Invariant definition of relativistic spin states in classical and quantum theories with an external field

1984 ◽  
Vol 59 (2) ◽  
pp. 465-467 ◽  
Author(s):  
V. A. Bordovitsyn ◽  
I. M. Ternov
Keyword(s):  
External Field ◽  
Spin States ◽  
Quantum Theories ◽  
Relativistic Spin ◽  
Definition Of ◽  
Invariant Definition

Anisotropy induced localization of pseudo-relativistic spin states in graphene double quantum wire structures

2010 ◽  
Vol 21 (36) ◽  
pp. 365401 ◽  
Author(s):  
Cesar E P Villegas ◽  
Marcos R S Tavares ◽  
G E Marques
Keyword(s):  
Quantum Wire ◽  
Double Quantum ◽  
Spin States ◽  
Relativistic Spin

scholarly journals Gauge invariant definition of the jet quenching parameter

2013 ◽  
Vol 2013 (2) ◽  
Author(s):  
Michael Benzke ◽  
Nora Brambilla ◽  
Miguel A. Escobedo ◽  
Antonio Vairo
Keyword(s):  
Jet Quenching ◽  
Gauge Invariant ◽  
Definition Of ◽  
Invariant Definition

scholarly journals Helicity Amplitudes for Generic Multibody Particle Decays Featuring Multiple Decay Chains

2020 ◽  
Vol 2020 ◽  
pp. 1-15
Author(s):  
Daniele Marangotto
Keyword(s):  
General Expression ◽  
Spin States ◽  
Full Generality ◽  
Final Particle ◽  
Particle Spin ◽  
Helicity Amplitudes ◽  
Definition Of ◽  
First Time ◽  
Particle Decays ◽  
Exact Definition

We present the general expression of helicity amplitudes for generic multibody particle decays characterised by multiple decay chains. This is achieved by addressing for the first time the issue of the matching of the final particle spin states among different decay chains in full generality for generic multibody decays, proposing a method able to match the exact definition of spin states relative to the decaying particle ones. We stress the importance of our result by showing that one of the matching methods used in the literature is incorrect, leading to amplitude models violating rotational invariance. The results presented are therefore relevant for performing numerous amplitude analyses, notably those searching for exotic structures like pentaquarks.

Quantum anomalies: A few physics applications

2019 ◽  
pp. 283-318
Author(s):  
Jean Zinn-Justin
Keyword(s):  
Particle Physics ◽  
Anomaly Cancellation ◽  
Quantum Theories ◽  
Axial Anomaly ◽  
Gauge Symmetries ◽  
Classical Symmetries ◽  
Lattice Regularization ◽  
The Standard Model ◽  
Quantum Anomalies ◽  
Definition Of

Chapter 17 exhibits various examples where classical symmetries cannot be transferred to quantum theories. The obstructions are characterized by anomalies. The examples involve chiral symmetries combined with currents or gauge symmetries, leading to chiral anomalies. In particular, anomalies lead to obstruction in the construction of theories. In particular, the structure of the Standard Model of particle physics is constrained by the requirement of anomaly cancellation. Other applications, like the relation between electromagnetic pi0 decay and the axial anomaly, are described. Anomalies are related to the Dirac operator index, leading to relations between anomaly and topology. To prove anomaly cancellation beyond perturbation theory, one can use lattice regularization. However, the definition of lattice chiral transformations is non–trivial. It is based on solutions of the Ginsparg–Wilson relation.

