Antonio CAPOLUPO | QUANTUM FIELD THEORY IN CURVED SPACE TIME AND APPLICATIONS
Antonio CAPOLUPO QUANTUM FIELD THEORY IN CURVED SPACE TIME AND APPLICATIONS
cod. 8860200023
QUANTUM FIELD THEORY IN CURVED SPACE TIME AND APPLICATIONS
| 8860200023 | |
| DEPARTMENT OF PHYSICS "E. R. CAIANIELLO" | |
| Corso di Dottorato (D.M.226/2021) | |
| PHYSICS AND EMERGENT TECHNOLOGIES | |
| 2024/2025 |
| YEAR OF COURSE 1 | |
| YEAR OF DIDACTIC SYSTEM 2024 | |
| SPRING SEMESTER |
| SSD | CFU | HOURS | ACTIVITY | |
|---|---|---|---|---|
| FIS/02 | 2 | 10 | LESSONS |
| Objectives | |
|---|---|
| THE COURSE WANTS TO PROVIDE, IN A WAY COMPLETE AND SUITABLE FOR APPLICATIONS, THE KNOWLEDGE OF SOME ARGUMENTS OF PARTICULAR RELEVANCE IN ADVANCED THEORETICAL PHYSICS. EXPECTED LEARNING OUTCOMES: KNOWLEDGE AND ABILITY TO UNDERSTAND: THE PURPOSE OF THE COURSE IS TO INTRODUCE STUDENTS TO THE FOUNDATIONS OF QUANTUM FIELD THEORY IN CURVED SPACE TIME, PROVIDING AN ADVANCED KNOWLEDGE ABOUT ARGUMENTS OF THEORETICAL PHYSICS THAT ARE NOT STUDIED IN DEGREE COURSES, SUCH AS THE FIELD QUANTIZATION IN CURVED SPACES, THE QUANTUM VACUUM FLUCTUATIONS, THE UNRHU EFFECT, THE HAWKING RADIATION AND THE THERMODYNAMICS OF THE BLACK HOLES. PARTICULAR EMPHASIS IS PLACED ON THE APPLICATION OF SUCH PHENOMENA TO DIFFERENT BRANCHES OF MODERN PHYSICS, SUCH AS COSMOLOGY AND PARTICLE PHYSICS. CAPABILITY TO APPLY KNOWLEDGE AND UNDERSTANDING: THE PURPOSE IS TO PROVIDE THE ANALYTICAL INSTRUMENTS FOR THE STUDY OF QUANTUM FIELD THEORY IN CURVED SPACE TIME AND OF ITS APPLICATIONS, MAKING THE STUDENT ABLE TO CONTROL THE THEORETICAL NOTIONS PROVIDED IN THE COURSE. THE MULTIDISCIPLINARITY OF THE TOPICS COVERED WILL ALLOW THE STUDENT TO APPLY THE ACQUIRED KNOWLEDGE TO DIFFERENT PHYSICAL SYSTEMS. THESE SKILLS ARE USEFUL FOR THE INSERTION IN NATIONAL AND INTERNATIONAL RESEARCH INSTITUTIONS AND IN THE INDUSTRY. JUDGMENT AUTONOMY: TO BE ABLE TO DETERMINE THE APPROPRIATE METHODS TO ANALYZE THE ARGUMENTS OF ADVANCED THEORETICAL PHYSICS. COMMUNICATION SKILLS: TO BE ABLE TO DESCRIBE, CLEARLY AND EXHAUSTIVELY, THE STUDIED TOPICS. LEARNING ABILITY: TO BE ABLE TO APPLY THE ACQUIRED KNOWLEDGE TO CONTEXTS DIFFERENT FROM THE ONES PRESENTED IN THE COURSE, AND TO STUDY IN DEEP THE TREATED TOPICS BY USING BOOKS DIFFERENT WITH RESPECT TO THE ONES PROPOSED. |
| Prerequisites | |
|---|---|
| THE KNOWLEDGE OBTAINED THROUGH THE FIVE-YEAR DEGREE IN PHYSICS ARE REQUIRED, WITH PARTICULAR REFERENCE TO THE FUNDAMENTAL ARGUMENTS OF THEORETICAL PHYSICS; QUANTUM FIELD THEORY; COSMOLOGY; THEORY OF FUNDAMENTAL INTERACTIONS. |
