scholarly journals ON THE UNIQUENESS OF D = 11 INTERACTIONS AMONG A GRAVITON, A MASSLESS GRAVITINO AND A THREE-FORM III: GRAVITON AND GRAVITINI

2008 ◽  
Vol 23 (30) ◽  
pp. 4861-4875 ◽  
Author(s):  
EUGEN-MIHĂIŢĂ CIOROIANU ◽  
EUGEN DIACONU ◽  
SILVIU CONSTANTIN SĂRARU
Keyword(s):  
Coupling Constant ◽  
Lorentz Covariance

Under the hypotheses of smoothness of the interactions in the coupling constant, locality, Poincaré invariance, Lorentz covariance and the preservation of the number of derivatives on each field in the Lagrangian of the interacting theory (the same number of derivatives like in the free Lagrangian), we prove that in D = 11 there are no cross-interactions between the graviton and the massless gravitino and also no self-interactions in the Rarita–Schwinger sector. A comparison with the case D = 4 is briefly discussed.

scholarly journals ON THE UNIQUENESS OF D = 11 INTERACTIONS AMONG A GRAVITON, A MASSLESS GRAVITINO AND A THREE-FORM II: THREE-FORM AND GRAVITINI

2008 ◽  
Vol 23 (30) ◽  
pp. 4841-4859 ◽  
Author(s):  
EUGEN-MIHĂIŢĂ CIOROIANU ◽  
EUGEN DIACONU ◽  
SILVIU CONSTANTIN SĂRARU
Keyword(s):  
Master Equation ◽  
Gauge Field ◽  
Space Time ◽  
Free Solution ◽  
Coupling Constant ◽  
Abelian Gauge ◽  
Gauge Transformations ◽  
Lorentz Covariance ◽  
Brst Cohomology ◽  
Chern Simons

The interactions that can be introduced between a massless Rarita–Schwinger field and an Abelian three-form gauge field in 11 space–time dimensions are analyzed in the context of the deformation of the "free" solution of the master equation combined with local BRST cohomology. Under the hypotheses of smoothness of the interactions in the coupling constant, locality, Poincaré invariance, Lorentz covariance, and the presence of at most two derivatives in the Lagrangian of the interacting theory (the same number of derivatives as in the free Lagrangian), we prove that there are neither cross-couplings nor self-interactions for the gravitino in D = 11. The only possible term that can be added to the deformed solution to the master equation is nothing but a generalized Chern–Simons term for the three-form gauge field, which brings contributions to the deformed Lagrangian, but does not modify the original, Abelian gauge transformations.

scholarly journals ON THE UNIQUENESS OF D = 11 INTERACTIONS AMONG A GRAVITON, A MASSLESS GRAVITINO AND A THREE-FORM IV: PUTTING THINGS TOGETHER

2008 ◽  
Vol 23 (30) ◽  
pp. 4877-4923 ◽  
Author(s):  
EUGEN-MIHĂIŢĂ CIOROIANU ◽  
EUGEN DIACONU ◽  
SILVIU CONSTANTIN SĂRARU
Keyword(s):  
Coupling Constant ◽  
Lorentz Covariance

Under the hypotheses of smoothness of the interactions in the coupling constant, locality, Poincaré invariance, Lorentz covariance and the preservation of the number of derivatives on each field in the Lagrangian of the interacting theory (the same number of derivatives like in the free Lagrangian), we prove that the only consistent interactions in D = 11 among massless gravitini, a graviton, and a three-form are described by N = 1, D = 11 SUGRA.

scholarly journals ON THE UNIQUENESS OF D = 11 INTERACTIONS AMONG A GRAVITON, A MASSLESS GRAVITINO AND A THREE-FORM I: PAULI–FIERZ AND THREE-FORM

2008 ◽  
Vol 23 (29) ◽  
pp. 4721-4755 ◽  
Author(s):  
EUGEN-MIHĂIŢĂ CIOROIANU ◽  
EUGEN DIACONU ◽  
SILVIU CONSTANTIN SĂRARU
Keyword(s):  
General Relativity ◽  
Gauge Field ◽  
Deformation Theory ◽  
Coupling Constant ◽  
Lorentz Covariance ◽  
Massless Spin ◽  
Brst Cohomology

