Thesis Chapters by Alessio Miscioscia
The space of two dimensional quantum field theories: deformations of conformal models, 2022
In this thesis we study some deformations of conformal minimal models. In particular we study the... more In this thesis we study some deformations of conformal minimal models. In particular we study the imaginary magnetic deformation of the tricritical Ising model.
The results and methodologies of this thesis are to be considered linked to what was known and discovered by the authors at the time of writing the thesis. There are errors (in the last chapter), then corrected in the paper: 2211.01123
Meccanica quantistica supersimmetrica e teoria di Morse, 2020
Presentazione e discussione con esempio del toro bidimensionale della teoria di Morse-Witten.
Notes by Alessio Miscioscia
In these notes we explore the basic ideas of the Island proposal, its relation with AdS/CFT and i... more In these notes we explore the basic ideas of the Island proposal, its relation with AdS/CFT and information paradox. Notes prepared for the Desy theory Workshop (7.05.2024) and Desy theory workshop (14.05.2024).
In these notes we explore the basics of Hawking radiation in black holes’ physics. Notes prepared... more In these notes we explore the basics of Hawking radiation in black holes’ physics. Notes prepared for the Desy theory Workshop (13.06.2023).
In these notes we are going to discuss some basic results in conformal field theories; in particu... more In these notes we are going to discuss some basic results in conformal field theories; in particular we will see why the two dimensional case is a special case and we will discuss how to construct the Hilbert space, compute correlation functions and the Hamiltonian of the theory.
This are some notes of introduction on string theories. This notes include
-Classical Strings ... more This are some notes of introduction on string theories. This notes include
-Classical Strings ( Why string theory?, The point particle theory, The Nambu-Goto Action and the Polyakov action, Equations of motion, constrains and mode expansion)
-Quantization of strings( Covariant quantization, Lightcone quantization, Casimir energy, String Spectrum, Lorentz invariance, Comments on superstrings)
- Open strings and D − Branes (Open strings spectra, The Dirac action, Multiple branes: where are strings?)
-CFT (Stress energy tensor and Nöether charges, Operator product expansion, Virasoro Algebra, Example: The free scalar field, central charges, Something about CFTs with boundary)
-Path integral formulation of strings (The ghost CFT, An aside: Liouville quantum gravity, States and vertex operators, Examples: closed and open string in flat space).
-String interactions (closed string amplitude, open string amplitude, one loop amplitude, partition function: a node to string field theory).
-Effective action and low energy (Einstein equations, string effective action, solution of e.o.m., compactification and moduli)
-Sugra (from global to local Susy, the gravitino, Gravity as (a sort of) gauge theory, pure N=1 Sugra in D= 4, pure N=1 Sugra in D= 4 with Cosmological constant , matter couplings, physical feature of Sugra, Super-Higgs mechanism, Duality , extended SuGra, Black holes in N=2 Sugra)
Spin-Statistics theorem, 2021
In quantum mechanics the Pauli exclusion principle plays a crucial role in the description of nat... more In quantum mechanics the Pauli exclusion principle plays a crucial role in the description of nature (not least for the explaination of the Mendelejev's table of elements). This principle connects the symmetry or antisymmetry of the N −particle wave functions of identical particles with the spins, in particular with integer or half-integer spins, respectively. Our pourpose is to discuss the nature of this principle from a QFT point of view, in particular we will prove the Spin-statistics theorem, which is the rigorous statement of the Pauli principle, assuming the Wightman's axioms (to be honest the Wightman axioms for the Wightman's distributions). In order to do that, after a review of theWightaman's axioms, we will discuss first the free case, since this case is somehow special and we don't need many assumptions; then we will discuss the general case.