| Contents | |
|---|---|
| - OVERVIEW. A TASTE OF QUANTUM FIELDS (FRONTAL LESSONS: 1 HOUR): THE HARMONIC OSCILLATOR AND ITS VACUUM STATE; FREE QUANTUM FIELDS AND VACUUM; THE ZERO-POINT ENERGY; QUANTUM FLUCTUATIONS IN THE VACUUM STATE; AMPLITUDE OF FLUCTUATIONS; OBSERVABLE EFFECTS OF VACUUM FLUCTUATIONS; PARTICLE INTERPRETATION OF QUANTUM FIELDS; QUANTUM FIELD THEORY IN CLASSICAL BACKGROUNDS; EXAMPLES OF PARTICLE CREATION; TIME-DEPENDENT OSCILLATOR; THE SCHWINGER EFFECT; PRODUCTION OF PARTICLES BY GRAVITY; THE UNRUH EFFECT. - QUANTIZING A DRIVEN HARMONIC OSCILLATOR (FRONTAL LESSONS: 1 HOUR): CLASSICAL OSCILLATOR UNDER FORCE; QUANTIZATION; THE “IN” AND “OUT” REGIONS; EXCITED STATES; RELATION BETWEEN “IN” AND “OUT” STATES; CALCULATIONS OF MATRIX ELEMENTS. - FROM HARMONIC OSCILLATORS TO FIELDS (FRONTAL LESSONS: 1 HOUR): QUANTIZATION OF FREE FIELDS; FROM OSCILLATORS TO FIELDS; QUANTIZING FIELDS IN FLAT SPACE-TIME; A FIRST LOOK AT MODE EXPANSIONS; ZERO-POINT ENERGY; THE SCHRÖDINGER EQUATION FOR A QUANTUM FIELD. - OVERVIEW OF CLASSICAL FIELD THEORY (FRONTAL LESSONS: 2 HOURS): THE ACTION FUNCTIONAL; EQUATIONS OF MOTION FOR FIELDS; REAL SCALAR FIELD; GAUGE SYMMETRY AND GAUGE FIELDS; THE U(1) GAUGE SYMMETRY; ACTION FOR GAUGE FIELDS; ENERGY-MOMENTUM TENSOR FOR FIELDS AND ITS CONSERVATION. - QUANTUM FIELDS IN EXPANDING UNIVERSE (FRONTAL LESSONS: 2 HOURS): SCALAR FIELD IN FRW UNIVERSE; MODE FUNCTIONS; MODE EXPANSIONS; QUANTIZATION OF SCALAR FIELD; THE VACUUM STATE AND PARTICLE STATES; BOGOLYUBOV TRANSFORMATIONS; MEAN PARTICLE NUMBER; CHOICE OF VACUUM; THE INSTANTANEOUS LOWEST-ENERGY STATE; THE MEANING OF VACUUM; VACUUM AT SHORT DISTANCES; ADIABATIC VACUUM; A QUANTUM-MECHANICAL ANALOGY. - QUANTUM FIELDS IN DE SITTER SPACETIME (FRONTAL LESSONS: 1 HOUR) : AMPLITUDE OF QUANTUM FLUCTUATIONS; CORRELATION FUNCTIONS; FLUCTUATIONS IN VACUUM AND NONVACUUM STATES; A WORKED-OUT EXAMPLE; FIELD QUANTIZATION IN DE SITTER SPACETIME; QUANTIZATION OF SCALAR FIELDS; MODE FUNCTIONS; CHOICE OF VACUUM; EVOLUTION OF FLUCTUATIONS. - THE UNRUH EFFECT (FRONTAL LESSONS: 1 HOUR): KINEMATICS OF UNIFORMLY ACCELERATED MOTION; COORDINATES IN THE PROPER FRAME; THE RINDLER SPACETIME; QUANTUM FIELDS IN THE RINDLER SPACETIME; QUANTIZATION; LIGHTCONE MODE EXPANSIONS; THE BOGOLYUBOV TRANSFORMATION; DENSITY OF PARTICLES; THE UNRUH TEMPERATURE. - THE HAWKING EFFECT. THERMODYNAMICS OF BLACK HOLES (FRONTAL LESSONS: 1 HOUR): THE HAWKING RADIATION; SCALAR FIELD IN A BLACK HOLE SPACETIME; THE KRUSKAL COORDINATES; FIELD QUANTIZATION; CHOICE OF VACUUM; THE HAWKING TEMPERATURE; THE HAWKING EFFECT IN 3+1 DIMENSIONS; REMARKS ON OTHER DERIVATIONS; THERMODYNAMICS OF BLACK HOLES; EVAPORATION OF BLACK HOLES; LAWS OF BLACK HOLE THERMODYNAMICS. |
