25,713 research outputs found
Fermionization, Number of Families
We investigate bosonization/fermionization for free massless fermions being
equivalent to free massless bosons with the purpose of checking and correcting
the old rule by Aratyn and one of us (H.B.F.N.) for the number of boson species
relative to the number of fermion species which is required to have
bosonization possible. An important application of such a counting of degrees
of freedom relation would be to invoke restrictions on the number of families
that could be possible under the assumption, that all the fermions in nature
are the result of fermionizing a system of boson species. Since a theory of
fundamental fermions can be accused for not being properly local because of
having anticommutativity at space like distances rather than commutation as is
more physically reasonable to require, it is in fact called for to have all
fermions arising from fermionization of bosons. To make a realistic scenario
with the fermions all coming from fermionizing some bosons we should still have
at least some not fermionized bosons and we are driven towards that being a
gravitational field, that is not fermionized. Essentially we reach the
spin-charge-families theory by one of us (N.S.M.B.) with the detail that the
number of fermion components and therefore of families get determined from what
possibilities for fermionization will finally turn out to exist. The
spin-charge-family theory has long been plagued by predicting 4 families rather
than the phenomenologically more favoured 3. Unfortunately we do not yet
understand well enough the unphysical negative norm square components in the
system of bosons that can fermionize in higher dimensions because we have no
working high dimensional case of fermionization. But suspecting they involve
gauge fields with complicated unphysical state systems the corrections from
such states could putatively improve the family number prediction.Comment: 30 pages, H.B. Nielsen presented the talk at Workshop
"What Comes Beyond the Standard Models", Bled, 09-17 of July, 201
Why Nature has made a choice of one time and three space coordinates?
We propose a possible answer to one of the most exciting open questions in
physics and cosmology, that is the question why we seem to experience four-
dimensional space-time with three ordinary and one time dimensions. We have
known for more than 70 years that (elementary) particles have spin degrees of
freedom, we also know that besides spin they also have charge degrees of
freedom, both degrees of freedom in addition to the position and momentum
degrees of freedom. We may call these ''internal degrees of freedom '' the
''internal space'' and we can think of all the different particles, like quarks
and leptons, as being different internal states of the same particle. The
question then naturally arises: Is the choice of the Minkowski metric and the
four-dimensional space-time influenced by the ''internal space''?
Making assumptions (such as particles being in first approximation massless)
about the equations of motion, we argue for restrictions on the number of space
and time dimensions. (Actually the Standard model predicts and experiments
confirm that elementary particles are massless until interactions switch on
masses.)
Accepting our explanation of the space-time signature and the number of
dimensions would be a point supporting (further) the importance of the
''internal space''.Comment: 13 pages, LaTe
Domain-wall fermions with dynamical gauge fields
We have carried out a numerical simulation of a domain-wall model in
-dimensions, in the presence of a dynamical gauge field only in an extra
dimension, corresponding to the weak coupling limit of a ( 2-dimensional )
physical gauge coupling. Using a quenched approximation we have investigated
this model at 0.5 ( ``symmetric'' phase),
1.0, and 5.0 (``broken'' phase), where is the gauge coupling constant of
the extra dimension. We have found that there exists a critical value of a
domain-wall mass which separates a region with a fermionic zero
mode on the domain-wall from the one without it, in both symmetric and broken
phases. This result suggests that the domain-wall method may work for the
construction of lattice chiral gauge theories.Comment: 27 pages (11 figures), latex (epsf style-file needed
Perturbative study for domain-wall fermions in 4+1 dimensions
We investigate a U(1) chiral gauge model in 4+1 dimensions formulated on the
lattice via the domain-wall method. We calculate an effective action for smooth
background gauge fields at a fermion one loop level. From this calculation we
discuss properties of the resulting 4 dimensional theory, such as gauge
invariance of 2 point functions, gauge anomalies and an anomaly in the fermion
number current.Comment: 39 pages incl. 9 figures, REVTeX+epsf, uuencoded Z-compressed .tar
fil
Constraints on the Existence of Chiral Fermions in Interacting Lattice Theories
It is shown that an interacting theory, defined on a regular lattice, must
have a vector-like spectrum if the following conditions are satisfied:
(a)~locality, (b)~relativistic continuum limit without massless bosons, and
(c)~pole-free effective vertex functions for conserved currents.
The proof exploits the zero frequency inverse retarded propagator of an
appropriate set of interpolating fields as an effective quadratic hamiltonian,
to which the Nielsen-Ninomiya theorem is applied.Comment: LaTeX, 9 pages, WIS--93/56--JUNE--P
Spin Chains as Perfect Quantum State Mirrors
Quantum information transfer is an important part of quantum information
processing. Several proposals for quantum information transfer along linear
arrays of nearest-neighbor coupled qubits or spins were made recently. Perfect
transfer was shown to exist in two models with specifically designed strongly
inhomogeneous couplings. We show that perfect transfer occurs in an entire
class of chains, including systems whose nearest-neighbor couplings vary only
weakly along the chain. The key to these observations is the Jordan-Wigner
mapping of spins to noninteracting lattice fermions which display perfectly
periodic dynamics if the single-particle energy spectrum is appropriate. After
a half-period of that dynamics any state is transformed into its mirror image
with respect to the center of the chain. The absence of fermion interactions
preserves these features at arbitrary temperature and allows for the transfer
of nontrivially entangled states of several spins or qubits.Comment: Abstract extended, introduction shortened, some clarifications in the
text, one new reference. Accepted by Phys. Rev. A (Rapid Communications
Chiral Symmetry Breaking on the Lattice: a Study of the Strongly Coupled Lattice Schwinger Model
We revisit the strong coupling limit of the Schwinger model on the lattice
using staggered fermions and the hamiltonian approach to lattice gauge
theories. Although staggered fermions have no continuous chiral symmetry, they
posses a discrete axial invari ance which forbids fermion mass and which must
be broken in order for the lattice Schwinger model to exhibit the features of
the spectrum of the continuum theory. We show that this discrete symmetry is
indeed broken spontaneously in the strong coupling li mit. Expanding around a
gauge invariant ground state and carefully considering the normal ordering of
the charge operator, we derive an improved strong coupling expansion and
compute the masses of the low lying bosonic excitations as well as the chiral
co ndensate of the model. We find very good agreement between our lattice
calculations and known continuum values for these quantities already in the
fourth order of strong coupling perturbation theory. We also find the exact
ground state of the antiferromag netic Ising spin chain with long range Coulomb
interaction, which determines the nature of the ground state in the strong
coupling limit.Comment: 24 pages, Latex, no figure
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