Naturalness problem in Standard model, 2021
Naturalness has been for many years a very hot topic in particle physics, but in particular after... more Naturalness has been for many years a very hot topic in particle physics, but in particular after the last run of LHC in 2016 it has become more and more important. Not finding evidence for new processes at the TeV energies made the community doubt of their understanding of modern physics. We want to discuss what is this problem and how does it present itself in the Standard Model. Then we continue with the calculation for the correction to the mass of the Higgs, which is the particle protagonist of this report; calculate its β function and in the end describe qualitatively some of the solutions proposed for the naturalness problem.
Effective field theory, 2021
This are some note on effective field theory. The content are
-Introduction
-Classification o... more This are some note on effective field theory. The content are
-Introduction
-Classification of operator
-Wilsonian action
-Fermi Theory
-Non relativistic QED
-S matrix equivalence theorem
-Loops and EFT
-Low energy QED
-Birifrangence of vacuum
-Positivity bound
-Loops, dimension and EFT
-Accidental symmetries
-EFT at the non-perturbative level
-Anomalies in QFT
-Chiral anomaly in QED and pion decay
-Exercies
Mathematical Physics, 2021
This are some notes on mathematical physics.
Contents:
- Introduction and basics in different... more This are some notes on mathematical physics.
Contents:
- Introduction and basics in differential geometry
-Symplectic geometry
-Symplectic vector space
-Symplectic mfd
-Symplectic structure of cotangent bundle
-Symplectomorphism and canonical transformation
-Darboux Theorem
-Newtonian Mechanics
-Poisson brackets
-Physical interpretation
-Integrability
-Co-adjoint orbits
-Poisson Manifold
-Poisson fields
-Poisson cohomology
-Classical R-matrix
-Lax Representation
-Deformation quantization (with Kontsevich's thm)
Representation Theory of Group, 2021
Representation theory of groups: the first part concern the representation theory of finite group... more Representation theory of groups: the first part concern the representation theory of finite groups (with also character theory) and the second part the discussion is focused on the Lie Groups/Algebras.
The topics are:
Introduction
Basic notions
One dimensional representations (abelian groups)
Character of a representation
Reduction and induction of representations
Non finite groups ( Algebraic sets , Lie algebra)
Solvability and (semi-)simplicity
Root systems and Dynkin diagrams
Universal enveloping Lie algebra
At the end many exercises are solved
Statistical mechanics, 2020
This are some notes on Statistical mechanics.
The topics are
-Recap of thermodynamics ... more This are some notes on Statistical mechanics.
The topics are
-Recap of thermodynamics
-Thermodynamic of phase transitions
-recap of theory of ensamble
-Statistical mechanics and phase transition
-Models (Ising in particular)
-Role of symmetry (symmetry breaking), dimension and range of interaction
-Mean field theory (and Vann der Walls)
-Landau Theory
-Ginzburg criterium
-Scaling theory (Windom)
-Renormalization group
-Symmetry breaking in other parts of physics (particles physics)
General Relativity, 2020
Notes on general relativity.
The topics that are covered
-Fast introduction and recap of sp... more Notes on general relativity.
The topics that are covered
-Fast introduction and recap of special relativity
-Gravity and metrics (Rindler spacetime)
-Basics in differential geometry
-Free Point particles dynamics
-Covariant derivatives
-Newtonian limit
-Curvature and Gravity: Eintein equation (+perfect fluid)
-Gravitational waves
-Vielbein formalism ( Schwarzschild)
-Symmetries and study of Schawazschild
-Cosmological space-time (De Sitter spacetime, Godesic and Perfect Fluid)
-BH Introduction (Approaching a horizon, Carter-Penrose diagram , hyperbolic spacetime, Surface gravity, charged BH, rotating BH, Intro to Thermodynamics)
-Exercises
II EDIZIONE:
Risposte alle domande di teoria del corso di fisica matematica (FISICA, UNIPD, II... more II EDIZIONE:
Risposte alle domande di teoria del corso di fisica matematica (FISICA, UNIPD, II ANNO)
Geometria differenziale, 2019
Note di geometria differenziale!