| Teaching Methods | |
|---|---|
| THE COURSE IS CARRIED OUT IN FRONTAL LESSONS (10 HOURS), TAKING SPECIAL CARE OF METHODS, DEMONSTRATIONS AND APPLICATIONS. THE PURPOSE IS TO PROVIDE STUDENTS WITH SPECIFIC KNOWLEDGE SUITABLE TO FORMULATE MODELS FOR THE DESCRIPTION OF COSMOLOGICAL AND ASTROPARTICELLAR PHYSICAL PHENOMENA. THE COURSE IS ALSO FINALIZED TO PROVIDE SKILLS SUITABLE TO RESEARCH ACTIVITIES IN UNIVERSITIES AND INSTITUTIONS. THE PRESENCE OF STUDENTS IN THE COURSE IS NOT MANDATORY, BUT STRONGLY RECOMMENDED. |
| Verification of learning | |
|---|---|
| THE EXAM CONSISTS IN AN ORAL EXAMINATION ON THE TOPICS OF THE COURSE IN ORDER TO VERIFY THE UNDERSTANDING OF THE TOPICS STUDIED. IT IS ALSO REQUESTED THAT THE STUDENT EXPOSES IN EXHAUSTIVE WAY AND THAT HE SHOWS CRITICAL AND AUTONOMOUS JUDGMENT. THE DURATION OF THE EXAM IS ABOUT ONE HOUR, AND IT WILL BE TAKEN, AFTER THE END OF THE COURSE, IN THE EXAM SESSIONS. THE FINAL VOTE IS IN THIRTY. THE EXAM IS PASSED WHEN THE VOTE OF THE ORAL PRESENTATIONE IS AT LEAST 18/30. THE MINIMUM EVALUATION LEVEL (18) IS ASSIGNED WHEN THE STUDENT HAS A SUFFICIENT KNOWLEDGE OF THEORETICAL CONTENTS AND HE SHOWS A SUFFICIENT CAPACITY TO CONNECT THE FOLLOWING TOPICS: QUANTUM AND CLASSICAL FIELD THEORY; QUANTUM FIELD IN EXPANDING UNIVERSE; UNRUH EFFECT; HAWKING RADIATION AND BLACK HOLE THERMODYNAMICS. THE MAXIMUM LEVEL (30) IS ATTRIBUTED WHEN THE STUDENT SHOWS A COMPLETE AND DEPTH KNOWLEDGE OF THE THEORETICAL CONTENTS AND HE SHOWS A NOTABLE CAPACITY TO CONNECT THE ANALYZED TOPICS. 30 WITH LAUD IS ATTRIBUTED WHEN THE CANDIDATE PROVIDES A SIGNIFICANT MASTERY OF THE CONTENT OF THE PROGRAM AND HE EXHIBITS TO KNOW THE ARGUMENTS WITH REMARKABLE VOCABULARY AND ABILITY OF AUTONOMOUS PROCESSING. |
| Texts | |
|---|---|
| - V.F MUKANOV, S. WINITZKI "INTRODUCTION TO QUANTUM EFFECTS IN GRAVITY" (CAMBRIDGE UNIVERSITY PRESS) - N.D. BIRRELL, P.C. DAVIS, "QUANTUM FIELDS IN CURVED SPACE", (CAMBRIDGE UNIVERSITY PRESS) THE DIDACTIC MATERIAL, ALTHOUGH PRESENT IN THE RECOMMENDED TEXTS, WILL BE INTEGRATED DURING THE COURSE BY THE TEACHER. |
| More Information | |
|---|---|
| THE STUDENTS ARE INVITED TO CONTACT THE TEACHER FOR MEETINGS (ALSO OUTSIDE THE RECEPTION TIMES) FOR FURTHER CLARIFICATION OF THE COURSE TOPICS. |
BETA VERSION Data source ESSE3 [Ultima Sincronizzazione: 2025-07-16]
