scholarly journals Decomposition of spectral flow and Bott-type iteration formula

2020 ◽  
Vol 28 (1) ◽  
pp. 127-148
Author(s):  
Xijun Hu ◽  
◽  
Li Wu
Keyword(s):  
Spectral Flow ◽  
Iteration Formula

GROUND STATE CHARGE OF FERMION SOLITON SYSTEM IN 1+1 AND 3+1 DIMENSIONS

1993 ◽  
Vol 08 (04) ◽  
pp. 705-721
Author(s):  
M. RAVENDRANADHAN ◽  
M. SABIR
Keyword(s):  
Ground State ◽  
Energy State ◽  
Flow Analysis ◽  
Background Field ◽  
Bound State ◽  
Fermion Mass ◽  
Spectral Flow ◽  
Bound State Spectrum ◽  
Spectral Asymmetry ◽  
State Charge

Ground state charge of some fermion soliton system without C-invariance is calculated in 1+1 and 3+1 dimensions by a combination of adiabatic method and spectral flow analysis. Induced charge is calculated by evolving adiabatically the fields from a vacuum having a background field which has a zero energy state and spectral symmetry. The spectral flow is calculated by an analysis of the bound state spectrum. In 1+1 dimension our calculations are in agreement with the results already found in the literature. In 3+1 dimension we study the interaction of fermions with monopoles and dyons. In the case of monopoles, even though there is spectral asymmetry, ground state charge is found to be ±1/2. It is shown that ground state charge gets contribution only from the lowest angular momentum states and is discontinuous at the fermion mass.

scholarly journals Higher spectral flow and an entire bivariant JLO cocycle

2012 ◽  
Vol 11 (1) ◽  
pp. 183-232 ◽  
Author(s):  
Moulay-Tahar Benameur ◽  
Alan L. Carey
Keyword(s):  
Dirac Operator ◽  
Chern Character ◽  
Dirac Operators ◽  
Cyclic Cohomology ◽  
Closed Manifold ◽  
Spectral Flow ◽  
Smooth Functions ◽  
Base Manifold ◽  
K Theory ◽  
Higher Spectral Flow

AbstractFor a single Dirac operator on a closed manifold the cocycle introduced by Jaffe-Lesniewski-Osterwalder [19] (abbreviated here to JLO), is a representative of Connes' Chern character map from the K-theory of the algebra of smooth functions on the manifold to its entire cyclic cohomology. Given a smooth fibration of closed manifolds and a family of generalized Dirac operators along the fibers, we define in this paper an associated bivariant JLO cocycle. We then prove that, for any l ≥ 0, our bivariant JLO cocycle is entire when we endow smoooth functions on the total manifold with the Cl+1 topology and functions on the base manifold with the Cl topology. As a by-product of our theorem, we deduce that the bivariant JLO cocycle is entire for the Fréchet smooth topologies. We then prove that our JLO bivariant cocycle computes the Chern character of the Dai-Zhang higher spectral flow.

SPECTRAL FLOW AND FREE FIELD REALIZATIONS OF BOSONIC STRINGS ON NAPPI–WITTEN GROUP MANIFOLD

2011 ◽  
Vol 26 (01) ◽  
pp. 149-160
Author(s):  
GANG CHEN
Keyword(s):  
Lie Algebra ◽  
Bosonic Strings ◽  
Free Field ◽  
Geometric Interpretation ◽  
Closed String ◽  
Space Time ◽  
Spectral Flow ◽  
Affine Lie Algebra ◽  
Group Manifold ◽  
Free Field Realization

In this paper we study some aspects of closed string theories in the Nappi–Witten space–time. The effects of spectral flow on the geodesics are studied in terms of an explicit parametrization of the group manifold. The worldsheets of the closed strings under the spectral flow of the geodesics can be classified into four classes, each with a geometric interpretation. We also obtain a free field realization of the Nappi–Witten affine Lie algebra in the most general conditions using a different but equivalent parametrization of the group manifold.

scholarly journals Limiting eigenfunctions of Sturm–Liouville operators subject to a spectral flow

2020 ◽  
Author(s):  
Thomas Beck ◽  
Isabel Bors ◽  
Grace Conte ◽  
Graham Cox ◽  
Jeremy L. Marzuola
Keyword(s):  
Spectral Flow ◽  
Sturm Liouville ◽  
Liouville Operators

scholarly journals Spectral Flow in Fredholm Modules, Eta Invariants and the JLO Cocycle

K-Theory ◽  
2004 ◽  
Vol 31 (2) ◽  
pp. 135-194 ◽  
Author(s):  
Alan Carey ◽  
John Phillips
Keyword(s):  
Spectral Flow ◽  
Eta Invariants

The Spectral Flow of Families of Self-Adjoint Operators

1993 ◽  
pp. 138-160
Author(s):  
Bernhelm Booß-Bavnbek ◽  
Krzysztof P. Wojciechowski
Keyword(s):  
Spectral Flow ◽  
Adjoint Operators

scholarly journals A note on machine method for root extraction

2022 ◽  
Vol 40 ◽  
pp. 1-6
Author(s):  
Saroj Kumar Padhan ◽  
S. Gadtia
Keyword(s):  
Real Number ◽  
Newton’S Method ◽  
Newton's Method ◽  
Extraction Methods ◽  
Critical Study ◽  
Square Root ◽  
Machine Method ◽  
Iteration Formula ◽  
Root Extraction

The present investigation deals with the critical study of the works of Lancaster and Traub, who have developed $n$th root extraction methods of a real number. It is found that their developed methods are equivalent and the particular cases of Halley's and Householder's methods. Again the methods presented by them are easily obtained from simple modifications of Newton's method, which is the extension of Heron's square root iteration formula. Further, the rate of convergency of their reported methods are studied.

scholarly journals Computation of the Maslov index and the spectral flow via partial signatures

2004 ◽  
Vol 338 (5) ◽  
pp. 397-402 ◽  
Author(s):  
Roberto Giambò ◽  
Paolo Piccione ◽  
Alessandro Portaluri
Keyword(s):  
Maslov Index ◽  
Spectral Flow
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