49,869 research outputs found
The M\"obius Symmetry of Quantum Mechanics
The equivalence postulate approach to quantum mechanics aims to formulate
quantum mechanics from a fundamental geometrical principle. Underlying the
formulation there exists a basic cocycle condition which is invariant under
--dimensional M\"obius transformations with respect to the Euclidean or
Minkowski metrics. The invariance under global M\"obius transformations implies
that spatial space is compact. Furthermore, it implies energy quantisation and
undefinability of quantum trajectories without assuming any prior
interpretation of the wave function. The approach may be viewed as conventional
quantum mechanics with the caveat that spatial space is compact, as dictated by
the M\"obius symmetry, with the classical limit corresponding to the
decompactification limit. Correspondingly, there exists a finite length scale
in the formalism and consequently an intrinsic regularisation scheme. Evidence
for the compactness of space may exist in the cosmic microwave background
radiation.Comment: 16 pages. Talk presented at the DICE 2014 international conference,
Castiglioncello, Tuscany, September 15-19, 201
Equivalence Principle: Tunnelling, Quantized Spectra and Trajectories from the Quantum HJ Equation
A basic aspect of the recently proposed approach to quantum mechanics is that
no use of any axiomatic interpretation of the wave function is made. In
particular, the quantum potential turns out to be an intrinsic potential energy
of the particle, which, similarly to the relativistic rest energy, is never
vanishing. This is related to the tunnel effect, a consequence of the fact that
the conjugate momentum field is real even in the classically forbidden regions.
The quantum stationary Hamilton-Jacobi equation is defined only if the ratio
psi^D/psi of two real linearly independent solutions of the Schroedinger
equation, and therefore of the trivializing map, is a local homeomorphism of
the extended real line into itself, a consequence of the Moebius symmetry of
the Schwarzian derivative. In this respect we prove a basic theorem relating
the request of continuity at spatial infinity of psi^D/psi, a consequence of
the q - 1/q duality of the Schwarzian derivative, to the existence of L^2(R)
solutions of the corresponding Schroedinger equation. As a result, while in the
conventional approach one needs the Schroedinger equation with the L^2(R)
condition, consequence of the axiomatic interpretation of the wave function,
the equivalence principle by itself implies a dynamical equation that does not
need any assumption and reproduces both the tunnel effect and energy
quantization.Comment: 1+10 pages, LaTeX. Typos corrected, to appear in Phys. Lett.
Hamilton-Jacobi meet M\uf6bius
Adaptation of the Hamilton\u2013Jacobi formalism to quantum mechanics leads to a cocycle
condition, which is invariant under D\u2013dimensional M\ua8obius transformations with Euclidean or
Minkowski metrics. In this paper we aim to provide a pedagogical presentation of the proof
of the M\ua8obius symmetry underlying the cocycle condition. The M\ua8obius symmetry implies
energy quantization and undefinability of quantum trajectories, without assigning any prior
interpretation to the wave function. As such, the Hamilton\u2013Jacobi formalism, augmented with
the global M\ua8obius symmetry, provides an alternative starting point, to the axiomatic probability
interpretation of the wave function, for the formulation of quantum mechanics and the quantum
spacetime. The M\ua8obius symmetry can only be implemented consistently if spatial space is
compact, and correspondingly if there exist a finite ultraviolet length scale. Evidence for non\u2013
trivial space topology may exist in the cosmic microwave background radiation
Macroeconomic policy and elections: Theories and challenges
This paper reviews recent developments in the literature of economic policy-making. It focuses in particular on the relation between elections and macroeconomic policy. It should also be noted that in spite of tremendous advances in the area, there are still many important unresolved issues. In particular, both the normative and empirical areas are the ones in most urgent need study.
On maxitive integration
The Shilkret integral is maxitive (i.e., the integral of a pointwise supremum of functions is the supremum of their integrals), but defined only for nonnegative functions. In the present paper, some properties of this integral (such as subadditivity and a law of iterated expectations) are studied, in comparison with the additive and Choquet integrals. Furthermore, the definition of a maxitive integral for all real functions is discussed. In particular, a convex, maxitive integral is introduced and some of its properties are derived
Dendritic spike induction of postsynaptic cerebellar LTP
The architecture of parallel fiber (PF) axons contacting cerebellar Purkinje neurons (PNs) retains spatial information over long distances. PF synapses can trigger local dendritic calcium spikes, but whether and how this calcium signal leads to plastic changes that decode the PF input organization is unknown. By combining voltage and calcium imaging, we show that PF-elicited calcium signals, mediated by voltage-gated calcium channels, increase non-linearly during high-frequency bursts of electrically constant calcium spikes because they locally and transiently saturate the endogenous buffer. We demonstrate that these non-linear calcium signals, independently of NMDA or metabotropic glutamate receptor activation, can induce PF long-term potentiation (LTP). Two-photon imaging in coronal slices revealed that calcium signals inducing LTP can be observed by stimulating either the PF or the ascending fiber pathway. We propose that local dendritic calcium spikes, evoked by synaptic potentials, provide a unique mechanism to spatially decode PF signals into cerebellar circuitry changes
Extra s and s in Heterotic--String Derived Models
The ATLAS collaboration recently recorded possible excess in the di--boson
production at the di--boson invariant mass at around 2 TeV. Such an excess may
be produced if there exist additional and/or at that
scale. We survey the extra s and s that may arise from
semi--realistic heterotic string vacua in the free fermionic formulation in
seven distinct cases including: ; family universal
not in ; non--universal ; hidden
sector symmetries and kinetic mixing; left--right symmetric models;
Pati--Salam models; leptophobic and custodial symmetries. Each case has a
distinct signature associated with the extra symmetry breaking scale. In one of
the cases we explore the discovery potential at the LHC using resonant
leptoproduction. Existence of extra vector boson with the reported properties
will significantly constrain the space of allowed string vacua.Comment: 25 pages, 2 figures. Standard LaTeX. References added. Published
versio
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