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## Weyl Group Multiple Dirichlet Series: Type A Combinatorial Theory (AM-175)

*Ben Brubaker, Daniel Bump, and Solomon Friedberg*

- Published in print:
- 2011
- Published Online:
- October 2017
- ISBN:
- 9780691150659
- eISBN:
- 9781400838998
- Item type:
- book

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691150659.001.0001
- Subject:
- Mathematics, Combinatorics / Graph Theory / Discrete Mathematics

Weyl group multiple Dirichlet series are generalizations of the Riemann zeta function. Like the Riemann zeta function, they are Dirichlet series with analytic continuation and functional equations, ... More

## Holomorphic functions

*Simon Donaldson*

### in Riemann Surfaces

- Published in print:
- 2011
- Published Online:
- December 2013
- ISBN:
- 9780198526391
- eISBN:
- 9780191774874
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198526391.003.0001
- Subject:
- Mathematics, Geometry / Topology, Analysis

This chapter reviews some examples of holomorphic functions in complex analysis. It emphasizes the idea of ‘analytic continuation’, which is a fundamental motivation for Riemann surface theory.

## Thermodynamic Green’s Functions and Spectral Structure

*Norman J. Morgenstern Horing*

### in Quantum Statistical Field Theory: An Introduction to Schwinger's Variational Method with Green's Function Nanoapplications, Graphene and Superconductivity

- Published in print:
- 2017
- Published Online:
- January 2018
- ISBN:
- 9780198791942
- eISBN:
- 9780191834165
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198791942.003.0007
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

Multiparticle thermodynamic Green’s functions, defined in terms of grand canonical ensemble averages of time-ordered products of creation and annihilation operators, are interpreted as tracing the ... More

## Local Lie Groups

*Ercüment H. Ortaçgil*

### in An Alternative Approach to Lie Groups and Geometric Structures

- Published in print:
- 2018
- Published Online:
- September 2018
- ISBN:
- 9780198821656
- eISBN:
- 9780191860959
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198821656.003.0004
- Subject:
- Mathematics, Pure Mathematics

If the nonlinear curvature of a splitting vanishes, then the local solutions form a pseudogroup, and we the manifold is called a local Lie group. This is a global concept!

## Non-Equilibrium Green’s Functions: Variational Relations and Approximations for Particle Interactions

*Norman J. Morgenstern Horing*

### in Quantum Statistical Field Theory: An Introduction to Schwinger's Variational Method with Green's Function Nanoapplications, Graphene and Superconductivity

- Published in print:
- 2017
- Published Online:
- January 2018
- ISBN:
- 9780198791942
- eISBN:
- 9780191834165
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198791942.003.0009
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

Chapter 09 Nonequilibrium Green’s functions (NEGF), including coupled-correlated (C) single- and multi-particle Green’s functions, are defined as averages weighted with the time-development operator ... More

## Multi-instantons in quantum mechanics (QM)

*Jean Zinn-Justin*

### in Quantum Field Theory and Critical Phenomena: Fifth Edition

- Published in print:
- 2021
- Published Online:
- June 2021
- ISBN:
- 9780198834625
- eISBN:
- 9780191872723
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198834625.003.0042
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

In general, a linear combination of instanton solutions is not a solution of the imaginary-time equations of motion, because the equations not linear. Moreover, in quantum mechanics (QM), all ... More

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