Cross-couplings between a massless spin-two field (described in the free limit by the Pauli–Fierz action) and an Abelian three-form gauge field in D = 11 are investigated in the framework of the deformation theory based on local BRST cohomology. These consistent interactions are obtained on the grounds of smoothness in the coupling constant, locality, Lorentz covariance, Poincaré invariance, and the presence of at most two derivatives in the interacting Lagrangian. Our results confirm the uniqueness of the 11-dimensional interactions between a graviton and a three-form prescribed by general relativity.

scholarly journals YES-GO CROSS-COUPLINGS IN COLLECTIONS OF TENSOR FIELDS WITH MIXED SYMMETRIES OF THE TYPE (3, 1) AND (2, 2)

2010 ◽  
Vol 25 (06) ◽  
pp. 1211-1238
Author(s):  
CONSTANTIN BIZDADEA ◽  
EUGEN-MIHĂIŢĂ CIOROIANU ◽  
SOLANGE-ODILE SALIU ◽  
ELENA-MIRELA BĂBĂLÎC
Keyword(s):  
Quadratic Form ◽  
Deformation Theory ◽  
Riemann Tensor ◽  
Positive Definite ◽  
Coupling Constant ◽  
Tensor Fields ◽  
Lorentz Covariance ◽  
Mixed Symmetry ◽  
Type 3 ◽  
Derivatives Of

Under the hypotheses of analyticity, locality, Lorentz covariance, and Poincaré invariance of the deformations, combined with the requirement that the interaction vertices contain at most two space–time derivatives of the fields, we investigate the consistent cross-couplings between two collections of tensor fields with the mixed symmetries of the type (3, 1) and (2, 2). The computations are done with the help of the deformation theory based on a cohomological approach in the context of the antifield-BRST formalism. Our results can be synthesized in: (i) there appear consistent cross-couplings between the two types of field collections at order one and two in the coupling constant such that some of the gauge generators and of the reducibility functions are deformed, and (ii) the existence or not of cross-couplings among different fields with the mixed symmetry of the Riemann tensor depends on the indefinite or respectively positive-definite behavior of the quadratic form defined by the kinetic terms from the free Lagrangian.

Exchange-Correlation Energy Densities and Response Potentials: Connection Between Two Definitions and Analytical Model for the Strong-Coupling Limit of a Stretched Bond

2019 ◽  
Author(s):  
S. Giarrusso ◽  
Paola Gori-Giorgi
Keyword(s):  
Density Functional Theory ◽  
Strong Coupling ◽  
Density Functional ◽  
Correlation Energy ◽  
Order Term ◽  
Strong Coupling Limit ◽  
Local Form ◽  
Coupling Constant ◽  
Functional Theory ◽  
Exchange Correlation

We analyze in depth two widely used definitions (from the theory of conditional probablity amplitudes and from the adiabatic connection formalism) of the exchange-correlation energy density and of the response potential of Kohn-Sham density functional theory. We introduce a local form of the coupling-constant-dependent Hohenberg-Kohn functional, showing that the difference between the two definitions is due to a corresponding local first-order term in the coupling constant, which disappears globally (when integrated over all space), but not locally. We also design an analytic representation for the response potential in the strong-coupling limit of density functional theory for a model single stretched bond.<br>

Assessing the Calculation of Exchange Coupling Constants and Spin Crossover Gaps Using the Approximate Projection Model to Improve Density Function Calculations

2019 ◽  
Author(s):  
Xianghai Sheng ◽  
Lee Thompson ◽  
Hrant Hratchian
Keyword(s):  
Density Functional Theory ◽  
Exchange Coupling ◽  
Density Functional ◽  
Spin Crossover ◽  
Coupling Constants ◽  
Spin Projection ◽  
Coupling Constant ◽  
Projection Model ◽  
Functional Theory

This work evaluates the quality of exchange coupling constant and spin crossover gap calculations using density functional theory corrected by the Approximate Projection model. Results show that improvements using the Approximate Projection model range from modest to significant. This study demonstrates that, at least for the class of systems examined here, spin-projection generally improves the quality of density functional theory calculations of J-coupling constants and spin crossover gaps. Furthermore, it is shown that spin-projection can be important for both geometry optimization and energy evaluations. The Approximate Project model provides an affordable and practical approach for effectively correcting spin-contamination errors in molecular exchange coupling constant and spin crossover gap calculations.

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