1,868 research outputs found
The Equivalence Principle of Quantum Mechanics: Uniqueness Theorem
Recently we showed that the postulated diffeomorphic equivalence of states
implies quantum mechanics. This approach takes the canonical variables to be
dependent by the relation p=\partial_q S_0 and exploits a basic
GL(2,C)-symmetry which underlies the canonical formalism. In particular, we
looked for the special transformations leading to the free system with
vanishing energy. Furthermore, we saw that while on the one hand the
equivalence principle cannot be consistently implemented in classical
mechanics, on the other it naturally led to the quantum analogue of the
Hamilton-Jacobi equation, thus implying the Schroedinger equation. In this
letter we show that actually the principle uniquely leads to this solution.
Furthermore, we find the map reducing any system to the free one with vanishing
energy and derive the transformations on S_0 leaving the wave function
invariant. We also express the canonical and Schroedinger equations by means of
the brackets recently introduced in the framework of N=2 SYM. These brackets
are the analogue of the Poisson brackets with the canonical variables taken as
dependent.Comment: 18 pages, LaTeX. A limit was missing in Eq.8
N=2 SYM RG Scale as Modulus for WDVV Equations
We derive a new set of WDVV equations for N=2 SYM in which the
renormalization scale is identified with the distinguished modulus
which naturally arises in topological field theories.Comment: 6 pages, LaTe
Algebraic-geometrical formulation of two-dimensional quantum gravity
We find a volume form on moduli space of double punctured Riemann surfaces
whose integral satisfies the Painlev\'e I recursion relations of the genus
expansion of the specific heat of 2D gravity. This allows us to express the
asymptotic expansion of the specific heat as an integral on an infinite
dimensional moduli space in the spirit of Friedan-Shenker approach. We outline
a conjectural derivation of such recursion relations using the
Duistermaat-Heckman theorem.Comment: 10 pages, Latex fil
Polo Ponies
Polo has been developed in speed to a point where it is second only to ice hockey. It is one of the roughest sports and certainly the one requiring the most skill and training on the part of the player and his horse. As a consequence the sport has been limited in the past to those with the means to purchase well trained stock and able to devote sufficient time to practice. Collegiate team members playing on army or university mounts, and local teams of cowboys and farmers have played much polo, though of a lower class
Taming open/closed string duality with a Losev trick
A target space string field theory formulation for open and closed B-model is
provided by giving a Batalin-Vilkovisky quantization of the holomorphic
Chern-Simons theory with off-shell gravity background. The target space
expression for the coefficients of the holomorphic anomaly equation for open
strings are obtained. Furthermore, open/closed string duality is proved from a
judicious integration over the open string fields. In particular, by
restriction to the case of independence on continuous open moduli, the shift
formulas of [7] are reproduced and shown therefore to encode the data of a
closed string dual.Comment: 22 pages, no figures; v.2 Refs. and a comment added
The stringy instanton partition function
We perform an exact computation of the gauged linear sigma model associated to a D1-D5 brane system on a resolved A 1 singularity. This is accomplished via supersymmetric localization on the blown-up two-sphere. We show that in the blow-down limit the partition function reduces to the Nekrasov partition function evaluating the equivariant volume of the instanton moduli space. For finite radius we obtain a tower of world-sheet instanton corrections, that we identify with the equivariant Gromov-Witten invariants of the ADHM moduli space. We show that these corrections can be encoded in a deformation of the Seiberg-Witten prepotential. From the mathematical viewpoint, the D1-D5 system under study displays a twofold nature: the D1-branes viewpoint captures the equivariant quantum cohomology of the ADHM instanton moduli space in the Givental formalism, and the D5-branes viewpoint is related to higher rank equivariant Donaldson-Thomas invariants
Combining environmental niche models, multi-grain analyses, and species traits identifies pervasive effects of land use on butterfly biodiversity across Italy.
Understanding how species respond to human activities is paramount to ecology and conservation science, one outstanding question being how large-scale patterns in land use affect biodiversity. To facilitate answering this question, we propose a novel analytical framework that combines environmental niche models, multi-grain analyses, and species traits. We illustrate the framework capitalizing on the most extensive dataset compiled to date for the butterflies of Italy (106,514 observations for 288 species), assessing how agriculture and urbanization have affected biodiversity of these taxa from landscape to regional scales (3-48 km grains) across the country while accounting for its steep climatic gradients. Multiple lines of evidence suggest pervasive and scale-dependent effects of land use on butterflies in Italy. While land use explained patterns in species richness primarily at grains ≤12 km, idiosyncratic responses in species highlighted "winners" and "losers" across human-dominated regions. Detrimental effects of agriculture and urbanization emerged from landscape (3-km grain) to regional (48-km grain) scales, disproportionally affecting small butterflies and butterflies with a short flight curve. Human activities have therefore reorganized the biogeography of Italian butterflies, filtering out species with poor dispersal capacity and narrow niche breadth not only from local assemblages, but also from regional species pools. These results suggest that global conservation efforts neglecting large-scale patterns in land use risk falling short of their goals, even for taxa typically assumed to persist in small natural areas (e.g., invertebrates). Our study also confirms that consideration of spatial scales will be crucial to implementing effective conservation actions in the Post-2020 Global Biodiversity Framework. In this context, applications of the proposed analytical framework have broad potential to identify which mechanisms underlie biodiversity change at different spatial scales
RG Flow Irreversibility, C-Theorem and Topological Nature of 4D N=2 SYM
We determine the exact beta function and a RG flow Lyapunov function for N=2
SYM with gauge group SU(n). It turns out that the classical discriminants of
the Seiberg-Witten curves determine the RG potential. The radial
irreversibility of the RG flow in the SU(2) case and the non-perturbative
identity relating the -modulus and the superconformal anomaly, indicate the
existence of a four dimensional analogue of the c-theorem for N=2 SYM which we
formulate for the full SU(n) theory. Our investigation provides further
evidence of the essentially topological nature of the theory.Comment: 9 pages, LaTeX file. Discussion on WDVV and integrability. References
added. Version published in PR
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