THE NUCLEAR MASS AT FINITE ANGULAR MOMENTA

2004 ◽  
Vol 13 (01) ◽  
pp. 87-96 ◽  
Author(s):  
INGEMAR RAGNARSSON ◽  
FILIP G. KONDEV ◽  
EDWARD S. PAUL ◽  
MARK A. RILEY ◽  
JOHN SIMPSON
Keyword(s):  
High Spin ◽  
Ground States ◽  
Spin States ◽  
Nuclear Mass ◽  
High Spin States ◽  
Angular Momenta ◽  
Systematic Expansion ◽  
Definition Of

The definition of experimental shell energies for nuclear ground states is generalized to finite angular momenta corresponding to a systematic expansion of the (N,Z)-plane to an (N,Z,I) space. Special emphasis is put on high-spin states where it is expected that odd and even nuclei should have similar properties. Different coupling schemes are compared and energetically favoured conditions to build high-spin states are discussed.

scholarly journals SOME REMARKS ON THE CHEMICAL POTENTIAL OF A SYSTEM IN AN EXTERNAL FIELD

2019 ◽  
Vol 16 (31) ◽  
pp. 341-346
Author(s):  
Stefano SALVESTRINI ◽  
Luigi AMBROSONE ◽  
Pasquale IOVINO ◽  
Sante CAPASSO
Keyword(s):  
Surface Tension ◽  
External Field ◽  
Electric Field ◽  
Chemical Process ◽  
Chemical Potential ◽  
Potential Change ◽  
State Function ◽  
External Fields ◽  
Definition Of ◽  
Physical And Chemical

The chemical potential change provides a criterion for predicting the spontaneity of any physical and chemical process. If asked to calculate the chemical potential change of a system in which several forces vary, a student might find the task quite complicate at first glance. However, the chemical potential is a state function. This property permits a precise definition of the contribution of each force to the chemical potential when all other relevant parameters are kept constant. The total chemical potential change can easily be calculated by summing up the above contributions. After a brief review of the role played by some parameters of the system, like activity of the components, temperature (T), pressure (p) and surface tension (y), as well as of external fields, i.e. gravitational (, centrifugal (Mcq) and electric field (), an equation for the computation of the chemical potential (μ) including all the above contributes is reported: µ = µ° ′ + RT lna + V¯ (p — p°) — S̅ (T — T°) + Mgℎ + Mcq + Fz Φ + 2yV¯1, bar but also to a chosen value of T, h, r, Φ and r. Finally, applicative examples are illustrated.

scholarly journals Chain of matrices, loop equations, and topological recursion

2018 ◽  
Author(s):  
Marco Bertola
Keyword(s):  
External Field ◽  
Random Matrices ◽  
Recursive Solution ◽  
Matrix Integral ◽  
Discrete Surfaces ◽  
Topological Recursion ◽  
Matrix Integrals ◽  
A Chain ◽  
The One ◽  
Definition Of

This article considers the so-called loop equations satisfied by integrals over random matrices coupled in a chain as well as their recursive solution in the perturbative case when the matrices are Hermitian. Random matrices are used in fields such as the study of multi-orthogonal polynomials or the enumeration of discrete surfaces, both of which are based on the analysis of a matrix integral. However, this term can be confusing since the definition of a matrix integral in these two applications is not the same. The article discusses these two definitions, perturbative and non-perturbative, along with their relationship. It first provides an overview of a matrix integral before comparing convergent and formal matrix integrals. It then describes the loop equations and their solution in the one-matrix model. It also examines matrices coupled in a chain plus external field and concludes with a generalization of the topological recursion.

Reply by the authors to F. J. Esparza and E. Gómez‐Treviño

Geophysics ◽  
1997 ◽  
Vol 62 (2) ◽  
pp. 692-692 ◽  
Author(s):  
David L. B. Jupp ◽  
Keeva Vozoff
Keyword(s):  
Short Discussion ◽  
Rotation Invariant ◽  
Definition Of ◽  
Invariant Definition

Despite the time that has passed since the original short discussion, I think some useful points can be made regarding the note by Esparza and Gómez‐Treviño. First, the authors are quite correct to point out that (3) of their note is not a rotation invariant definition of phase as was claimed in the original discussion. This slip most likely carried into later texts unchallenged. The fact is, however, that (3) is rotation invariant for a 2‐D earth. It was in this context that the change was made to the definition in Vozoff (1971).

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