A 100% online Professional master’s degree, with a syllabus available 24 hours a day, so that you can advance whenever you wish in the key concepts of Quantum Physics"

The research field of Quantum Physics offers a wide range of lines of development with great potential for engineering professionals who decide to delve into this field of exploration and discovery in energy production, ultracold atoms, trapped ions or photonics.

Recent advances in this field have opened multiple lines of study and actions in other disciplines such as astrophysics, cosmology, chemistry, biology, medicine or artificial intelligence: possibilities as vast as the universe. That is why TECH has designed this Professional master’s degree in Quantum Physics, which will allow graduates to achieve, in only 12 months, the most advanced knowledge about the most common physical processes in planetary and solar physics, the studies of Paul Dirac or Richard Feynman and quantum field theory.

All this, through a program taught exclusively online, which will allow them to delve, whenever they wish, into Einstein's equations, Schwarzschild's solution, dark matter and energies or the thermodynamics of the early universe. The case studies will also help them to integrate the practice into their daily professional work.

This academic institution thus offers an excellent opportunity for engineering specialists who wish to progress in their professional career through a quality university education that is compatible with their work and/or personal responsibilities. They only need an electronic device with an Internet connection to view the content hosted on the virtual platform. With no classroom attendance or fixed class schedules, students have the freedom to distribute the course load according to their needs.

Thanks to the knowledge acquired in this Professional master’s degree you will be able to contribute to solve the problems of dark matter" 

This Professional master’s degree in Quantum Physics contains the most complete and up-to-date program on the market. The most important features include:

• Practical case studies are presented by experts in Physics
• The graphic, schematic, and practical contents with which they are created, provide scientific and practical information on the disciplines that are essential for professional practice
• Practical exercises where the self-assessment process can be carried out to improve learning
• Its special emphasis on innovative methodologies 
• Theoretical lessons, questions to the expert, debate forums on controversial topics, and individual reflection assignments
• Content that is accessible from any fixed or portable device with an Internet connection

The library of multimedia resources of this course will allow you to learn the main contributions to Quantum Physics from Richard Feynman, Paul Dirac, Peter Higgs or Schrödinger”

The program includes, in its teaching staff, professionals from the sector who bring to this program the experience of their work, in addition to recognized specialists from prestigious reference societies and universities. 

Its multimedia content, developed with the latest educational technology, will allow professionals to learn in a contextual and situated learning environment, i.e., a simulated environment that will provide them with immersive education programmed to learn them in real situations. 

The design of this program focuses on Problem-Based Learning, by means of which professionals must try to solve the different professional practice situations that arise during the academic course. For this purpose, students will be assisted by an innovative interactive video system developed by renowned experts. 

Click now and obtain a diploma that will allow you to progress in your Engineer professional career in Quantum Physics"

Enroll in a Professional master’s degree that will lead you to be able to solve the main existing problems in quantum mechanics"

TECH has prepared a Professional master’s degree in Quantum Physics based on the most current and advanced knowledge in this field. Thus, throughout the 10 modules that make up the syllabus, engineering professionals will be able to delve into astrophysics, the dynamics of quantum mechanics, the problems of dark matter or the latest advances in cosmology. In addition, thanks to the Relearning system, the graduates will be able to progress through the content in a more natural way, reducing the long hours of study that are so common in other methodologies.

Thanks to the practical case studies you will easily delve into Feynman's rules"

Module 1. Introduction to Modern Physics

1.1. Introduction to Medical Physics

1.1.1. How to Apply Physics to Medicine
1.1.2. Energy of Charged Particles in Tissues
1.1.3. Photons through Tissues 
1.1.4. Applications

1.2. Introduction to Particle Physics

1.2.1. Introduction and Objectives
1.2.2. Quantified Particles
1.2.3. Fundamental Forces and Charges
1.2.4. Particle Detection
1.2.5. Classification of Fundamental Particles and Standard Model
1.2.6. Beyond the Standard Model
1.2.7. Current Generalization Theories
1.2.8. High Energy Experiments

1.3. Particle Accelerators

1.3.1. Particle Acceleration Processes
1.3.2. Linear Accelerators
1.3.3. Cyclotrons
1.3.4. Synchrotrons

1.4. Introduction to Nuclear Physics

1.4.1. Nuclear Stability
1.4.2. New Methods in Nuclear Fission
1.4.3. Nuclear Fusion
1.4.4. Synthesis of Superheavy Elements

