2,694 research outputs found
Adelic geometry on arithmetic surfaces I: idelic and adelic interpretation of the Deligne pairing
For an arithmetic surface the Deligne
pairing \left \colon \operatorname{Pic}(X) \times
\operatorname{Pic}(X) \to \operatorname{Pic}(B) gives the "schematic
contribution" to the Arakelov intersection number. We present an idelic and
adelic interpretation of the Deligne pairing; this is the first crucial step
for a full idelic and adelic interpretation of the Arakelov intersection
number. For the idelic approach we show that the Deligne pairing can be lifted
to a pairing \left_i:\ker(d^1_\times)\times
\ker(d^1_\times)\to\operatorname{Pic}(B) , where is an
important subspace of the two dimensional idelic group . On
the other hand, the argument for the adelic interpretation is entirely
cohomological.Comment: Some typos have been correcte
Deterministic Quantization by Dynamical Boundary Conditions
We propose an unexplored quantization method. It is based on the assumption
of dynamical space-time intrinsic periodicities for relativistic fields, which
in turn can be regarded as dual to extra-dimensional fields. As a consequence
we obtain a unified and consistent interpretation of Special Relativity and
Quantum Mechanics in terms of Deterministic Geometrodynamics.Comment: 4 pages. Based on the talk given at Frontiers Of Fundamental And
Computational Physics: 10th International Symposiu
Elementary spacetime cycles
Every system in physics is described in terms of interacting elementary
particles characterized by modulated spacetime recurrences. These intrinsic
periodicities, implicit in undulatory mechanics, imply that every free particle
is a reference clock linking time to the particle's mass, and every system is
formalizable by means of modulated elementary spacetime cycles. We propose a
novel consistent relativistic formalism based on intrinsically cyclic spacetime
dimensions, encoding the quantum recurrences of elementary particles into
spacetime geometrodynamics. The advantage of the resulting theory is a formal
derivation of quantum behaviors from relativistic mechanics, in which the
constraint of intrinsic periodicity turns out to quantize the elementary
particles; as well as a geometrodynamical description of gauge interaction
which, similarly to gravity, turns out to be represented by relativistic
modulations of the internal clocks of the elementary particles. The
characteristic classical to quantum correspondence of the theory brings novel
conceptual and formal elements to address fundamental open questions of modern
physics.Comment: 6 pages. Accepted for publication in Europhysics Letters (EPL) 30
April 201
AdS/CFT as classical to quantum correspondence in a Virtual Extra Dimension
The correspondence between classical extra dimensional geometry and quantum
behavior, typical of the AdS/CFT, has a heuristic semiclassical interpretation
in terms of undulatory mechanics and relativistic geometrodynamics. We note, in
fact, that the quantum recurrence of ordinary particles enters into the
equations of motions in formal duality with the extra dimensional dynamics of a
Kaluza-Klein theory. The kinematics of the particle in a generic interaction
scheme can be described as modulations of the spacetime recurrences and encoded
in corresponding geometrodynamics. The quantization can be obtained
semiclassically by means of boundary conditions, so that the interference of
the classical paths with different windings numbers associated to the resulting
recurrences turns out to be described by the ordinary Feynman Path Integral.
This description applied to the Quark-Gluon-Plasma freeze-out yields basic
aspects of AdS/QCD phenomenology.Comment: 6 pages. 36th International Conference on High Energy Physics - ICHEP
2012, Melbourne, Australia. Minor corrections. Comments welcom
On certain modules of covariants in exterior algebras
We study the structure of the space of covariants for a
certain class of infinitesimal symmetric spaces
such that the space of invariants is an exterior algebra with
. We prove that they are free modules over
the subalgebra of rank . In addition we
will give an explicit basis of . As particular cases we will recover same
classical results. In fact we will describe the structure of , the space of the equivariant matrix
valued alternating multilinear maps on the space of (skew-symmetric or
symmetric with respect to a specific involution) matrices, where is the
symplectic group or the odd orthogonal group. Furthermore we prove new
polynomial trace identities.Comment: Title changed. Results have been generalised to other infinitesimal
symmetric space
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