{"title":"BACK MATTER","authors":"M. Asorey, E. Ercolessi, Valter Moretti","doi":"10.1142/9789811210495_bmatter","DOIUrl":"https://doi.org/10.1142/9789811210495_bmatter","url":null,"abstract":"","PeriodicalId":173240,"journal":{"name":"From Classical Mechanics to Quantum Field Theory, A Tutorial","volume":"18 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121537188","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"FRONT MATTER","authors":"M. Asorey, E. Ercolessi, Valter Moretti","doi":"10.1142/9789811210495_fmatter","DOIUrl":"https://doi.org/10.1142/9789811210495_fmatter","url":null,"abstract":"","PeriodicalId":173240,"journal":{"name":"From Classical Mechanics to Quantum Field Theory, A Tutorial","volume":"97 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131771101","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"A Concise Introduction to Quantum Field Theory","authors":"M. Asorey","doi":"10.1142/S021988781940005X","DOIUrl":"https://doi.org/10.1142/S021988781940005X","url":null,"abstract":"We review the basic principles of Quantum Field Theory (QFT) in a brief but comprehensive introduction to the foundations of QFT. The principles of QFT are introduced in canonical and covariant formalisms. The problem of ultraviolet (UV) divergences and its renormalization is analyzed in the canonical formalism. As an application, we review the roots of Casimir effect. For simplicity, we focus on the scalar field theory but the generalization for fermion fields is straightforward. However, the quantization of gauge fields require extra techniques which are beyond the scope of this paper. The special cases of free field theories and conformal invariant theories in lower space-time dimensions illustrate the relevance of the foundations of the theory. Finally, a short introduction to functional integrals and perturbation theory in the Euclidean formalism is included in the last section.","PeriodicalId":173240,"journal":{"name":"From Classical Mechanics to Quantum Field Theory, A Tutorial","volume":"44 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-01-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116977166","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"A Short Course on Quantum Mechanics and Methods of Quantization","authors":"E. Ercolessi","doi":"10.1142/S0219887815600087","DOIUrl":"https://doi.org/10.1142/S0219887815600087","url":null,"abstract":"These notes collect the lectures given by the author to the \"XXIII International Workshop on Geometry and Physics\" held in Granada (Spain) in September 2014. The first part of this paper aims at introducing a mathematical oriented reader to the realm of Quantum Mechanics (QM) and then to present the geometric structures that underline the mathematical formalism of QM which, contrary to what is usually done in Classical Mechanics (CM), are usually not taught in introductory courses. The mathematics related to Hilbert spaces and Differential Geometry are assumed to be known by the reader. In the second part, we concentrate on some quantization procedures, that are founded on the geometric structures of QM — as we have described them in the first part — and represent the ones that are more operatively used in modern theoretical physics. We will discuss first the so-called Coherent State Approach which, mainly complemented by \"Feynman Path Integral Technique\", is the method which is most widely used in quantum field theory. Finally, we will describe the \"Weyl Quantization Approach\" which is at the origin of modern tomographic techniques, originally used in optics and now in quantum information theory.","PeriodicalId":173240,"journal":{"name":"From Classical Mechanics to Quantum Field Theory, A Tutorial","volume":"166 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-09-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133805524","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Mathematical Foundations of Quantum Mechanics: An Advanced Short Course","authors":"Valter Moretti","doi":"10.1142/S0219887816300117","DOIUrl":"https://doi.org/10.1142/S0219887816300117","url":null,"abstract":"This paper collects and extends the lectures I gave at the \"XXIV International Fall Workshop on Geometry and Physics\" held in Zaragoza (Spain) August 31 - September 4, 2015. Within these lectures I review the formulation of Quantum Mechanics, and quantum theories in general, from a mathematically advanced viewpoint, essentially based on the orthomodular lattice of elementary propositions, discussing some fundamental ideas, mathematical tools and theorems also related to the representation of physical symmetries. The final step consists of an elementary introduction the so-called (C*-) algebraic formulation of quantum theories.","PeriodicalId":173240,"journal":{"name":"From Classical Mechanics to Quantum Field Theory, A Tutorial","volume":"131 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-08-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133829880","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}