144 research outputs found
MiniBooNE and a (CP)^2 = -1 sterile neutrino
It has been taken as granted that the observation of two independent
mass-squared differences necessarily fixes the number of underlying mass
eigenstates as three, and that the addition of a sterile neutrino provides an
additional mass-squared difference. The purpose of this Letter is to argue that
if one considers a sterile neutrino component that belongs to the (CP)^2 = - 1
sector, then both of the stated claims are false. We also outline how the
results reported here, when combined with the forthcoming MiniBooNE data and
other experiments, can help settle the issue of the CP properties of the
sterile neutrino; if such a component does indeed exist.Comment: Mod. Phys. Lett. A (in press, 8 pages
Decoherence of spin echoes
We define a quantity, the so-called purity fidelity, which measures the rate
of dynamical irreversibility due to decoherence, observed e.g in echo
experiments, in the presence of an arbitrary small perturbation of the total
(system + environment) Hamiltonian. We derive a linear response formula for the
purity fidelity in terms of integrated time correlation functions of the
perturbation. Our relation predicts, similarly to the case of fidelity decay,
faster decay of purity fidelity the slower decay of time correlations is. In
particular, we find exponential decay in quantum mixing regime and faster,
initially quadratic and later typically gaussian decay in the regime of
non-ergodic, e.g. integrable quantum dynamics. We illustrate our approach by an
analytical calculation and numerical experiments in the Ising spin 1/2 chain
kicked with tilted homogeneous magnetic field where part of the chain is
interpreted as a system under observation and part as an environment.Comment: 22 pages, 10 figure
Dark matter: A spin one half fermion field with mass dimension one?
We report an unexpected theoretical discovery of a spin one half matter field
with mass dimension one. It is based on a complete set of eigenspinors of the
charge conjugation operator. Due to its unusual properties with respect to
charge conjugation and parity it belongs to a non standard Wigner class.
Consequently, the theory exhibits non-locality with (CPT)^2 = - I. Its dominant
interaction with known forms of matter is via Higgs, and with gravity. This
aspect leads us to contemplate it as a first-principle candidate for dark
matter.Comment: 5 pages, RevTex, v2: slightly extended discussion, new refs. and note
adde
The Stabilized Poincare-Heisenberg algebra: a Clifford algebra viewpoint
The stabilized Poincare-Heisenberg algebra (SPHA) is the Lie algebra of
quantum relativistic kinematics generated by fifteen generators. It is obtained
from imposing stability conditions after attempting to combine the Lie algebras
of quantum mechanics and relativity which by themselves are stable, however not
when combined. In this paper we show how the sixteen dimensional Clifford
algebra CL(1,3) can be used to generate the SPHA. The Clifford algebra path to
the SPHA avoids the traditional stability considerations, relying instead on
the fact that CL(1,3) is a semi-simple algebra and therefore stable. It is
therefore conceptually easier and more straightforward to work with a Clifford
algebra. The Clifford algebra path suggests the next evolutionary step toward a
theory of physics at the interface of GR and QM might be to depart from working
in space-time and instead to work in space-time-momentum.Comment: 14 page
Isotopic liftings of Clifford algebras and applications in elementary particle mass matrices
Isotopic liftings of algebraic structures are investigated in the context of
Clifford algebras, where it is defined a new product involving an arbitrary,
but fixed, element of the Clifford algebra. This element acts as the unit with
respect to the introduced product, and is called isounit. We construct
isotopies in both associative and non-associative arbitrary algebras, and
examples of these constructions are exhibited using Clifford algebras, which
although associative, can generate the octonionic, non-associative, algebra.
The whole formalism is developed in a Clifford algebraic arena, giving also the
necessary pre-requisites to introduce isotopies of the exterior algebra. The
flavor hadronic symmetry of the six u,d,s,c,b,t quarks is shown to be exact,
when the generators of the isotopic Lie algebra su(6) are constructed, and the
unit of the isotopic Clifford algebra is shown to be a function of the six
quark masses. The limits constraining the parameters, that are entries of the
representation of the isounit in the isotopic group SU(6), are based on the
most recent limits imposed on quark masses.Comment: 19 page
Revisiting Clifford algebras and spinors III: conformal structures and twistors in the paravector model of spacetime
This paper is the third of a series of three, and it is the continuation of
math-ph/0412074 and math-ph/0412075. After reviewing the conformal spacetime
structure, conformal maps are described in Minkowski spacetime as the twisted
adjoint representation of the group Spin_+(2,4), acting on paravectors.
