scholarly journals Matrix elements for type 1 unitary irreducible representations of the Lie superalgebra gl(m|n)

2014 ◽  
Vol 55 (1) ◽  
pp. 011703 ◽  
Author(s):  
Mark D. Gould ◽  
Phillip S. Isaac ◽  
Jason L. Werry
Keyword(s):  
Lie Superalgebra ◽  
Irreducible Representations ◽  
Matrix Elements

scholarly journals GENERIC IRREDUCIBLE REPRESENTATIONS OF FINITE-DIMENSIONAL LIE SUPERALGEBRAS

1994 ◽  
Vol 05 (03) ◽  
pp. 389-419 ◽  
Author(s):  
IVAN PENKOV ◽  
VERA SERGANOVA
Keyword(s):  
Irreducible Module ◽  
Lie Superalgebra ◽  
Lie Superalgebras ◽  
Irreducible Representations ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Highest Weight ◽  
Finite Dimensional ◽  
Finite Dimensionality ◽  
Necessary And Sufficient

A theory of highest weight modules over an arbitrary finite-dimensional Lie superalgebra is constructed. A necessary and sufficient condition for the finite-dimensionality of such modules is proved. Generic finite-dimensional irreducible representations are defined and an explicit character formula for such representations is written down. It is conjectured that this formula applies to any generic finite-dimensional irreducible module over any finite-dimensional Lie superalgebra. The conjecture is proved for several classes of Lie superalgebras, in particular for all solvable ones, for all simple ones, and for certain semi-simple ones.

Matrix factorizations for the Coulomb interaction between electrons in atoms

1969 ◽  
Vol 309 (1497) ◽  
pp. 185-194 ◽  
Keyword(s):  
Coulomb Interaction ◽  
Irreducible Representations ◽  
Matrix Factorizations ◽  
Matrix Elements ◽  
Spin Orientation ◽  
Straightforward Application ◽  
Basic States

In contrast to what would be expected from a straightforward application of the Wigner-Eckart theorem, a simple factorization can often be made of matrix elements of operators that represent parts of the Coulomb interaction between f electrons in atoms. This property, which was discovered by Racah, is explained by using as basic states those in which the electrons are divided into two classes according to their spin orientation. The two collections of electrons are coupled through the irreducible representations of the group G 2 to which they belong, and this permits many of Racah’s proportionality constants to be related to isoscalar factors. The analogous factorizations that Feneuille found for the configurations (s + d) N are also discussed.

scholarly journals Polynomial identities for simple Lie superalgebras

1987 ◽  
Vol 28 (3) ◽  
pp. 310-327 ◽  
Author(s):  
M. D. Gould
Keyword(s):  
Tensor Product ◽  
Lie Superalgebra ◽  
Weight Vector ◽  
Lie Superalgebras ◽  
Irreducible Representations ◽  
Polynomial Identities ◽  
Minimal Weight ◽  
Finite Dimensional ◽  
Basic Classical Lie Superalgebra

AbstractPolynomial identities for the generators of a simple basic classical Lie superalgebra are derived in arbitrary representations generated by a maximal (or minimal) weight vector. The infinitesimal characters occurring in the tensor product of two finite dimensional irreducible representations are also determined.

Theoretical studies in nuclear structure. II. Nuclear d 2 , d 3 and d 4 configurations. Fractional parentage coefficients and central force matrix elements

1951 ◽  
Vol 205 (1081) ◽  
pp. 192-237 ◽  
Keyword(s):  
Group Theory ◽  
Nuclear Structure ◽  
Central Force ◽  
Irreducible Representations ◽  
Theoretical Studies ◽  
Matrix Elements ◽  
Energy Matrix ◽  
Body Interaction ◽  
Fractional Parentage

The orbital and charge-spin fractional parentage coefficients for the nuclear d 3 and d 4 con­figurations are derived using group theory. The orbital coefficients are given in a form appropriate to the new subclassification of the states according to irreducible representations of R 5 discussed in part I (Jahn 1950). Using these coefficients the complete energy matrices for the d 3 and d 4 configurations are derived, for a general charge-symmetric central two-body interaction, from the known energy matrix for the d 2 configuration.

scholarly journals Corrections to Wigner–Eckart Relations by Spontaneous Symmetry Breaking

Symmetry ◽  
2020 ◽  
Vol 12 (7) ◽  
pp. 1120
Author(s):  
Carlo Heissenberg ◽  
Franco Strocchi
Keyword(s):  
Symmetry Breaking ◽  
Spontaneous Symmetry Breaking ◽  
Irreducible Representations ◽  
Matrix Elements ◽  
Infinite Dimensional ◽  
Infinite Dimensional Systems ◽  
Goldstone Bosons ◽  
The Matrix ◽  
Symmetry Breaking Term ◽  
Breaking Term

The matrix elements of operators transforming as irreducible representations of an unbroken symmetry group G are governed by the well-known Wigner–Eckart relations. In the case of infinite-dimensional systems, with G spontaneously broken, we prove that the corrections to such relations are provided by symmetry breaking Ward identities, and simply reduce to a tadpole term involving Goldstone bosons. The analysis extends to the case in which an explicit symmetry breaking term is present in the Hamiltonian, with the tadpole term now involving pseudo Goldstone bosons. An explicit example is discussed, illustrating the two cases.

BRST AND l(1, 1)

1993 ◽  
Vol 05 (01) ◽  
pp. 191-208 ◽  
Author(s):  
S. S. HORUZHY ◽  
A. V. VORONIN
Keyword(s):  
Brst Symmetry ◽  
Lie Superalgebra ◽  
Irreducible Representations ◽  
Close Connection ◽  
Infinite Dimensional ◽  
Brst Charge ◽  
New Formula

A very close connection between the BRST symmetry and the Lie superalgebra l(1, 1) is pointed out and studied. Structure of l(1, 1), its involutions and automorphisms are described. Absence of infinite-dimensional irreducible representations (IR) of l(1, 1) is proved. The rigorous construction and decomposition into IR is performed for the class of l(1, 1) representations corresponding to physical BRST theories and consisting of infinite-dimensional doubly involutive representations in J-spaces. As a first output of the l(1, 1) formalism, a new formula for the BRST charge is derived.

Sign in / Sign up

Export Citation Format

Share Document