Best Matching: Technical Details

2018 ◽  
Author(s):  
Flavio Mercati
Keyword(s):  
Point Particle ◽  
Euclidean Group ◽  
Scale Invariant ◽  
Similarity Group ◽  
N Body Problem ◽  
Technical Details ◽  
Matching Procedure ◽  
Principal Fibre ◽  
Principal Fibre Bundle ◽  
Gauge Connection

The best matching procedure described in Chapter 4 is equivalent to the introduction of a principal fibre bundle in configuration space. Essentially one introduces a one-dimensional gauge connection on the time axis, which is a representation of the Euclidean group of rotations and translations (or, possibly, the similarity group which includes dilatations). To accommodate temporal relationalism, the variational principle needs to be invariant under reparametrizations. The simplest way to realize this in point–particle mechanics is to use Jacobi’s reformulation of Mapertuis’ principle. The chapter concludes with the relational reformulation of the Newtonian N-body problem (and its scale-invariant variant).

Construction of N = 2 Supergravity on Principal Fibre Bundle

1988 ◽  
Vol 79 (6) ◽  
pp. 1431-1450 ◽  
Author(s):  
K. Kakazu ◽  
S. Matsumoto
Keyword(s):  
Fibre Bundle ◽  
Principal Fibre ◽  
Principal Fibre Bundle

Induced Connections and Imbedded Riemannian Spaces

1956 ◽  
Vol 10 ◽  
pp. 15-25 ◽  
Author(s):  
Shoshichi Kobayashi
Keyword(s):  
Fibre Bundle ◽  
Principal Fibre ◽  
Definition Of ◽  
Principal Fibre Bundle ◽  
The Right ◽  
Riemannian Spaces

Let P be a principal fibre bundle over M with group G and with projection π : P → M. By definition of a principal fibre bundle, G acts on P on the right. We shall denote this transformation law by ρ

scholarly journals Can You Hear the Shape of a Market? Geometric Arbitrage and Spectral Theory

Axioms ◽  
2021 ◽  
Vol 10 (4) ◽  
pp. 242
Author(s):  
Simone Farinelli ◽  
Hideyuki Takada
Keyword(s):  
Cash Flow ◽  
Fibre Bundle ◽  
Asset Bubbles ◽  
Gauge Symmetries ◽  
Curvature Measures ◽  
Principal Fibre ◽  
Topological Obstructions ◽  
Principal Fibre Bundle ◽  
Risk Neutral Measures ◽  
No Free Lunch

Utilizing gauge symmetries, the Geometric Arbitrage Theory reformulates any asset model, allowing for arbitrage by means of a stochastic principal fibre bundle with a connection whose curvature measures the “instantaneous arbitrage capability”. The cash flow bundle is the associated vector bundle. The zero eigenspace of its connection Laplacian parameterizes all risk-neutral measures equivalent to the statistical one. A market satisfies the No-Free-Lunch-with-Vanishing-Risk (NFLVR) condition if and only if 0 is in the discrete spectrum of the Laplacian. The Jarrow–Protter–Shimbo theory of asset bubbles and their classification and decomposition extend to markets not satisfying the NFLVR. Euler’s characteristic of the asset nominal space and non-vanishing of the homology group of the cash flow bundle are both topological obstructions to NFLVR.

PHASE TRANSITION IN RIGID QED

1994 ◽  
Vol 09 (23) ◽  
pp. 4077-4099 ◽  
Author(s):  
MOUSTAFA AWADA ◽  
DAVID ZOLLER
Keyword(s):  
World Line ◽  
Mean Field Theory ◽  
Mean Field ◽  
Continuum Theory ◽  
Experimental Tests ◽  
Point Particle ◽  
Kinetic Term ◽  
Scale Invariant ◽  
Majorana Mass ◽  
Curvature Term

We present a new model of QED which exhibits two distinct phases. The model emerges in the first-quantized formalism where it is possible to generalize QED by adding the curvature of the world line to the usual kinetic term, the arc length action of the point particle. The Boltzmann factor associated with the curvature term favors rigid paths. The curvature term is not only scale-invariant and hence renormalizable but it is also the unique reparametrization-invariant term with second derivatives with this property. The new term transforms a single electron of mass m into an infinite number of particles with masses varying inversely with the spin (Majorana mass spectrum). The value of the bare curvature coupling determines which phase the theory is in. For bare curvature coupling α0 less than a certain critical coupling αc, we recover conventional QED as one phase where the curvature term is absent at large distance scales in the continuum theory. For α0 greater than αc, we have a new phase characterized by a curvature law. Using mean field theory methods, we determine αc to be of the order of one. We argue that the positronium spectrum in the strong curvature phase is approximately described by a Majorana mass formula. Even though the GSI experiments might not survive further experimental tests, we nevertheless examine the Majorana spectrum with the three observed narrow e+ e− peaks observed in the GSI experiments and make some possible new predictions.

scholarly journals Supergravity on Principal Fibre Bundle

1987 ◽  
Vol 78 (4) ◽  
pp. 932-950 ◽  
Author(s):  
K. Kakazu ◽  
S. Matsumoto
Keyword(s):  
Fibre Bundle ◽  
Principal Fibre ◽  
Principal Fibre Bundle

CONNECTIONS ON A PRINCIPAL FIBRE BUNDLE

2000 ◽  
pp. 303-371
Author(s):  
YVONNE CHOQUET-BRUHAT ◽  
CÉCILE DEWITT-MORETTE
Keyword(s):  
Fibre Bundle ◽  
Principal Fibre ◽  
Principal Fibre Bundle
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