scholarly journals The de Sitter groupL 4,1 and the bound states of hydrogen atom

1966 ◽  
Vol 41 (2) ◽  
pp. 222-234 ◽  
Author(s):  
H. Bacry
Keyword(s):  
Hydrogen Atom ◽  
Bound States ◽  
De Sitter

scholarly journals Dynamical Symmetries of the H Atom, One of the Most Important Tools of Modern Physics: SO(4) to SO(4,2), Background, Theory, and Use in Calculating Radiative Shifts

Symmetry ◽  
2020 ◽  
Vol 12 (8) ◽  
pp. 1323 ◽  
Author(s):  
G. Jordan Maclay
Keyword(s):  
Hydrogen Atom ◽  
Quantum Electrodynamics ◽  
Particle Physics ◽  
Bound States ◽  
Integrated Treatment ◽  
Invariance Group ◽  
Elementary Particle Physics ◽  
Background Theory ◽  
Modern Physics ◽  
History Of

Understanding the hydrogen atom has been at the heart of modern physics. Exploring the symmetry of the most fundamental two body system has led to advances in atomic physics, quantum mechanics, quantum electrodynamics, and elementary particle physics. In this pedagogic review, we present an integrated treatment of the symmetries of the Schrodinger hydrogen atom, including the classical atom, the SO(4) degeneracy group, the non-invariance group or spectrum generating group SO(4,1), and the expanded group SO(4,2). After giving a brief history of these discoveries, most of which took place from 1935–1975, we focus on the physics of the hydrogen atom, providing a background discussion of the symmetries, providing explicit expressions for all of the manifestly Hermitian generators in terms of position and momenta operators in a Cartesian space, explaining the action of the generators on the basis states, and giving a unified treatment of the bound and continuum states in terms of eigenfunctions that have the same quantum numbers as the ordinary bound states. We present some new results from SO(4,2) group theory that are useful in a practical application, the computation of the first order Lamb shift in the hydrogen atom. By using SO(4,2) methods, we are able to obtain a generating function for the radiative shift for all levels. Students, non-experts, and the new generation of scientists may find the clearer, integrated presentation of the symmetries of the hydrogen atom helpful and illuminating. Experts will find new perspectives, even some surprises.

scholarly journals AdS3 GRAVITATIONAL INSTANTONS FROM CONFORMAL FIELD THEORY

1999 ◽  
Vol 14 (28) ◽  
pp. 1961-1981 ◽  
Author(s):  
SHUHEI MANO
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Bound States ◽  
Three Dimensional ◽  
Partition Functions ◽  
De Sitter ◽  
Btz Black Hole ◽  
Gravitational Instantons ◽  
Conformal Field ◽  
Horizon Geometry

A conformal field theory on the boundary of three-dimensional asymptotic anti-de Sitter spaces which appear as near horizon geometry of D-brane bound states is discussed. It is shown that partition functions of gravitational instantons appear as high and low temperature limits of the partition function of the conformal field theory. The result reproduces phase transition between the anti-de Sitter space and the BTZ black hole in the bulk gravity.

scholarly journals Relationship between the Behavior of Hydrogen and Hydrogen Bubble Nucleation in Vanadium

Materials ◽  
2020 ◽  
Vol 13 (2) ◽  
pp. 322
Author(s):  
Zhengxiong Su ◽  
Sheng Wang ◽  
Chenyang Lu ◽  
Qing Peng
Keyword(s):  
Hydrogen Atom ◽  
First Principles ◽  
Bound States ◽  
Hydrogen Molecule ◽  
Vacancy Cluster ◽  
Bubble Nucleation ◽  
Hydrogen Bubble ◽  
First Principles Calculations ◽  
Hydrogen Atoms ◽  
Macroscopic Deformation

Hydrogen plays a significant role in the microstructure evolution and macroscopic deformation of materials, causing swelling and surface blistering to reduce service life. In the present work, the atomistic mechanisms of hydrogen bubble nucleation in vanadium were studied by first-principles calculations. The interstitial hydrogen atoms cannot form significant bound states with other hydrogen atoms in bulk vanadium, which explains the absence of hydrogen self-clustering from the experiments. To find the possible origin of hydrogen bubble in vanadium, we explored the minimum sizes of a vacancy cluster in vanadium for the formation of hydrogen molecule. We show that a freestanding hydrogen molecule can form and remain relatively stable in the center of a 54-hydrogen atom saturated 27-vacancy cluster.

scholarly journals REVIEW OF THE N-QUANTUM APPROACH TO BOUND STATES

2011 ◽  
Vol 26 (06) ◽  
pp. 935-945 ◽  
Author(s):  
O. W. GREENBERG
Keyword(s):  
Hydrogen Atom ◽  
Bound States ◽  
Bound State ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Asymptotic Field ◽  
Quantum Approach ◽  
Future Work ◽  
Asymptotic Fields

We describe a method of solving quantum field theories using operator techniques based on the expansion of interacting fields in terms of asymptotic fields. For bound states, we introduce an asymptotic field for each (stable) bound state. We choose the nonrelativistic hydrogen atom as an example to illustrate the method. Future work will apply this N-quantum approach to relativistic theories that include bound states in motion.

scholarly journals Duality and Integrability in Superstring and Gauge Field Theory

