Role of Darboux’s theorem in supersymmetric quantum mechanics

1986 ◽  
Vol 33 (2) ◽  
pp. 594-595 ◽  
Author(s):  
Pinaki Roy ◽  
Rajkumar Roychoudhury
Keyword(s):  
Quantum Mechanics ◽  
Supersymmetric Quantum Mechanics ◽  
Darboux's Theorem

Randomness and Complexity

2018 ◽  
Author(s):  
Steven E. Vigdor
Keyword(s):  
Quantum Mechanics ◽  
Natural Selection ◽  
Rna World ◽  
Biological Evolution ◽  
Variable Theory ◽  
Cosmological Natural Selection ◽  
Einstein Podolsky Rosen ◽  
World Hypothesis ◽  
Rna World Hypothesis

Chapter 7 describes the fundamental role of randomness in quantum mechanics, in generating the first biomolecules, and in biological evolution. Experiments testing the Einstein–Podolsky–Rosen paradox have demonstrated, via Bell’s inequalities, that no local hidden variable theory can provide a viable alternative to quantum mechanics, with its fundamental randomness built in. Randomness presumably plays an equally important role in the chemical assembly of a wide array of polymer molecules to be sampled for their ability to store genetic information and self-replicate, fueling the sort of abiogenesis assumed in the RNA world hypothesis of life’s beginnings. Evidence for random mutations in biological evolution, microevolution of both bacteria and antibodies and macroevolution of the species, is briefly reviewed. The importance of natural selection in guiding the adaptation of species to changing environments is emphasized. A speculative role of cosmological natural selection for black-hole fecundity in the evolution of universes is discussed.

scholarly journals ABCD of ’t Hooft operators

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Hirotaka Hayashi ◽  
Takuya Okuda ◽  
Yutaka Yoshida
Keyword(s):  
Quantum Mechanics ◽  
Gauge Theories ◽  
Supersymmetric Quantum Mechanics ◽  
Type Ii ◽  
Expectation Values ◽  
String Theories

Abstract We compute by supersymmetric localization the expectation values of half-BPS ’t Hooft line operators in $$ \mathcal{N} $$ N = 2 U(N ), SO(N ) and USp(N ) gauge theories on S1 × ℝ3 with an Ω-deformation. We evaluate the non-perturbative contributions due to monopole screening by calculating the supersymmetric indices of the corresponding supersymmetric quantum mechanics, which we obtain by realizing the gauge theories and the ’t Hooft operators using branes and orientifolds in type II string theories.

scholarly journals Local G2-manifolds, Higgs bundles and a colored quantum mechanics

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Max Hübner
Keyword(s):  
Quantum Mechanics ◽  
Gauge Theories ◽  
Supersymmetric Quantum Mechanics ◽  
Higgs Bundle ◽  
Higgs Bundles ◽  
View Point ◽  
Yang Mills ◽  
G2 Manifolds ◽  
Supersymmetric Gauge ◽  
M Theory

Abstract M-theory on local G2-manifolds engineers 4d minimally supersymmetric gauge theories. We consider ALE-fibered G2-manifolds and study the 4d physics from the view point of a partially twisted 7d supersymmetric Yang-Mills theory and its Higgs bundle. Euclidean M2-brane instantons descend to non-perturbative effects of the 7d supersymmetric Yang-Mills theory, which are found to be in one to one correspondence with the instantons of a colored supersymmetric quantum mechanics. We compute the contributions of M2-brane instantons to the 4d superpotential in the effective 7d description via localization in the colored quantum mechanics. Further we consider non-split Higgs bundles and analyze their 4d spectrum.

scholarly journals Wronskian differential formula for confluent supersymmetric quantum mechanics

2012 ◽  
Vol 376 (5) ◽  
pp. 692-696 ◽  
Author(s):  
David Bermudez ◽  
David J. Fernández C. ◽  
Nicolás Fernández-García
Keyword(s):  
Quantum Mechanics ◽  
Supersymmetric Quantum Mechanics

A Golden-Thompson inequality in supersymmetric quantum mechanics

1991 ◽  
Vol 21 (3) ◽  
pp. 237-244 ◽  
Author(s):  
Slawomir Klimek ◽  
Andrzej Lesniewski
Keyword(s):  
Quantum Mechanics ◽  
Supersymmetric Quantum Mechanics
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