1.5. Introduction to Astrophysics

1.5.1. The Solar System
1.5.2. Birth and Death of a Star
1.5.3. Space Exploration
1.5.4. Exoplanets

1.6. Introduction to Cosmology

1.6.1. Distance Calculation in Astronomy
1.6.2. Velocity Calculations in Astronomy
1.6.3. Dark Matter and Energy
1.6.4. The Expansion of the Universe
1.6.5. Gravitational Waves

1.7. Geophysics and Atmospheric Physics

1.7.1. Geophysics
1.7.2. Atmospheric Physics
1.7.3. Meteorology
1.7.4. Climate Change

1.8. Introduction to Condensed Matter Physics

1.8.1. Aggregate States of Matter
1.8.2. Matter Allotropes
1.8.3. Crystalline Solids
1.8.4. Soft Matter

1.9. Introduction to Quantum Computing

1.9.1. Introduction to the Quantum World
1.9.2. Qubits
1.9.3. Multiple Qubits
1.9.4. Logic Gates
1.9.5. Quantum Programs
1.9.6. Quantum Computers

1.10. Introduction to Quantum Cryptography

1.10.1. Classic Information
1.10.2. Quantum Information
1.10.3. Quantum Encryption
1.10.4. Protocols in Quantum Cryptography

Module 2. Mathematical methods

2.1. Pre-Hibertian Spaces

2.1.1. Vector Spaces
2.1.2. Positive Hermitian Scalar Product
2.1.3. Single Vector Module
2.1.4. Schwartz Inequality
2.1.5. Minkowsky Inequality
2.1.6. Orthogonality
2.1.7. Dirac Notation

2.2. Topology of Metric Spaces

2.2.1. Definition of Distance
2.2.2. Definition of Metric Space
2.2.3. Elements of Topology of Metric Spaces
2.2.4. Convergent Successions
2.2.5. Cauchy Successions
2.2.6. Complete Metric Space

2.3. Hilbert Spaces

2.3.1. Hilbert Spaces: Definition
2.3.2. Herbatian Base
2.3.3. Schrödinger vs. Heisenberg. Lebesgue Integral
2.3.4. Continuous Frames of a Hilbert Space
2.3.5. Change of Basis Matrix

2.4. Linear Operations

2.4.1. Linear Operators: Basic Concepts
2.4.2. Inverse Operator
2.4.3. Adjoint Operator
2.4.4. Self-Adjoint Operator
2.4.5. Positive Definite Operator
2.4.6. Unitary Operator I: Change of Basis
2.4.6. Antiunitary Operator
2.4.7. Projector

2.5. Stumr-Liouville Theory

2.5.1. Eigenvalue Theorem
2.5.2. Eigenvector Theorem
2.5.3. Sturm-Liouville Problem
2.5.4. Important Theorems for Sturm-Liouville Theory

2.6. Introduction to Group Theory

2.6.1. Definition of Group and Characteristics
2.6.2. Symmetries
2.6.3. Study of SO (3), SU(2) and SU(N) Groups
2.6.4. Lie Algebra
2.6.5. Groups of Quantum Physics

2.7. Introduction to Representations

2.7.1. Definitions
2.7.2. Fundamental Representation
2.7.3. Adjoint Representation
2.7.4. Unitary Representation
2.7.5. Product of Representation
2.7.6. Young Tables
2.7.7. Okubo Theorems
2.7.8. Applications to Particle Physics

2.8.  Introduction to Tensors

2.8.1. Definition of Covariant and Contravariant Tensors
2.8.2. Kronecker Delta 
2.8.3. Levi-Civita Tensor
2.8.4. Study of SO(N) i SO (3)
2.8.5. Study of SO(N)
2.8.6. Relation between tensors and representations

2.9. Group Theory Applied to Physics 

2.9.1. Translation Group
2.9.2. Lorentz Group
2.9.3. Discrete Groups
2.9.4. Continuous Groups

2.10. Representations and Particle Physics

2.10.1. Representations of SU(N) Groups
2.10.2. Fundamental Representations
2.10.3. Multiplication of Representations
2.10.4. Okubo Theorem and Eightfold Ways

