scholarly journals Gauge-invariant response functions in algebraic Fermi liquids

2003 ◽  
Vol 68 (2) ◽  
Author(s):  
M. Franz ◽  
T. Pereg-Barnea ◽  
D. E. Sheehy ◽  
Z. Tešanović
Keyword(s):  
Fermi Liquids ◽  
Response Functions ◽  
Gauge Invariant ◽  
Invariant Response

scholarly journals Gauge-invariant response functions of fermions coupled to a gauge field

1994 ◽  
Vol 50 (24) ◽  
pp. 17917-17932 ◽  
Author(s):  
Yong Baek Kim ◽  
Akira Furusaki ◽  
Xiao-Gang Wen ◽  
Patrick A. Lee
Keyword(s):  
Gauge Field ◽  
Response Functions ◽  
Gauge Invariant ◽  
Invariant Response

The Standard Theory

2017 ◽  
Author(s):  
John Iliopoulos
Keyword(s):  
Gauge Theory ◽  
Invariant Theory ◽  
Standard Theory ◽  
Strong Interactions ◽  
Gauge Invariant ◽  
Electromagnetic Interactions ◽  
Protons And Neutrons ◽  
Free Particles ◽  
Theoretical Predictions ◽  
Theory And Experiment

All ingredients of the previous chapters are combined in order to build a gauge invariant theory of the interactions among the elementary particles. We start with a unified model of the weak and the electromagnetic interactions. The gauge symmetry is spontaneously broken through the BEH mechanism and we identify the resulting BEH boson. Then we describe the theory known as quantum chromodynamics (QCD), a gauge theory of the strong interactions. We present the property of confinement which explains why the quarks and the gluons cannot be extracted out of the protons and neutrons to form free particles. The last section contains a comparison of the theoretical predictions based on this theory with the experimental results. The agreement between theory and experiment is spectacular.

scholarly journals Time Decay for Nonlinear Dissipative Schrödinger Equations in Optical Fields

2016 ◽  
Vol 2016 ◽  
pp. 1-7 ◽  
Author(s):  
Nakao Hayashi ◽  
Chunhua Li ◽  
Pavel I. Naumkin
Keyword(s):  
Lower Bound ◽  
Positive Root ◽  
Schrodinger Equations ◽  
Schrödinger Equations ◽  
Time Decay ◽  
Large Initial Data ◽  
Initial Value ◽  
Optical Fields ◽  
Gauge Invariant ◽  
Dissipative Condition

We consider the initial value problem for the nonlinear dissipative Schrödinger equations with a gauge invariant nonlinearityλup-1uof orderpn<p≤1+2/nfor arbitrarily large initial data, where the lower boundpnis a positive root ofn+2p2-6p-n=0forn≥2andp1=1+2forn=1.Our purpose is to extend the previous results for higher space dimensions concerningL2-time decay and to improve the lower bound ofpunder the same dissipative condition onλ∈C:Im⁡ λ<0andIm⁡ λ>p-1/2pRe λas in the previous works.

scholarly journals Development of dose-response functions for historic paper degradation using exposure to natural conditions and multivariate regression

2019 ◽  
Vol 168 ◽  
pp. 108944 ◽  
Author(s):  
Gianluca Pastorelli ◽  
Shuo Cao ◽  
Irena Kralj Cigić ◽  
Costanza Cucci ◽  
Abdelrazek Elnaggar ◽  
...  
Keyword(s):  
Dose Response ◽  
Multivariate Regression ◽  
Response Functions ◽  
Natural Conditions ◽  
Paper Degradation ◽  
Historic Paper
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