scholarly journals The Matrix Elements of Area Operator in (2+1) Euclidean Loop Quantum Gravity

2021 ◽  
Vol 1949 (1) ◽  
pp. 012010
Author(s):  
K Fahmi ◽  
F P Zen
Keyword(s):  
Quantum Gravity ◽  
Loop Quantum Gravity ◽  
Matrix Elements ◽  
Area Operator ◽  
The Matrix

scholarly journals On the distribution of the eigenvalues of the area operator in loop quantum gravity

2018 ◽  
Vol 35 (6) ◽  
pp. 065008 ◽  
Author(s):  
J Fernando Barbero G ◽  
Juan Margalef-Bentabol ◽  
Eduardo J S Villaseñor
Keyword(s):  
Quantum Gravity ◽  
Loop Quantum Gravity ◽  
Area Operator

scholarly journals Area Operator in Loop Quantum Gravity

2017 ◽  
Vol 18 (11) ◽  
pp. 3719-3735 ◽  
Author(s):  
Adrian P. C. Lim
Keyword(s):  
Quantum Gravity ◽  
Loop Quantum Gravity ◽  
Area Operator

scholarly journals Matrix elements of Thiemann's Hamiltonian constraint in loop quantum gravity

1997 ◽  
Vol 14 (10) ◽  
pp. 2793-2823 ◽  
Author(s):  
Roumen Borissov ◽  
Roberto De Pietri ◽  
Carlo Rovelli
Keyword(s):  
Quantum Gravity ◽  
Loop Quantum Gravity ◽  
Hamiltonian Constraint ◽  
Matrix Elements

scholarly journals Review on hermiticity of the volume operators in Loop Quantum Gravity

2019 ◽  
Vol 51 (5) ◽  
Author(s):  
S. Ariwahjoedi ◽  
I. Husin ◽  
I. Sebastian ◽  
F. P. Zen
Keyword(s):  
Quantum Gravity ◽  
Loop Quantum Gravity

scholarly journals On the Modular Operator of Mutli-component Regions in Chiral CFT

2021 ◽  
Author(s):  
Stefan Hollands
Keyword(s):  
Field Theory ◽  
Integral Equation ◽  
Hilbert Problem ◽  
Matrix Elements ◽  
New Approach ◽  
Conformal Field ◽  
The Matrix ◽  
Kms Condition ◽  
Modular Operator ◽  
Riemann Hilbert Problem

AbstractWe introduce a new approach to find the Tomita–Takesaki modular flow for multi-component regions in general chiral conformal field theory. Our method is based on locality and analyticity of primary fields as well as the so-called Kubo–Martin–Schwinger (KMS) condition. These features can be used to transform the problem to a Riemann–Hilbert problem on a covering of the complex plane cut along the regions, which is equivalent to an integral equation for the matrix elements of the modular Hamiltonian. Examples are considered.

scholarly journals Analytical angular solutions for the atom–diatom interaction potential in a basis set of products of two spherical harmonics: two approaches

2021 ◽  
Author(s):  
Mariusz Pawlak ◽  
Marcin Stachowiak
Keyword(s):  
Spherical Harmonics ◽  
Interaction Potential ◽  
Chem Phys ◽  
Basis Set ◽  
Matrix Elements ◽  
Trigonometric Functions ◽  
Variational Theory ◽  
Molecular Collision ◽  
The Matrix ◽  
Analytical Expressions

AbstractWe present general analytical expressions for the matrix elements of the atom–diatom interaction potential, expanded in terms of Legendre polynomials, in a basis set of products of two spherical harmonics, especially significant to the recently developed adiabatic variational theory for cold molecular collision experiments [J. Chem. Phys. 143, 074114 (2015); J. Phys. Chem. A 121, 2194 (2017)]. We used two approaches in our studies. The first involves the evaluation of the integral containing trigonometric functions with arbitrary powers. The second approach is based on the theorem of addition of spherical harmonics.

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