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Thesis Chapters by Alessio Miscioscia
The results and methodologies of this thesis are to be considered linked to what was known and discovered by the authors at the time of writing the thesis. There are errors (in the last chapter), then corrected in the paper: 2211.01123
Notes by Alessio Miscioscia
-Classical Strings ( Why string theory?, The point particle theory, The Nambu-Goto Action and the Polyakov action, Equations of motion, constrains and mode expansion)
-Quantization of strings( Covariant quantization, Lightcone quantization, Casimir energy, String Spectrum, Lorentz invariance, Comments on superstrings)
- Open strings and D − Branes (Open strings spectra, The Dirac action, Multiple branes: where are strings?)
-CFT (Stress energy tensor and Nöether charges, Operator product expansion, Virasoro Algebra, Example: The free scalar field, central charges, Something about CFTs with boundary)
-Path integral formulation of strings (The ghost CFT, An aside: Liouville quantum gravity, States and vertex operators, Examples: closed and open string in flat space).
-String interactions (closed string amplitude, open string amplitude, one loop amplitude, partition function: a node to string field theory).
-Effective action and low energy (Einstein equations, string effective action, solution of e.o.m., compactification and moduli)
-Sugra (from global to local Susy, the gravitino, Gravity as (a sort of) gauge theory, pure N=1 Sugra in D= 4, pure N=1 Sugra in D= 4 with Cosmological constant , matter couplings, physical feature of Sugra, Super-Higgs mechanism, Duality , extended SuGra, Black holes in N=2 Sugra)
-Introduction
-Classification of operator
-Wilsonian action
-Fermi Theory
-Non relativistic QED
-S matrix equivalence theorem
-Loops and EFT
-Low energy QED
-Birifrangence of vacuum
-Positivity bound
-Loops, dimension and EFT
-Accidental symmetries
-EFT at the non-perturbative level
-Anomalies in QFT
-Chiral anomaly in QED and pion decay
-Exercies
Contents:
- Introduction and basics in differential geometry
-Symplectic geometry
-Symplectic vector space
-Symplectic mfd
-Symplectic structure of cotangent bundle
-Symplectomorphism and canonical transformation
-Darboux Theorem
-Newtonian Mechanics
-Poisson brackets
-Physical interpretation
-Integrability
-Co-adjoint orbits
-Poisson Manifold
-Poisson fields
-Poisson cohomology
-Classical R-matrix
-Lax Representation
-Deformation quantization (with Kontsevich's thm)
The topics are:
Introduction
Basic notions
One dimensional representations (abelian groups)
Character of a representation
Reduction and induction of representations
Non finite groups ( Algebraic sets , Lie algebra)
Solvability and (semi-)simplicity
Root systems and Dynkin diagrams
Universal enveloping Lie algebra
At the end many exercises are solved
The topics are
-Recap of thermodynamics
-Thermodynamic of phase transitions
-recap of theory of ensamble
-Statistical mechanics and phase transition
-Models (Ising in particular)
-Role of symmetry (symmetry breaking), dimension and range of interaction
-Mean field theory (and Vann der Walls)
-Landau Theory
-Ginzburg criterium
-Scaling theory (Windom)
-Renormalization group
-Symmetry breaking in other parts of physics (particles physics)
The topics that are covered
-Fast introduction and recap of special relativity
-Gravity and metrics (Rindler spacetime)
-Basics in differential geometry
-Free Point particles dynamics
-Covariant derivatives
-Newtonian limit
-Curvature and Gravity: Eintein equation (+perfect fluid)
-Gravitational waves
-Vielbein formalism ( Schwarzschild)
-Symmetries and study of Schawazschild
-Cosmological space-time (De Sitter spacetime, Godesic and Perfect Fluid)
-BH Introduction (Approaching a horizon, Carter-Penrose diagram , hyperbolic spacetime, Surface gravity, charged BH, rotating BH, Intro to Thermodynamics)
-Exercises
Risposte alle domande di teoria del corso di fisica matematica (FISICA, UNIPD, II ANNO)
The results and methodologies of this thesis are to be considered linked to what was known and discovered by the authors at the time of writing the thesis. There are errors (in the last chapter), then corrected in the paper: 2211.01123
-Classical Strings ( Why string theory?, The point particle theory, The Nambu-Goto Action and the Polyakov action, Equations of motion, constrains and mode expansion)
-Quantization of strings( Covariant quantization, Lightcone quantization, Casimir energy, String Spectrum, Lorentz invariance, Comments on superstrings)
- Open strings and D − Branes (Open strings spectra, The Dirac action, Multiple branes: where are strings?)
