340 research outputs found
Discrete versions of some Dirac type equations and plane wave solutions
A discrete version of the plane wave solution to some discrete Dirac type
equations in the spacetime algebra is established. The conditions under which a
discrete analogue of the plane wave solution satisfies the discrete Hestenes
equation are briefly discussed.Comment: 12 pages. arXiv admin note: text overlap with arXiv:1609.0459
On finitely ambiguous B\"uchi automata
Unambiguous B\"uchi automata, i.e. B\"uchi automata allowing only one
accepting run per word, are a useful restriction of B\"uchi automata that is
well-suited for probabilistic model-checking. In this paper we propose a more
permissive variant, namely finitely ambiguous B\"uchi automata, a
generalisation where each word has at most accepting runs, for some fixed
. We adapt existing notions and results concerning finite and bounded
ambiguity of finite automata to the setting of -languages and present a
translation from arbitrary nondeterministic B\"uchi automata with states to
finitely ambiguous automata with at most states and at most accepting
runs per word
An interpolation problem arising in a coupling of the finite element method with holomorphic basis functions
The purpose of this paper is to prove an interpolation theorem which arises in a method of coupling of a finite
element and an analytical solution for boundary value problems with singularities
On local boundary CFT and non-local CFT on the boundary
The holographic relation between local boundary conformal quantum field
theories (BCFT) and their non-local boundary restrictions is reviewed, and
non-vacuum BCFT's, whose existence was conjectured previously, are constructed.Comment: 16 pages. Contribution to "Rigorous Quantum Field Theory", Symposium
in honour of J. Bros, Paris, July 2004. Based on joint work math-ph/0405067
with R. Long
Note on Dirac--K\"ahler massless fields
We obtain the canonical and symmetrical Belinfante energy-momentum tensors of
Dirac--K\"{a}hler's fields. It is shown that the traces of the energy-momentum
tensors are not equal to zero. We find the canonical and Belinfante dilatation
currents which are not conserved, but a new conserved dilatation current is
obtained. It is pointed out that the conformal symmetry is broken. The
canonical quantization is performed and the propagator of the massless fields
in the first-order formalism is found.Comment: 16 pages, minor corrections in the text, published versio
Positivity and conservation of superenergy tensors
Two essential properties of energy-momentum tensors T_{\mu\nu} are their
positivity and conservation. This is mathematically formalized by,
respectively, an energy condition, as the dominant energy condition, and the
vanishing of their divergence \nabla^\mu T_{\mu\nu}=0. The classical Bel and
Bel-Robinson superenergy tensors, generated from the Riemann and Weyl tensors,
respectively, are rank-4 tensors. But they share these two properties with
energy momentum tensors: the Dominant Property (DP) and the divergence-free
property in the absence of sources (vacuum). Senovilla defined a universal
algebraic construction which generates a basic superenergy tensor T{A} from any
arbitrary tensor A. In this construction the seed tensor A is structured as an
r-fold multivector, which can always be done. The most important feature of the
basic superenergy tensors is that they satisfy automatically the DP,
independently of the generating tensor A. In a previous paper we presented a
more compact definition of T{A} using the r-fold Clifford algebra. This form
for the superenergy tensors allowed to obtain an easy proof of the DP valid for
any dimension. In this paper we include this proof. We explain which new
elements appear when we consider the tensor T{A} generated by a
non-degree-defined r-fold multivector A and how orthogonal Lorentz
transformations and bilinear observables of spinor fields are included as
particular cases of superenergy tensors. We find some sufficient conditions for
the seed tensor A, which guarantee that the generated tensor T{A} is
divergence-free. These sufficient conditions are satisfied by some physical
fields, which are presented as examples.Comment: 19 pages, no figures. Language and minor changes. Published versio
Hypercomplex Integrable Systems
In this paper we study hypercomplex manifolds in four dimensions. Rather than
using an approach based on differential forms, we develop a dual approach using
vector fields. The condition on these vector fields may then be interpreted as
Lax equations, exhibiting the integrability properties of such manifolds. A
number of different field equations for such hypercomplex manifolds are
derived, one of which is in Cauchy-Kovaleskaya form which enables a formal
general solution to be given. Various other properties of the field equations
and their solutions are studied, such as their symmetry properties and the
associated hierarchy of conservation laws.Comment: Latex file, 19 page
A condensed matter interpretation of SM fermions and gauge fields
We present the bundle Aff(3) x C x /(R^3), with a geometric Dirac equation on
it, as a three-dimensional geometric interpretation of the SM fermions. Each C
x /(R^3) describes an electroweak doublet. The Dirac equation has a
doubler-free staggered spatial discretization on the lattice space Aff(3) x C
(Z^3). This space allows a simple physical interpretation as a phase space of a
lattice of cells in R^3. We find the SM SU(3)_c x SU(2)_L x U(1)_Y action on
Aff(3) x C x /(R^3) to be a maximal anomaly-free special gauge action
preserving E(3) symmetry and symplectic structure, which can be constructed
using two simple types of gauge-like lattice fields: Wilson gauge fields and
correction terms for lattice deformations. The lattice fermion fields we
propose to quantize as low energy states of a canonical quantum theory with
Z_2-degenerated vacuum state. We construct anticommuting fermion operators for
the resulting Z_2-valued (spin) field theory. A metric theory of gravity
compatible with this model is presented too.Comment: Minimal modifications in comparison with the published versio
New Results in Sasaki-Einstein Geometry
This article is a summary of some of the author's work on Sasaki-Einstein
geometry. A rather general conjecture in string theory known as the AdS/CFT
correspondence relates Sasaki-Einstein geometry, in low dimensions, to
superconformal field theory; properties of the latter are therefore reflected
in the former, and vice versa. Despite this physical motivation, many recent
results are of independent geometrical interest, and are described here in
purely mathematical terms: explicit constructions of infinite families of both
quasi-regular and irregular Sasaki-Einstein metrics; toric Sasakian geometry;
an extremal problem that determines the Reeb vector field for, and hence also
the volume of, a Sasaki-Einstein manifold; and finally, obstructions to the
existence of Sasaki-Einstein metrics. Some of these results also provide new
insights into Kahler geometry, and in particular new obstructions to the
existence of Kahler-Einstein metrics on Fano orbifolds.Comment: 31 pages, no figures. Invited contribution to the proceedings of the
conference "Riemannian Topology: Geometric Structures on Manifolds"; minor
typos corrected, reference added; published version; Riemannian Topology and
Geometric Structures on Manifolds (Progress in Mathematics), Birkhauser (Nov
2008
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