Built on

J. Schwinger, Four-dimensional euclidean formulation of quantum field theory
1958
Earlier work this paper cites.
J. S. Schwinger, Brownian motion of a quantum oscillator
1961
Earlier work this paper cites.
L. Keldysh, Diagram technique for nonequilibrium processes
1964
Earlier work this paper cites.
A. I. Larkin and Y. N. Ovchinnikov, Quasiclassical method in the theory of superconductivity
1969
Earlier work this paper cites.
R. C. Entringer, Enumeration of permutations of ( 1 , ⋯ , n ) (1,\cdots,n) by number of maxima
1969
Earlier work this paper cites.
K. Osterwalder and R. Schrader, Axioms for Euclidean Green’s Functions
1973
Earlier work this paper cites.
K. Osterwalder and R. Schrader, Axioms for Euclidean Green’s Functions. 2
1975
Earlier work this paper cites.
K.-c. Chou, Z.-b. Su, B.-l. Hao, and L. Yu, Equilibrium and Nonequilibrium Formalisms Made Unified
1985
Earlier work this paper cites.
S. Sachdev and J. Ye, Gapless spin fluid ground state in a random, quantum Heisenberg magnet
1993
Earlier work this paper cites.
J. Polchinski, L. Susskind, and N. Toumbas, Negative energy, superluminosity and holography
1999
Earlier work this paper cites.
V. E. Hubeny, Precursors see inside black holes
2003
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A. Hodges and C. Sukumar, Bernoulli, euler, permutations and quantum algebras
2007
Earlier work this paper cites.
C. Sukumar and A. Hodges, Quantum algebras and parity-dependent spectra
2007
Earlier work this paper cites.

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2017

Classification of out-of-time-order correlators

Haehl, Felix M., Loganayagam, R., Narayan, Prithvi et al.

Understand

The space of n-point correlation functions, for all possible time-orderings of operators, can be computed by a non-trivial path integral contour, which depends on how many time-ordering violations are present in the correlator.

These contours, which have come to be known as timefolds, or out-of-time-order (OTO) contours, are a natural generalization of the Schwinger-Keldysh contour (which computes singly out-of-time-ordered correlation functions).
We provide a detailed discussion of such higher OTO functional integrals, explaining their general structure, and the myriad ways in which a particular correlation function may be encoded in such contours.
Our discussion may be seen as a natural generalization of the Schwinger-Keldysh formalism to higher OTO correlation functions.

Built on

J. Schwinger, Four-dimensional euclidean formulation of quantum field theory
1958
Earlier work this paper cites.
J. S. Schwinger, Brownian motion of a quantum oscillator
1961
Earlier work this paper cites.
L. Keldysh, Diagram technique for nonequilibrium processes
1964
Earlier work this paper cites.
A. I. Larkin and Y. N. Ovchinnikov, Quasiclassical method in the theory of superconductivity
1969
Earlier work this paper cites.
R. C. Entringer, Enumeration of permutations of ( 1 , ⋯ , n ) (1,\cdots,n) by number of maxima
1969
Earlier work this paper cites.
K. Osterwalder and R. Schrader, Axioms for Euclidean Green’s Functions
1973
Earlier work this paper cites.
K. Osterwalder and R. Schrader, Axioms for Euclidean Green’s Functions. 2
1975
Earlier work this paper cites.
K.-c. Chou, Z.-b. Su, B.-l. Hao, and L. Yu, Equilibrium and Nonequilibrium Formalisms Made Unified
1985
Earlier work this paper cites.
S. Sachdev and J. Ye, Gapless spin fluid ground state in a random, quantum Heisenberg magnet
1993
Earlier work this paper cites.
J. Polchinski, L. Susskind, and N. Toumbas, Negative energy, superluminosity and holography
1999
Earlier work this paper cites.
V. E. Hubeny, Precursors see inside black holes
2003
Earlier work this paper cites.
A. Hodges and C. Sukumar, Bernoulli, euler, permutations and quantum algebras
2007
Earlier work this paper cites.
C. Sukumar and A. Hodges, Quantum algebras and parity-dependent spectra
2007
Earlier work this paper cites.