-CFT (Stress energy tensor and Nöether charges, Operator product expansion, Virasoro Algebra, Example: The free scalar field, central charges, Something about CFTs with boundary)
-Path integral formulation of strings (The ghost CFT, An aside: Liouville quantum gravity, States and vertex operators, Examples: closed and open string in flat space).
-String interactions (closed string amplitude, open string amplitude, one loop amplitude, partition function: a node to string field theory).
-Effective action and low energy (Einstein equations, string effective action, solution of e.o.m., compactification and moduli)
-Sugra (from global to local Susy, the gravitino, Gravity as (a sort of) gauge theory, pure N=1 Sugra in D= 4, pure N=1 Sugra in D= 4 with Cosmological constant , matter couplings, physical feature of Sugra, Super-Higgs mechanism, Duality , extended SuGra, Black holes in N=2 Sugra)
-Introduction
-Classification of operator
-Wilsonian action
-Fermi Theory
-Non relativistic QED
-S matrix equivalence theorem
-Loops and EFT
-Low energy QED
-Birifrangence of vacuum
-Positivity bound
-Loops, dimension and EFT
-Accidental symmetries
-EFT at the non-perturbative level
-Anomalies in QFT
-Chiral anomaly in QED and pion decay
-Exercies
Contents:
- Introduction and basics in differential geometry
-Symplectic geometry
-Symplectic vector space
-Symplectic mfd
-Symplectic structure of cotangent bundle
-Symplectomorphism and canonical transformation
-Darboux Theorem
-Newtonian Mechanics
-Poisson brackets
-Physical interpretation
-Integrability
-Co-adjoint orbits
-Poisson Manifold
-Poisson fields
-Poisson cohomology
-Classical R-matrix
-Lax Representation
-Deformation quantization (with Kontsevich's thm)
The topics are:
Introduction
Basic notions
One dimensional representations (abelian groups)
Character of a representation
Reduction and induction of representations
Non finite groups ( Algebraic sets , Lie algebra)
Solvability and (semi-)simplicity
Root systems and Dynkin diagrams
Universal enveloping Lie algebra
At the end many exercises are solved
The topics are
-Recap of thermodynamics
-Thermodynamic of phase transitions
-recap of theory of ensamble
-Statistical mechanics and phase transition
-Models (Ising in particular)
-Role of symmetry (symmetry breaking), dimension and range of interaction
-Mean field theory (and Vann der Walls)
-Landau Theory
-Ginzburg criterium
-Scaling theory (Windom)
-Renormalization group
-Symmetry breaking in other parts of physics (particles physics)
The topics that are covered
-Fast introduction and recap of special relativity
-Gravity and metrics (Rindler spacetime)
-Basics in differential geometry
-Free Point particles dynamics
-Covariant derivatives
-Newtonian limit
-Curvature and Gravity: Eintein equation (+perfect fluid)
-Gravitational waves
-Vielbein formalism ( Schwarzschild)
-Symmetries and study of Schawazschild
-Cosmological space-time (De Sitter spacetime, Godesic and Perfect Fluid)
-BH Introduction (Approaching a horizon, Carter-Penrose diagram , hyperbolic spacetime, Surface gravity, charged BH, rotating BH, Intro to Thermodynamics)
-Exercises
Risposte alle domande di teoria del corso di fisica matematica (FISICA, UNIPD, II ANNO)