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Entropic Dynamics: Reconstructing Quantum Field Theory in Curved Space-time
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The Entropic Dynamics reconstruction of quantum mechanics is extended to quantum field theory in curved space-time. The Entropic Dynamics framework, which derives quantum theory as an application of the method of maximum entropy, is combined with the covariant methods of Dirac, Hojman, Kucha\v{r}, and Teitelboim, which they used to develop a framework for classical covariant Hamiltonian theories. The goal is to formulate an information-based alternative to current approaches based on algebraic quantum field theory. One key ingredient is the adoption of a local notion of entropic time in which instants are defined on curved three-dimensional surfaces and time evolution consists of the accumulation of changes induced by local deformations of these surfaces. The resulting dynamics is a non-dissipative diffusion that is constrained by the requirements of foliation invariance and incorporates the necessary local quantum potentials. As applications of the formalism we derive the Ehrenfest relations for fields in curved-spacetime and briefly discuss the nature of divergences in quantum field theory.
Forward citations
Cited by 4 Pith papers
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Entropic Dynamics of Jump-Diffusion Option Pricing
The Merton jump-diffusion process, the Esscher transform, and the implied volatility smile are derived from Maximum Entropy inference applied to log-price dynamics with continuity, directionality, and jump constraints.
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The Entropic Dynamics approach to Quantum Mechanics
Requiring the entropic dynamics of a probability density and phase to preserve both symplectic and information-geometric structures yields the linear Schrödinger equation.
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Entropic Dynamics of Exchange Rates and Options
The authors show that maximum-entropy reasoning, together with a scale-invariance argument for log returns, yields the standard Garman-Kohlhagen foreign-exchange option pricing model.
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Entropic Dynamics of Stocks and European Options
The paper re-derives Geometric Brownian Motion, the Fokker-Planck equation, and the Black-Scholes-Merton equation as consequences of maximum-entropy inference with scale invariance, continuity, and a drift constraint.
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