scholarly journals Entropic Dynamics on Gibbs Statistical Manifolds

Entropy ◽  
2021 ◽  
Vol 23 (5) ◽  
pp. 494
Author(s):  
Pedro Pessoa ◽  
Felipe Xavier Costa ◽  
Ariel Caticha
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Exponential Family ◽  
Information Geometry ◽  
Arrow Of Time ◽  
Quantum Field ◽  
Statistical Manifold ◽  
Statistical Manifolds ◽  
Gibbs Distributions ◽  
Entropic Dynamics

Entropic dynamics is a framework in which the laws of dynamics are derived as an application of entropic methods of inference. Its successes include the derivation of quantum mechanics and quantum field theory from probabilistic principles. Here, we develop the entropic dynamics of a system, the state of which is described by a probability distribution. Thus, the dynamics unfolds on a statistical manifold that is automatically endowed by a metric structure provided by information geometry. The curvature of the manifold has a significant influence. We focus our dynamics on the statistical manifold of Gibbs distributions (also known as canonical distributions or the exponential family). The model includes an “entropic” notion of time that is tailored to the system under study; the system is its own clock. As one might expect that entropic time is intrinsically directional; there is a natural arrow of time that is led by entropic considerations. As illustrative examples, we discuss dynamics on a space of Gaussians and the discrete three-state system.

scholarly journals Entropic dynamics: reconstructing quantum field theory in curved space-time

2019 ◽  
Vol 36 (20) ◽  
pp. 205013 ◽  
Author(s):  
Selman Ipek ◽  
Mohammad Abedi ◽  
Ariel Caticha
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Space Time ◽  
Quantum Field ◽  
Curved Space ◽  
Entropic Dynamics

scholarly journals Symmetries and Metamorphoses

Symmetry ◽  
2020 ◽  
Vol 12 (6) ◽  
pp. 907
Author(s):  
Giuseppe Vitiello
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Arrow Of Time ◽  
Quantum Field ◽  
Continuous Symmetry ◽  
Spontaneous Breakdown ◽  
Symmetry Properties ◽  
Fractal Patterns ◽  
Symmetry Transformations ◽  
Self Similar

In quantum field theory with spontaneous breakdown of symmetry, the invariance of the dynamics under continuous symmetry transformations manifests itself in observable ordered patterns with different symmetry properties. Such a dynamical rearrangement of symmetry describes, in well definite formal terms, metamorphosis processes. The coherence of the correlations generating order and self-similar fractal patterns plays a crucial role. The metamorphosis phenomenon is generated by the loss of infrared contributions in physical states and observables due to their localized nature. The dissipative dynamics and evolution, the arising of the arrow of time and entanglement are also discussed. The conclusions may be extended to biology and neuroscience and to some aspects of linguistics in the transition from syntax to semantics (generation of meanings).

scholarly journals The Entropic Dynamics of Quantum Scalar Fields Coupled to Gravity

Symmetry ◽  
2020 ◽  
Vol 12 (8) ◽  
pp. 1324
Author(s):  
Selman Ipek ◽  
Ariel Caticha
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Relativistic Quantum ◽  
Superposition Principle ◽  
Hamiltonian Formalism ◽  
Scalar Fields ◽  
Space Time ◽  
Relativistic Quantum Mechanics ◽  
Quantum Field ◽  
Entropic Dynamics

Entropic dynamics (ED) are a general framework for constructing indeterministic dynamical models based on entropic methods. ED have been used to derive or reconstruct both non-relativistic quantum mechanics and quantum field theory in curved space-time. Here we propose a model for a quantum scalar field propagating in dynamical space-time. The approach rests on a few key ingredients: (1) Rather than modelling the dynamics of the fields, ED models the dynamics of their probabilities. (2) In accordance with the standard entropic methods of inference, the dynamics are dictated by information encoded in constraints. (3) The choice of the physically relevant constraints is dictated by principles of symmetry and invariance. The first of such principle imposes the preservation of a symplectic structure which leads to a Hamiltonian formalism with its attendant Poisson brackets and action principle. The second symmetry principle is foliation invariance, which, following earlier work by Hojman, Kuchař, and Teitelboim, is implemented as a requirement of path independence. The result is a hybrid ED model that approaches quantum field theory in one limit and classical general relativity in another, but is not fully described by either. A particularly significant prediction of this ED model is that the coupling of quantum fields to gravity implies violations of the quantum superposition principle.

A Review of Conformal Field Theory in 2D

2014 ◽  
Vol 6 (2) ◽  
pp. 1079-1105
Author(s):  
Rahul Nigam
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Conformal Field Theory ◽  
Statistical Mechanics ◽  
Critical Behavior ◽  
Verma Module ◽  
Virasoro Algebra ◽  
Quantum Field ◽  
Conformal Field ◽  
Insight Into

In this review we study the elementary structure of Conformal Field Theory in which is a recipe for further studies of critical behavior of various systems in statistical mechanics and quantum field theory. We briefly review CFT in dimensions which plays a prominent role for example in the well-known duality AdS/CFT in string theory where the CFT lives on the AdS boundary. We also describe the mapping of the theory from the cylinder to a complex plane which will help us gain an insight into the process of radial quantization and radial ordering. Finally we will develop the representation of the Virasoro algebra which is the well-known "Verma module".  

Some remarks on a deformed quantum field theory

2002 ◽  
Author(s):  
Marco Aurelio Do Rego Monteiro ◽  
V. B. Bezerra ◽  
E. M.F. Curado
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Quantum Field
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