Module 3. Quantum Physics

3.1. Origins of Quantum Physics

3.1.1. Blackbody Radiation
3.1.2. Photoelectric Effect
3.1.3. Compton Effect
3.1.4. Atomic Spectra and Models
3.1.5. Pauli Exclusion Principle

3.1.5.1. Zeeman Effect
3.1.5.2. Stern-Gerlach Experiment

3.1.6. Broglie Wavelength and the Double Slit Experiment

3.2. Mathematical Formulation

3.2.1. Hilbert Spaces
3.2.2. Dirac Nomenclature Bra - ket
3.2.3. Internal and External Product
3.2.4. Linear Operators
3.2.5. Hermetic Operators and Diagonalization
3.2.6. Sum and Tensor Product
3.2.7. Density Matrix

3.3. Quantum Mechanics Postulates

3.3.1. Postulate 1º: Definition of Status
3.3.2. Postulate 2º: Definition of Observables
3.3.3. Postulate 3º: Definition of Measurement
3.3.4. Postulate 4º: Probability of Measurement
3.3.5. Postulate 5º: Dynamics

3.4. Apply the postulates of quantum mechanics

3.4.1. Probability of Results Statistics
3.4.2. Indeterminism
3.4.3. Temporary Evolution of the Expected Values
3.4.4. Compatibility and Commuting of Observables
3.4.5. Pauli Matrices

3.5. Quantum Mechanics Dynamics 

3.5.1. Representation of Positions
3.5.2. Momentum Representation
3.5.3. Schrödinger Equation
3.5.4. Ehrenfest Theorem
3.5.5. Virial Theorem

3.6. Potential Barriers

3.6.1. Infinite Square Well 
3.6.2. Finite Square Well
3.6.3. Potential Step
3.6.4. Delta Potential
3.6.5. Tunnel Effect
3.6.6. Free Particle

3.7. Simple Harmonic Oscillator

3.7.1. Analogy with Classical Mechanics
3.7.2. Hamiltonian and eigenvalues of energy
3.7.3. Analytical Method
3.7.4. Blurred Quantum
3.7.5. Coherent States

3.8. 3D Operators and Observables

3.8.1. Review of Calculus Notions with Several Values
3.8.2. Position Operator
3.8.3. Linear Momentum Operator
3.8.4. Orbital Angular Momentum
3.8.5. Ladder Operators
3.8.6. Hamiltonian

3.9. Three-Dimensional Eigenvalues and Eigenfunctions

3.9.1. Position Operator
3.9.2. Linear Momentum Operator
3.9.3. Orbital Angular Momentum and Spherical Harmonics Operator
3.9.4. Angular Equation

3.10. Three-Dimensional Potential Barriers

3.10.1. Free Particle
3.10.2. Particle in a Box
3.10.3. Central Potentials and Radial Equations
3.10.4. Infinite Spheric Well
3.10.5. Hydrogen Atom
3.10.6. 3D Harmonic Oscillator

Module 4. Astrophysics

4.1. Introduction

4.1.1. Brief History of Astrophysics
4.1.2. Instruments
4.1.3. Observational Magnitude Scale
4.1.4. Calculation of Astronomical Distances
4.1.5. Color Index

4.2. Spectral Lines 

4.2.1. Historical Introduction
4.2.2. Kirchoff's Laws
4.2.3. Relationship between Spectrum and Temperature
4.2.4. Doppler Effect
4.2.5. Spectrograph

4.3. Radiation Field Study 

4.3.1. Prior Definitions
4.3.2. Lens opacity
4.3.3. Optical Depth
4.3.4. Microscopic Opacity Sources
4.3.5. Total Opacity
4.3.6. Extinction 
4.3.7. Structure of Spectral Lines

4.4. Stars

4.4.1. Classification of Stars
4.4.2. Methods for Determining the Mass of a Star
4.4.3. Binary Stars
4.4.4. Classification of Binary Stars
4.4.5. Determining the Masses of a Binary System

4.5. Life of Stars

4.5.1. Characteristics of a Star
4.5.2. Birth of a Star
4.5.3. Life of a Star. Hertzprung-Russell Diagrams
4.5.4. Death of a Star

