312 research outputs found
The CPT group of the spin-3/2 field
We find out that both the matrix and the operator CPT groups of the spin-3/2
field (with or without mass) are respectively isomorphic to
and . These groups are exactly
the same groups as for the Dirac field, though there is no a priori reason why
they should coincide.Comment: 9 pages. We are replacing the original version (v1) because there was
a mistake in the calculation which led to wrong group
Numerical Object Oriented Quantum Field Theory Calculations
The qft++ package is a library of C++ classes that facilitate numerical (not
algebraic) quantum field theory calculations. Mathematical objects such as
matrices, tensors, Dirac spinors, polarization and orbital angular momentum
tensors, etc. are represented as C++ objects in qft++. The package permits
construction of code which closely resembles quantum field theory expressions,
allowing for quick and reliable calculations.Comment: 9 pages, 3 figures, submitted to Comp. Phys. Com
Exclusive Decuplet-Baryon Pair Production in Two-Photon Collisions
This work extends our previous studies of two-photon annihilation into
baryon-antibaryon pairs from spin-1/2 octet to spin-3/2 decuplet baryons. Our
approach is based on perturbative QCD and treats baryons as quark-diquark
systems. Using the same model parameters as in our previous work, supplemented
by QCD sum-rule results for decuplet baryon wave functions, we are able to give
absolute predictions for decuplet baryon cross sections without introducing new
parameters. We find that the cross section is of the same order
of magnitude as the proton cross section, well within experimental bounds.Comment: 14 pages, 2 figure
Special metrics and Triality
We investigate a new 8-dimensional Riemannian geometry defined by a generic
closed and coclosed 3-form with stabiliser PSU(3), and which arises as a
critical point of Hitchin's variational principle. We give a Riemannian
characterisation of this structure in terms of invariant spinor-valued 1-forms,
which are harmonic with respect to the twisted Dirac operator \Db on
. We establish various obstructions to the existence of
topological reductions to PSU(3). For compact manifolds, we also give
sufficient conditions for topological PSU(3)-structures that can be lifted to
topological SU(3)-structures. We also construct the first known compact example
of an integrable non-symmetric PSU(3)-structure. In the same vein, we give a
new Riemannian characterisation for topological quaternionic K\"ahler
structures which are defined by an -invariant self-dual
4-form. Again, we show that this form is closed if and only if the
corresponding spinor-valued 1-form is harmonic for \Db and that these
equivalent conditions produce constraints on the Ricci tensor.Comment: 41 pages. v2: typos corrected, presentation improved v3: final
versio
Correspondence of consistent and inconsistent spin-3/2 couplings via the equivalence theorem
The Rarita-Schwinger theory of free massive spin-3/2 field obeys the physical
degrees of freedom counting, and one can distinguish ``consistent'' couplings
which maintain this property and ``inconsistent'' couplings which destroy it.
We show how one can obtain consistent couplings from inconsistent ones by a
redefinition of the spin-3/2 field. The field redefinition gives rise to
additional ``contact terms'' which, via the equivalence theorem, can be
associated with the contribution of the extra lower-spin degrees of freedom
involved by the inconsistent coupling.Comment: RevTeX, 10 pages, 2 figures; text and references substantially
revised, formulae unchange
The nucleon and Delta-resonance masses in relativistic chiral effective-field theory
We study the chiral behavior of the nucleon and -isobar masses within
a manifestly covariant chiral effective-field theory, consistent with the
analyticity principle. We compute the and one-loop
contributions to the mass and field-renormalization constant, and find that
they can be described in terms of universal relativistic loop functions,
multiplied by appropriate spin, isospin and coupling constants. We show that
these relativistic one-loop corrections, when properly renormalized, obey the
chiral power-counting and vanish in the chiral limit. The results including
only the -loop corrections compare favorably with the lattice QCD data
for the pion-mass dependence of the nucleon and masses, while
inclusion of the loops tends to spoil this agreement.Comment: 13 pages, 3 figs, 2 table
A No-Go Theorem for the Consistent Quantization of Spin 3/2 Fields on General Curved Spacetimes
It is well-known that coupling a spin -field to a gravitational or
electromagnetic background leads to potential problems both in the classical
and in the quantum theory. Various solutions to these problems have been
proposed so far, which are all restricted to a limited class of backgrounds. On
the other hand, negative results for general gravitational backgrounds have
been reported only for a limited set of couplings to the background to date.
Hence, to our knowledge, a comprehensive analysis of all possible couplings to
the gravitational field and general gravitational backgrounds including
off-shell ones has not been performed so far. In this work we analyse whether
it is possible to couple a spin -field to a gravitational field in
such a way that the resulting quantum theory is consistent on arbitrary
gravitational backgrounds. We find that this is impossible as all couplings
require the background to be an Einstein spacetime for consistency. This
enforces the widespread belief that supergravity theories are the only
meaningful models which contain spin fields as in these models such
restrictions of the gravitational background appear naturally as on-shell
conditions.Comment: 8 pages, substantially abridged, results unchange
Cones, Spins and Heat Kernels
The heat kernels of Laplacians for spin 1/2, 1, 3/2 and 2 fields, and the
asymptotic expansion of their traces are studied on manifolds with conical
singularities. The exact mode-by-mode analysis is carried out for 2-dimensional
domains and then extended to arbitrary dimensions. The corrections to the first
Schwinger-DeWitt coefficients in the trace expansion, due to conical
singularities, are found for all the above spins. The results for spins 1/2 and
1 resemble the scalar case. However, the heat kernels of the Lichnerowicz spin
2 operator and the spin 3/2 Laplacian show a new feature. When the conical
angle deficit vanishes the limiting values of these traces differ from the
corresponding values computed on the smooth manifold. The reason for the
discrepancy is breaking of the local translational isometries near a conical
singularity. As an application, the results are used to find the ultraviolet
divergences in the quantum corrections to the black hole entropy for all these
spins.Comment: latex file, 27 page
Tensionless strings, correspondence with SO(D,D) sigma model
String theory with perimeter action is tensionless by its geometrical nature
and has pure massless spectrum of higher spin gauge particles. I demonstrate
that liner transformation of the world-sheet fields defines a map to the
SO(D,D) sigma model equipped by additional Abelian constraint, which breaks
SO(D,D) to a diagonal SO(1,D-1). The effective tension is equal to the square
of the dimensional coupling constant of the perimeter action. This
correspondence allows to view the perimeter action as a "square root" of the
Nambu-Goto area action. The aforementioned map between tensionless strings and
SO(D,D) sigma model allows to introduce the vertex operators in full analogy
with the standard string theory and to confirm the form of the vertex operators
introduced earlier.Comment: Latex, 9 page
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