Built on

R. Bott, Nondegenerate critical manifolds
1954
Earlier work this paper cites.
R. Bott, An application of the morse theory to the topology of lie-groups
1956
Earlier work this paper cites.
F. Pham, Vanishing Homologies And The n n Variable Saddlepoint Method
1983
Earlier work this paper cites.
A. Mostafazadeh, PseudoHermiticity versus PT symmetry. The necessary condition for the reality of the spectrum
2002
Earlier work this paper cites.
A. Mostafazadeh, Exact PT symmetry is equivalent to Hermiticity
2003
Earlier work this paper cites.
C. M. Bender, D. C. Brody, and H. F. Jones, Complex extension of quantum mechanics
2004
Earlier work this paper cites.
M. G. Endres, Method for simulating O(N) lattice models at finite density
2007
Earlier work this paper cites.
H. F. Jones and R. J. Rivers, Which Green Functions Does the Path Integral for Quasi-Hermitian Hamiltonians Represent?
Original
2009
Earlier work this paper cites.
C. Pehlevan and G. Guralnik, Complex Langevin Equations and Schwinger-Dyson Equations
Original
2009
Earlier work this paper cites.
AuroraScience
Original
2012
Earlier work this paper cites.

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2015

The Lefschetz thimble and the sign problem

Scorzato, Luigi

Understand

In this talk I review the proposal to formulate quantum field theories (QFTs) on a Lefschetz thimble, which was put forward to enable Monte Carlo simulations of lattice QFTs affected by sign problem.

First I will review the theoretical justification of the approach, and comment on some open issues.
Then, I will review the algorithms that have been proposed and are being tested to represent and simulate a lattice QFT on a Lefschetz thimble.
In particular, I will review the lessons from the very first models of QFTs that have been studied with this approach.

Built on

R. Bott, Nondegenerate critical manifolds
1954
Earlier work this paper cites.
R. Bott, An application of the morse theory to the topology of lie-groups
1956
Earlier work this paper cites.
F. Pham, Vanishing Homologies And The n n Variable Saddlepoint Method
1983
Earlier work this paper cites.
A. Mostafazadeh, PseudoHermiticity versus PT symmetry. The necessary condition for the reality of the spectrum
2002
Earlier work this paper cites.
A. Mostafazadeh, Exact PT symmetry is equivalent to Hermiticity
2003
Earlier work this paper cites.
C. M. Bender, D. C. Brody, and H. F. Jones, Complex extension of quantum mechanics
2004
Earlier work this paper cites.
M. G. Endres, Method for simulating O(N) lattice models at finite density
2007
Earlier work this paper cites.
H. F. Jones and R. J. Rivers, Which Green Functions Does the Path Integral for Quasi-Hermitian Hamiltonians Represent?
Original
2009
Earlier work this paper cites.
C. Pehlevan and G. Guralnik, Complex Langevin Equations and Schwinger-Dyson Equations
Original
2009
Earlier work this paper cites.
AuroraScience
Original
2012
Earlier work this paper cites.