4.6. Death of Stars 

4.6.1. White Dwarf
4.6.2. Supernovas
4.6.3. Neutron Stars
4.6.4. Black Holes

4.7. Study of the Milky Way

4.7.1. Shape and Dimensions of the Milky Way
4.7.2. Dark Matter
4.7.3. Phenomenon of Gravitational Lensing
4.7.4. Massive Particles of Weak Interaction
4.7.5. Shape and Halo of the Milky Way
4.7.6. Spiral Structure of the Milky Way

4.8. Galaxy Clusters

4.8.1. Introduction
4.8.2. Classification of Galaxies
4.8.3. Photometry of Galaxies
4.8.4. Local Group: Introduction

4.9. Distribution of Large-Scale Galaxies

4.9.1. Shape and Age of the Universe
4.9.2. Standard Cosmological Model 
4.9.3. Formation of Cosmological Structures
4.9.4. Observational Methods in Cosmology

4.10. Dark Matter and Energies

4.10.1. Discovery and Characteristics
4.10.2. Consequences on the Distribution of Ordinary Matter
4.10.3. Dark Matter Problems
4.10.4. Candidate Particles for Dark Matter
4.10.5. Dark Energy and its Consequences

Module 5. Quantum Physics II

5.1. Descriptions of Quantum Mechanics: Images or Representations

5.1.1. Schrödinger Picture
5.1.2. Heisenberg Picture
5.1.3. Dirac Picture or Interaction Picture
5.1.4. Change of Pictures

5.2. 3D Harmonic Oscillator

5.2.1. Creation and annihilation operators
5.2.2. Wave Functions of Fock States
5.2.3. Coherent States
5.2.4. States of Minimum Indeterminacy
5.2.5. Squeezed States

5.3. Angular Momentum

5.3.1. Rotations
5.3.2. Switches of Angular Momentum
5.3.3. Angular Momentum Basis
5.3.4. Scale Operators
5.3.5. Matrix Representation
5.3.6. Intrinsic Angular Momentum: The Spin
5.3.7. Spin Cases 1/ 2, 1, 3/ 2

5.4. Multi-Component Wave Functions: Spinorials

5.4.1. Single-Component Wave Functions: Spin 0
5.4.2. Double-Component Wave Functions: Spin 1/2
5.4.3. Expected Value of Spin Observable
5.4.4. Atomic States
5.4.5. Addition of Angular Momentum
5.4.6. Clebsch-Gordan Coefficient

5.5. State of the Compound Systems

5.5.1. Distinguishable Particles
5.5.2. Indistinguishable Particles
5.5.3. Photon Case: Semitransparent Mirror Experiment
5.5.4. Quantum Bonding
5.5.5. Bell Inequalities
5.5.6. EPR Paradox
5.5.7. Bell Theorem

5.6. Introduction to Approximate Methods: Variational Method

5.6.1. Introduction to the Variational Method
5.6.2. Linear Variations
5.6.3. Rayleigh-Ritz Variational Method
5.6.4. Harmonic Oscillator: A Study by Variational Methods

5.7. Study of Atomic Models with the Variational Method

5.7.1. Hydrogen Atom
5.7.2. Helium Atom
5.7.3. Ionized Hydrogen Molecule
5.7.4. Discrete Symmetries
5.7.4.1. Parity
5.7.4.2. Temporary Inversion

5.8. Introduction to Disturbance Theory

5.8.1. Time-Independent Perturbations
5.8.2. Non-Degenerate Case
5.8.3. Degenerate Case
5.8.4. Fine Structure of Hydrogen Atom
5.8.5. Zeeman Effect
5.8.6. Coupling Constant between Spins. Hyperfine Structure
5.8.7. Time-Dependent Perturbation Theory

5.8.7.1. Two-Level Atom
5.8.7.2. Sinusoidal Perturbation

5.9. Adiabatic Approximation

5.9.1. Introduction to Adiabatic Approximation
5.9.2. The Adiabatic Theorem
5.9.3. Berry Phase
5.9.4. Aharonov-Bohm Effect

5.10. Wentzel-Kramers-Brillouin (WKB) Approximation

5.10.1. Introduction to the WKB Method
5.10.2. Classical Region
5.10.3. Tunnel Effect
5.10.4. Connection Formulas

Module 6. Nuclear and Particle Physics

6.1. Introduction to Nuclear Physics

6.1.1. Periodic Table of the Elements
6.1.2. Important Discoveries
6.1.3. Atomic Models
6.1.4. Important Definitions Scales and Units in Nuclear Physics
6.1.5. Segré's Diagram

