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Aspects of Entanglement in Quantum Field Theory and Quantum Gravity, using the Holography

Faraji Astaneh, Amin | 2015

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  1. Type of Document: Ph.D. Dissertation
  2. Language: Farsi
  3. Document No: 47032 (04)
  4. University: Sharif University of Technology
  5. Department: Physics
  6. Advisor(s): Arfaei, Hessamaddin; Mosaffa, Amir Esmaeil; Alishahiha, Mohsen
  7. Abstract:
  8. Entanglement is an immediate consequence of quantum mechanical pos- tulates and is thus an indispensable part of studying quantum systems. A very useful quantity which can appropriately quantify entanglement between the degrees of freedom of a composite quantum system is En- tanglement Entropy (EE).
    Over the last few years, this subject has attracted a lot of interest both in QFT and in the context of holography. On the one hand, an intu- itive geometrical Holographic model for entanglement entropy has been proposed in the context of gauge/gravity duality, and on the other, var- ious issues concerning entanglement have been explored, e.g. in quan- tum computation, quantum information theory, quantum field theories, string theory, supergravity and ... .The gravitational picture for EE has made it possible to investigate the crucial role of entanglement in causal evolutions of quantum mechanical systems, quantum phase transitions and ... in a wide range of models based on quantum mechanics.In addition, it seems that entanglement and its interpretation in both sides of the gauge/gravity duality is a good venue for a better under- standing of some fundamental issues such as the Holographic principle. Consequently, physicists in various branches are highly motivated to ad-dress the entanglement problem in their models which makes the subject an active research area.Our aim is to investigate the concept of entanglement in the context of auge/gravity duality, to find a deeper understanding of the subject, to simplify the former known results and also to explore some new aspects of EE and finally to predict the behavior of a strongly coupled quan- tum mechanical system, focusing on its entanglement pattern using the Holographic methods.Our computational tools are the usual methods in conformal field theo- ries and also the known methods inspired by the AdS/CFT duality. In this thesis, after a concise review of the basics of entanglement entropy in quantum mechanics, quantum field theory and also in Holography, we will report our recent findings in the field. Some of the achievements of this study are as follows: calculating the holographic EE for excited states, investigating certain properties of hy- persurfaces which maximize EE, explaining some disagreements in EE computed in field theory vs. gravity, calculating EE for field theories whose duals are gravitational theories with higher derivatives in curva- ture tensors such as the logarithmic conformal field theories (and also for conformal gravity) and finally investigating the role of EE as an order parameter in quantum quench.At the end, after a brief review of the results, we propose some new projects for future works
  9. Keywords:
  10. Quantum Entanglement ; Entanglement Entropy ; Entanglement ; Quantum Field Theory ; Strongly Coupled Quantum Fields Theory ; Gauge/Gravity Duality

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