DYNAMICAL EFFECTS IN PAIR PRODUCTION BY ELECTRIC FIELDS

1991 ◽  
Vol 06 (05) ◽  
pp. 695-725 ◽  
Author(s):  
A.B. BALANTEKIN ◽  
J.E. SEGER ◽  
S.H. FRICKE
Keyword(s):  
Pair Production ◽  
Electric Fields ◽  
Symmetric Functions ◽  
Semiclassical Approximation ◽  
Constant Field ◽  
Field Limit ◽  
Fermion Pair ◽  
Elementary Symmetric Functions ◽  
Multiplicity Distributions ◽  
Uniform Semiclassical Approximation

Nonperturbative dynamical effects in fermion-antifermion pair production by classical electric fields are investigated. Following a summary of the results previously given in the literature, a formal connection between fermion pair production in an external field and supersymmetric quantum mechanics is pointed out. Pair production probabilities are calculated in a uniform semiclassical approximation, which yields the Schwinger result in the constant field limit. The multiplicity distributions of the created pairs are shown to be related to the elementary symmetric functions.

scholarly journals A note on extrema of linear combinations of elementary symmetric functions

2012 ◽  
Vol 60 (2) ◽  
pp. 219-224 ◽  
Author(s):  
Alexander Kovačec ◽  
Salma Kuhlmann ◽  
Cordian Riener
Keyword(s):  
Symmetric Functions ◽  
Linear Combinations ◽  
Elementary Symmetric Functions

scholarly journals Some New Methods in the Theory of $m$-Quasi-Invariants

10.37236/1877 ◽  
2005 ◽  
Vol 11 (2) ◽  
Author(s):  
J. Bell ◽  
A. M. Garsia ◽  
N. Wallach
Keyword(s):  
Symmetric Functions ◽  
Free Module ◽  
Finitely Generated ◽  
Graded Algebras ◽  
New Approach ◽  
Elementary Symmetric Functions ◽  
New Methods ◽  
Regular Sequences

We introduce here a new approach to the study of $m$-quasi-invariants. This approach consists in representing $m$-quasi-invariants as $N^{tuples}$ of invariants. Then conditions are sought which characterize such $N^{tuples}$. We study here the case of $S_3$ $m$-quasi-invariants. This leads to an interesting free module of triplets of polynomials in the elementary symmetric functions $e_1,e_2,e_3$ which explains certain observed properties of $S_3$ $m$-quasi-invariants. We also use basic results on finitely generated graded algebras to derive some general facts about regular sequences of $S_n$ $m$-quasi-invariants

scholarly journals A Unified View of Determinantal Expansions for Jack Polynomials

10.37236/1547 ◽  
2000 ◽  
Vol 8 (1) ◽  
Author(s):  
Leigh Roberts
Keyword(s):  
Differential Geometry ◽  
Symmetric Functions ◽  
Jack Polynomials ◽  
Elementary Symmetric Functions ◽  
Fundamental Symmetry ◽  
Unified View

Recently Lapointe et. al. [3] have expressed Jack Polynomials as determinants in monomial symmetric functions $m_\lambda$. We express these polynomials as determinants in elementary symmetric functions $e_\lambda$, showing a fundamental symmetry between these two expansions. Moreover, both expansions are obtained indifferently by applying the Calogero-Sutherland operator in physics or quasi Laplace Beltrami operators arising from differential geometry and statistics. Examples are given, and comments on the sparseness of the determinants so obtained conclude the paper.

scholarly journals On the integrality of the first and second elementary symmetric functions of $1, 1/2^{s_2}, ...,1/n^{s_n}$

2017 ◽  
Vol 2 (4) ◽  
pp. 682-691 ◽  
Author(s):  
Wanxi Yang ◽  
◽  
Mao Li ◽  
Yulu Feng ◽  
Xiao Jiang ◽  
...  
Keyword(s):  
Symmetric Functions ◽  
Elementary Symmetric Functions
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