collision integral are important. Neglecting them yields a leading
correction of order , whereas including them can give a
correction of order . The latter opens up a counterintuitive
scenario with finite electron-hole coherent effects at Fermi energies
arbitrarily far above the neutrality point regime, for example in the form of a
shift that only depends on the dielectric constant. This residual
conductivity, possibly related to the one observed in recent experiments,
depends crucially on the approach and could offer a setting for experimentally
singling out one of the candidates. Concerning the different formalisms we
notice that the discrepancy between a density matrix approach and a Green's
function approach is removed if the Generalized Kadanoff-Baym Ansatz in the
latter is replaced by an anti-ordered version.Comment: 31 pages, 1 figure. An important sign error has been rectified in the
principal value terms in equation (52) in the vN & NSO expression. It has no
implications for the results on the leading quantum correction studied in
this paper. However, for the higher quantum corrections studied in
arXiv:1304.3929 (see comment in the latter) the implications are crucia
The Quest for Understanding in Relativistic Quantum Physics
We discuss the status and some perspectives of relativistic quantum physics.Comment: Invited contribution to the Special Issue 2000 of the Journal of
Mathematical Physics, 38 pages, typos corrected and references added, as to
appear in JM
Designing Dirac points in two-dimensional lattices
We present a framework to elucidate the existence of accidental contacts of
energy bands, particularly those called Dirac points which are the point
contacts with linear energy dispersions in their vicinity. A generalized
von-Neumann-Wigner theorem we propose here gives the number of constraints on
the lattice necessary to have contacts without fine tuning of lattice
parameters. By counting this number, one could quest for the candidate of Dirac
systems without solving the secular equation. The constraints can be provided
by any kinds of symmetry present in the system. The theory also enables the
analytical determination of k-point having accidental contact by selectively
picking up only the degenerate solution of the secular equation. By using these
frameworks, we demonstrate that the Dirac points are feasible in various
two-dimensional lattices, e.g. the anisotropic Kagome lattice under inversion
symmetry is found to have contacts over the whole lattice parameter space.
Spin-dependent cases, such as the spin-density-wave state in LaOFeAs with
reflection symmetry, are also dealt with in the present scheme.Comment: 15pages, 9figures (accepted to Phys. Rev. B
Relativistic resonances: Their masses, widths, lifetimes, superposition, and causal evolution
Whether one starts form the analytic S-matrix definition or the requirement
of gauge parameter independence in renormalization theory, a relativistic
resonance is given by a pole at a complex value s of energy squared. The
complex number s does not define the mass and width separately and this
definition does not lead to interfering Breit-Wigner if two or more resonances
are involved. To accomplish both we invoke the decaying particle aspect of a
resonance and associate to each pole a space of relativistic Gamow kets which
transform irreducibly under causal Poincare transformations. A Gamow state has
an exponential time evolution and one can choose of the many possible width
parameters, that parameter as the width of the relativistic resonance which
equals the inverse lifetime. This uniquely defines the mass and width
parameters for a relativistic resonance. Two or more poles in the same partial
wave are given by the sum of Breit-Wigners in the scattering amplitude and by a
superposition of Gamow vectors with each Gamow vector corresponding to one
Breit-Wigner. In addition to the sum of Breit-Wigners the scattering amplitude
contains a background amplitude representing direct production of the final
state (contact terms).This contact amplitude is associated to a background
vector which is a continuous superposition of Lippmann-Schwinger states.
Omitting this continuum gives the Weisskopf-Wigner approximation.Comment: 22 pages, REVTe
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