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Complex Effective Path: A Semi-Classical Probe of Quantum Effects
High Energy Physics - Theory · Submitted 29 Dec 2011
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim The imaginary part of the effective action is known to be related to the probability of particle creation by an external source and hence we expect the imaginary part of the effective path also to contain information about particle creation.
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The abstract, sentence by sentence
We discuss the notion of an effective, average, quantum mechanical path which is a solution of the dynamical equations obtained by extremizing the quantum effective action. Since the effective action can, in general, be complex, the effective path will also, in general, be complex. The imaginary part of the effective action is known to be related to the probability of particle creation by an external source and hence we expect the imaginary part of the effective path also to contain information about particle creation. We try to identify such features using simple examples including that of effective path through the black hole horizon leading to thermal radiation. Implications of this approach are discussed.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We discuss the notion of an effective, average, quantum mechanical path which is a solution of the dynamical equations obtained by extremizing the quantum effective action. | contribution 0.79 | 0.55 | 0.13 | asserted 0.99 |
| s1 | Since the effective action can, in general, be complex, the effective path will also, in general, be complex. | result 0.44 | 0.22 | 0.11 | asserted 0.73 |
| s2 | The imaginary part of the effective action is known to be related to the probability of particle creation by an external source and hence we expect the imaginary part of the effective path also to contain information about particle creation. | interpretation 0.51 | 0.08 | 0.20 | hedged possibility 0.75 |
| s3 | We try to identify such features using simple examples including that of effective path through the black hole horizon leading to thermal radiation. | contribution 0.59 | 0.84 | 0.10 | asserted 0.33 |
| s4 | Implications of this approach are discussed. | interpretation 0.87 | 0.42 | 0.05 | unclear 0.98 |
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The paper
Original abstract
We discuss the notion of an effective, average, quantum mechanical path which is a solution of the dynamical equations obtained by extremizing the quantum effective action. Since the effective action can, in general, be complex, the effective path will also, in general, be complex. The imaginary part of the effective action is known to be related to the probability of particle creation by an external source and hence we expect the imaginary part of the effective path also to contain information about particle creation. We try to identify such features using simple examples including that of effective path through the black hole horizon leading to thermal radiation. Implications of this approach are discussed.
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How the literature uses it
1 arXiv paper cite this in 20 sentences
Papers citing it · 15 sentences without a confident label
Builds on it 1 paper
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Since this Hamiltonian is related to both Kerr and SSSBH spacetimes, our model is capable of presenting a very general situation, rather than restricted to SSSBH as was done originally in [ref] .
Thermality of horizon through near horizon instability: a path integral approach · Introduction and basic formalism · 0.97
Compares with it 1 paper
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Note that unlike in [ref] , in our case, the “$a$" in Eq. [ref] is a complex value, given by, [equation] Substituting this value, in the limit $ϵ→0$, we get (see Appendix [ref]), [equation] and, [equation] The $θ_i$s, which are real, are defined in Appendix [ref].
Thermality of horizon through near horizon instability: a path integral approach · Complex Effective Path and temperature · 0.81
Cites it as support 1 paper
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Additionally, as ([ref]) is unstable (or unbounded) in nature, the outcome from this again confirms the robustness of the corollary, suggested in [ref] – the necessary (but maybe not sufficient) condition that the Hamiltonian must be unbounded in order to obtain a complex path.
Thermality of horizon through near horizon instability: a path integral approach · Introduction and basic formalism · 0.96
Cites it as background 1 paper
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The conception of the path through the above definition was initially put forward in [ref] but did not get attention until its application was made in [ref] .
Thermality of horizon through near horizon instability: a path integral approach · Introduction and basic formalism · 0.91
What it cites · 6 sentences without a confident label
Cites as background 2 papers
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Well known examples of these phenomena occur in the study of Schwinger effect [ref] , particle creation in expanding universe [ref] and black hole evaporation [ref] .
Gravity and the Thermodynamics of Horizons · Introduction · 0.89
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This feature is well-known in the tunneling derivation of black hole temperature and has been extensively discussed in the literature [ref] .
Method of complex paths and general covariance of Hawking radiation · Horizon thermodynamics · 0.84
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