Twistors are then presented via the paravector model of Clifford algebras and
related to conformal maps in the Clifford algebra over the lorentzian R{4,1}$
spacetime. We construct twistors in Minkowski spacetime as algebraic spinors
associated with the Dirac-Clifford algebra Cl(1,3)(C) using one lower spacetime
dimension than standard Clifford algebra formulations, since for this purpose
the Clifford algebra over R{4,1} is also used to describe conformal maps,
instead of R{2,4}. Although some papers have already described twistors using
the algebra Cl(1,3)(C), isomorphic to Cl(4,1), the present formulation sheds
some new light on the use of the paravector model and generalizations.Comment: 17 page
Geometric Algebra Model of Distributed Representations
Formalism based on GA is an alternative to distributed representation models
developed so far --- Smolensky's tensor product, Holographic Reduced
Representations (HRR) and Binary Spatter Code (BSC). Convolutions are replaced
by geometric products, interpretable in terms of geometry which seems to be the
most natural language for visualization of higher concepts. This paper recalls
the main ideas behind the GA model and investigates recognition test results
using both inner product and a clipped version of matrix representation. The
influence of accidental blade equality on recognition is also studied. Finally,
the efficiency of the GA model is compared to that of previously developed
models.Comment: 30 pages, 19 figure
Matrix exponential via Clifford algebras
We use isomorphism between matrix algebras and simple orthogonal
Clifford algebras \cl(Q) to compute matrix exponential of a real,
complex, and quaternionic matrix A. The isomorphic image in
\cl(Q), where the quadratic form has a suitable signature is
exponentiated modulo a minimal polynomial of using Clifford exponential.
Elements of \cl(Q) are treated as symbolic multivariate polynomials in
Grassmann monomials. Computations in \cl(Q) are performed with a Maple
package `CLIFFORD'. Three examples of matrix exponentiation are given
On the Decomposition of Clifford Algebras of Arbitrary Bilinear Form
Clifford algebras are naturally associated with quadratic forms. These
algebras are Z_2-graded by construction. However, only a Z_n-gradation induced
by a choice of a basis, or even better, by a Chevalley vector space isomorphism
Cl(V) \bigwedge V and an ordering, guarantees a multi-vector decomposition
into scalars, vectors, tensors, and so on, mandatory in physics. We show that
the Chevalley isomorphism theorem cannot be generalized to algebras if the
Z_n-grading or other structures are added, e.g., a linear form. We work with
pairs consisting of a Clifford algebra and a linear form or a Z_n-grading which
we now call 'Clifford algebras of multi-vectors' or 'quantum Clifford
algebras'. It turns out, that in this sense, all multi-vector Clifford algebras
of the same quadratic but different bilinear forms are non-isomorphic. The
usefulness of such algebras in quantum field theory and superconductivity was
shown elsewhere. Allowing for arbitrary bilinear forms however spoils their
diagonalizability which has a considerable effect on the tensor decomposition
of the Clifford algebras governed by the periodicity theorems, including the
Atiyah-Bott-Shapiro mod 8 periodicity. We consider real algebras Cl_{p,q} which
can be decomposed in the symmetric case into a tensor product Cl_{p-1,q-1}
\otimes Cl_{1,1}. The general case used in quantum field theory lacks this
feature. Theories with non-symmetric bilinear forms are however needed in the
analysis of multi-particle states in interacting theories. A connection to
q-deformed structures through nontrivial vacuum states in quantum theories is
outlined.Comment: 25 pages, 1 figure, LaTeX, {Paper presented at the 5th International
Conference on Clifford Algebras and their Applications in Mathematical
Physics, Ixtapa, Mexico, June 27 - July 4, 199
On Clifford Subalgebras, Spacetime Splittings and Applications
Z2-gradings of Clifford algebras are reviewed and we shall be concerned with
an alpha-grading based on the structure of inner automorphisms, which is
closely related to the spacetime splitting, if we consider the standard
conjugation map automorphism by an arbitrary, but fixed, splitting vector.
After briefly sketching the orthogonal and parallel components of products of
differential forms, where we introduce the parallel [orthogonal] part as the
space [time] component, we provide a detailed exposition of the Dirac operator
splitting and we show how the differential operator parallel and orthogonal
components are related to the Lie derivative along the splitting vector and the
angular momentum splitting bivector. We also introduce multivectorial-induced
alpha-gradings and present the Dirac equation in terms of the spacetime
splitting, where the Dirac spinor field is shown to be a direct sum of two
quaternions. We point out some possible physical applications of the formalism
developed.Comment: 22 pages, accepted for publication in International Journal of
Geometric Methods in Modern Physics 3 (8) (2006
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