日本語
College of Science and Engineering
/
Department of Robotics
(Male)
Kentaro
HAMACHI
Lecturer
■Graduate school/University/other
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03/1996 Kyoto University Graduate School, Division of Natural Science mathematics, mathematical science course Doctoral course first term (Master's) Completed
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05/2000 Kyoto University Graduate School, Division of Natural Science mathematics, mathematical science course Doctoral course second term (Doctoral) Completed
■Academic degrees
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Master's degree (science) (03/1996 Kyoto University)
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Doctoral degree (science) (05/2000 Kyoto University)
■Career history
04/1998-03/2000 日本学術振興会特別研究員（DC2）
10/2001-11/2002 フランス政府ポストドクター 給費奨学研究生
11/2002-12/2002 ブルゴーニュ大学ジュブレ数理物理学研究所 招聘研究員
04/2003-03/2004 立命館大学理工学部 非常勤講師
04/2004-03/2007 京都産業大学特約講師
04/2007-03/2012 立命館大学理工学部 非常勤講師
04/01/2012- 立命館大学理工学部 講師
■Subject of research
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The theory of deformation quantization, that is a non-commutative associative algebra defined on Poisson anifolds has studied. Especially, I study an algebraic invariants of deformation quantization which has a group action and a construction of representation theory of this algebra by using
■Research summary
Formulation of Quantum Dynamics Using Differential Geometrical Techniques, and Study of Non-commutative Geometry
Quantum dynamics' mathematically describes 'micro world' that 'classical dynamics' cannot account for, and it is considered that mathematical structure (CCR/CAR) and interpretation of currently standard quantum dynamics have succeeded so far without any large collapse. In recent years, however, more detailed and complicated experiments have been carried out even in micro scale. As a result, it seems gradually clear that 'the world where boundary between micro and macro is ambiguous' exists. This may rise doubt or limit about discussion using a quite mathematically different technique - operator on Hilbert space - assuming that 'quantum dynamics is different from classical dynamics.' Under these motives, my rough goal is to: study how to mathematically describe quantum dynamics with higher affinity with classical dynamics; and reveal the structure of the world where quantum and classical dynamics are ambiguous.
While such studies of 'correspondence between classical and quantum' have been conducted mainly in a way of exploring a technique to quantize classical system, it eventually seems to me that most of the studies have only reached a methodology to acquire algebraic system of quantum dynamics without contradiction by using operator on Hilbert space. So let's shift the paradigm. I will adopt a strategy of describing quantum system in classical system and then seeing how the classical system can be interpreted from the perspective of quantum system.
What I mainly use is deformation quantization of classical Hamilton system, developed from the middle of the 1970s, and this theory enables canonical quantization (configuration of corresponding algebraic) on any symplectic manifold. This theory, however is not yet completed in a way of 'description of quantum dynamics.' A critical problem, in particular, shows that state (quantum state) cannot be described. (In standard quantum dynamics, no one knows when the state was introduced as a vector of Hilbert space, and it has been used without making it certain what it corresponds to in terms of classical theory. Although Schrödinger and Bohm, among others, addressed this issue, it did not seem successful.)
Because non-commutative ring given by deformation quantization uses commutative function ring on manifold as indication of each element, the ring is generally an indefinite dimension that is not definitely generated, and cannot be a phase ring. This is a big obstacle against state definition. Despite this is an indefinite dimension, it significantly differs from a phase ring, such as C*ring or von Neuman ring, that can easily define the meaningful state using the techniques of function analysis. Deformation quantization has made it clear that it is generally difficult to appropriately define a state only from a algebraic structure. I, therefore, set up my subject of research as appropriate formulation of state in describing mathematical structure of quantum system.
■Research keywords
Symplectic geometry, Poisson geometry, deformation quantization, differential geometry, C*-algebra, von Neumann algebra, differential dynamics, singular Lagrange systems
■Research activities (Even top three results are displayed. In View details, all results for public presentation are displayed.)
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Grants-in-Aid for Scientific Research (KAKENHI)
Link to Grants-in-Aid for Scientific Research -KAKENHI-
■Teaching experience (Even top three results are displayed. In View details, all results for public presentation are displayed.)
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Courses taught
2017 Professional Lectures ２ Seminar
2017 Exercises in PhysicsⅠ Seminar
2017 Physical Science １ Lecture
View details...
■Tel
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077-561-4884
■E-mail
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■Research keywords(on a multiple-choice system)
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Geometry
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Particle/Nuclear/Cosmic ray/Astro physics
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Mathematical physics/ Fundamental condensed matter physics