Topic
Generating function (physics)
About: Generating function (physics) is a research topic. Over the lifetime, 1777 publications have been published within this topic receiving 23841 citations.
Papers published on a yearly basis
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Papers
TL;DR: The notion of cumulants and cumulant functions was introduced in this paper, where a moment generating function of a set of stochastic variables defines the cumulus or the semi-invariants and the cumULant function, and the definition of average may be greatly generalized as far as the condition of the average of unity is unity.
Abstract: The moment generating function of a set of stochastic variables defines the cumulants or the semi-invariants and the cumulant function. It is possible, simply by formal properties of exponential functions, to generaiize to a great extent the concepts of cumulants and cumulant function. The stochastic variables to be considered need not be ordinary c -numbers but they may be q -numbers such as used in quantum mechanics. The exponential function which defines a moment generating function may be any kind of generalized exponential, for example an ordered exponential with a certain prescription for ordering q -number variables. The definition of average may be greatly generalized as far as the condition is fulfilled that the average of unity is unity. After statements of a few basic theorems these generalizations are discussed here with certain examples of application. This generalized cumulant expansion provides us with a point of view from which many existent methods in quantum mechanics and statistical mec...
1,783 citations
TL;DR: In this paper, the authors proved an identity that equates the elliptic genus partition function of a supersymmetric sigma model on the N-fold symmetric product M N /SN of a manifold M to the partition function for a second quantized string theory on the space M × S 1, where the generating function of these elliptic genera is shown to be an automorphic form for O(3,2, Z).
Abstract: In this note we prove an identity that equates the elliptic genus partition function of a supersymmetric sigma model on the N-fold symmetric product M N /SN of a manifold M to the partition function of a second quantized string theory on the space M × S 1 . The generating function of these elliptic genera is shown to be (almost) an automorphic form for O(3,2, Z). In the context of D-brane dynamics, this result gives a precise computation of the free energy of a gas of D-strings inside a higher-dimensional brane.
609 citations
TL;DR: In this article, the authors developed a method of counting single-trace and multi-trace BPS operators with two supercharges, for world-volume gauge theories of D-brane probes for both $N \to \infty$ and finite $N$.
Abstract: We develop a systematic and efficient method of counting single-trace and multi-trace BPS operators with two supercharges, for world-volume gauge theories of $N$ D-brane probes for both $N \to \infty$ and finite $N$. The techniques are applicable to generic singularities, orbifold, toric, non-toric, complete intersections, et cetera, even to geometries whose precise field theory duals are not yet known. The so-called ``Plethystic Exponential'' provides a simple bridge between (1) the defining equation of the Calabi-Yau, (2) the generating function of single-trace BPS operators and (3) the generating function of multi-trace operators. Mathematically, fascinating and intricate inter-relations between gauge theory, algebraic geometry, combinatorics and number theory exhibit themselves in the form of plethystics and syzygies.
488 citations
TL;DR: In this article, generalized canonical transformations for generalized Hamiltonian systems are introduced, which convert a generalized Hamiltonians system into another one, and preserve the original structure of the original one.
307 citations
TL;DR: In this paper, the authors developed a method of counting single-trace and multi-trace BPS operators with two supercharges, for world-volume gauge theories of D-brane probes for both $N \to \infty$ and finite $N$.
Abstract: We develop a systematic and efficient method of counting single-trace and multi-trace BPS operators with two supercharges, for world-volume gauge theories of $N$ D-brane probes for both $N \to \infty$ and finite $N$. The techniques are applicable to generic singularities, orbifold, toric, non-toric, complete intersections, et cetera, even to geometries whose precise field theory duals are not yet known. The so-called ``Plethystic Exponential'' provides a simple bridge between (1) the defining equation of the Calabi-Yau, (2) the generating function of single-trace BPS operators and (3) the generating function of multi-trace operators. Mathematically, fascinating and intricate inter-relations between gauge theory, algebraic geometry, combinatorics and number theory exhibit themselves in the form of plethystics and syzygies.
303 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2022 | 2 |
| 2021 | 87 |
| 2020 | 67 |
| 2019 | 85 |
| 2018 | 93 |
| 2017 | 63 |