2021 ◽  
Author(s):  
◽  
Konstantinos Filippas
Keyword(s):  
Field Theory ◽  
Gauge Field ◽  
Bound States ◽  
Galois Theory ◽  
Field Theories ◽  
Gauge Field Theory ◽  
Differential Galois Theory ◽  
De Sitter ◽  
Algebraic Form ◽  
Integrable Dynamics

In the present thesis, we explore certain aspects of superstring and supersymmetric gauge field theory, independently as well as in the context of the holographic duality.The first part of the thesis is devoted to classical integrability and, in particular, to certain methods of analytic non-integrability, which are employed on various supergravity vacua. In Chapter 1, we introduce those tools of non-integrability, which consist of choosing an appro-priate string embedding and using differential Galois theory on the associated Hamiltonian system. The arena of all this, for the first chapter, is two classes of vacua in massive Type IIA supergravity, all of which are proven to be non-integrable, up to the trivial cases where the vacuum reduces to the Abelian and non-Abelian T-dual of known integrable backgrounds. Differential Galois theory, in this context, reduces to an algebraic form through Kovacic’s theorem, the proper use of which, on parametrized differential equations, is clarified in this application.In Chapter 2, we study integrability on the supergravity vacuum dual to the field-theoretical Ω-deformation of super Yang-Mills theory. The deformation manifests itself as turning on a Kalb-Ramond field on the dual supergravity vacuum and, by constructing appropriate string embeddings, we show that this space exhibits non-integrable dynamics. This, in turn, suggests that the Ω-deformation does not preserve classical integrability.In Chapter 3, we explore integrability on vacua in massive Type IIA supergravity, dual to six-dimensional superconformal quiver field theories. Analytic non-integrability illustrates that all vacua with a warped geometry, between Anti-de-Sitter space and the internal man-ifold, exhibit complete non-integrability, while in the special case of the unwarped space we prove the opposite to be true. In particular, we show that, besides the integrable dynamics on the symmetric Anti-de-Sitter subspace of the unwarped geometry, the σ-model on the internal manifold is an integrable deformation of the same model on the symmetric three-sphere, ultimately implying classical integrability of bosonic string theory on this special vacuum.The second part of the thesis is devoted to holography and, in particular, the AdS/CFT duality, which we exploit to study features of certain supersymmetric quantum field theories in two spacetime dimensions. More precisely, in Chapter 4, the final chapter, we study the duality between massive Type IIA supergravity vacua and two-dimensional quiver structures. After categorizing all kinds of gravity solutions, we demystify the ones that seem to reflect anomalous gauge theories. In particular, we prove that there are bound states of D-branes on the boundary of the space which provide the dual quiver theory with exactly the correct amount of matter in order to cancel its gauge anomalies. We also propose that the structure of the field theory should be complemented with additional bifundamental matter and, finally, we construct a BPS string configuration and use the old and new supersymmetric matter to build its dual ultraviolet operator.

Positive Fractal Dimensions of Bound States Spectral Measures: Application to the Hydrogen Atom

2022 ◽  
Vol 52 (2) ◽  
Author(s):  
Moacir Aloisio ◽  
Silas L. Carvalho ◽  
César R. de Oliveira
Keyword(s):  
Hydrogen Atom ◽  
Bound States ◽  
Fractal Dimensions ◽  
Spectral Measures

scholarly journals Condensates in quantum chromodynamics and the cosmological constant

2010 ◽  
Vol 108 (1) ◽  
pp. 45-50 ◽  
Author(s):  
Stanley J. Brodsky ◽  
Robert Shrock
Keyword(s):  
Cosmological Constant ◽  
Quantum Chromodynamics ◽  
Bound States ◽  
Condensed Matter ◽  
Chiral Symmetry Breaking ◽  
De Sitter ◽  
Conformal Field ◽  
Color Confinement ◽  
Gluon Condensates ◽  
Hadron Masses

Casher and Susskind [Casher A, Susskind L (1974) Phys Rev 9:436–460] have noted that in the light-front description, spontaneous chiral symmetry breaking is a property of hadronic wavefunctions and not of the vacuum. Here we show from several physical perspectives that, because of color confinement, quark and gluon condensates in quantum chromodynamics (QCD) are associated with the internal dynamics of hadrons. We discuss condensates using condensed matter analogues, the Anti de Sitter/conformal field theory correspondence, and the Bethe–Salpeter–Dyson–Schwinger approach for bound states. Our analysis is in agreement with the Casher and Susskind model and the explicit demonstration of “in-hadron” condensates by Roberts and coworkers [Maris P, Roberts CD, Tandy PC (1998) Phys Lett B 420:267–273], using the Bethe–Salpeter–Dyson–Schwinger formalism for QCD-bound states. These results imply that QCD condensates give zero contribution to the cosmological constant, because all of the gravitational effects of the in-hadron condensates are already included in the normal contribution from hadron masses.

scholarly journals Nonrelativistic bound states at finite temperature: The hydrogen atom

2008 ◽  
Vol 78 (3) ◽  
Author(s):  
Miguel Ángel Escobedo ◽  
Joan Soto
Keyword(s):  
Hydrogen Atom ◽  
Finite Temperature ◽  
Bound States
Sign in / Sign up

Export Citation Format

Share Document