6.2. Nuclear Properties

6.2.1. Binding Energy
6.2.2. Semiempirical Mass Formula
6.2.3. Fermi Gas Model
6.2.4. Nuclear Stability

6.2.4.1. Alpha Decay
6.2.4.2. Beta Decay
6.2.4.3. Nuclear Fusion

6.2.5. Nuclear Deexcitation
6.2.6. Double Beta Decay

6.3. Nuclear Scattering

6.3.1. Internal Structure: Dispersion Study
6.3.2. Effective Section
6.3.3. Rutherford's Experiment: Rutherford's Effective Section
6.3.4. Mott's Effective Section
6.3.5. Momentum Transfer and Shape Factors
6.3.6. Nuclear Charge Distribution
6.3.7. Neutron Scattering

6.4. Nuclear Structure and Strong Interaction

6.4.1. Nucleon Scattering
6.4.2. Bound States Deuterium
6.4.3. Strong Nuclear Interaction
6.4.4. Magic Numbers
6.4.5. The Layered Model of the Nucleus
6.4.6. Nuclear Spin and Parity
6.4.7. Electromagnetic Moments of the Nucleus
6.4.8. Collective Nuclear Excitations: Dipole Oscillations, Vibrational States and Rotational States

6.5. Nuclear Structure and Strong Interaction II

6.5.1. Classification of Nuclear Reactions
6.5.2. Reaction Kinematics
6.5.3. Conservation Laws
6.5.4. Nuclear Spectroscopy
6.5.5. The Compound Nucleus Model
6.5.6. Direct Reactions
6.5.7. Elastic Dispersion

6.6. Introduction to Particle Physics

6.6.1. Particles and Antiparticles
6.6.2. Fermions and Baryons
6.6.3. The Standard Model of Elementary Particles: Leptons and Quarks
6.6.4. The Quark Model
6.6.5. Intermediate Vector Bosons

6.7. Dynamics of Elementary Particles

6.7.1. The Four Fundamental Interactions
6.7.2. Quantum Electrodynamics
6.7.3. Quantum Chromodynamics
6.7.4. Weak Interaction
6.7.5. Disintegrations and Conservation Laws

6.8. Relativistic Kinematics

6.8.1. Lorentz Transformations
6.8.2. Quatrivectors
6.8.3. Energy and Linear Momentum
6.8.4. Collisions
6.8.5. Introduction to Feynman Diagrams

6.9. Symmetries

6.9.1. Groups, Symmetries and Conservation Laws
6.9.2. Spin and Angular Momentum
6.9.3. Addition of Angular Momentum
6.9.4. Flavor Symmetries 
6.9.5. Parity
6.9.6. Load Conjugation
6.9.7. CP Violation
6.9.8. Time Reversal
6.9.9. CPT Conservation

6.10. Bound States

6.10.1. Schrödinger's Equation for Central Potentials
6.10.2. Hydrogen Atom
6.10.3. Fine Structure
6.10.4. Hyperfine Structure
6.10.5. Positronium
6.10.6. Quarkonium
6.10.7. Lightweight Mesons
6.10.8. Baryons

Module 7. Quantum field theory

7.1. Classical Field Theory

7.1.1. Notation and Conventions
7.1.2. Lagrangian Formulation
7.1.3. Euler Lagrange Equations 
7.1.4. Symmetries and Conservation Laws

7.2. Klein-Gordon Field

7.2.1. Klein-Gordon Equations
7.2.2. Klein-Gordon Field Quantization
7.2.3. Lorentz Invariance of the Klein-Gordon Field
7.2.4. Vacuum Vacuum and Fock States
7.2.5. Vacuum Energy 
7.2.6. Normal Arrangement: Agreement
7.2.7. Energy and Momentum of States
7.2.8. Study of Causality 
7.2.9. Klein-Gordon propagator

7.3. Dirac Field

7.3.1. Dirac Equation
7.3.2. Dirac Matrices and their Properties
7.3.3. Representation of Dirac Matrices
7.3.4. Dirac Lagrangian
7.3.5. Solution to Dirac Equation: Plane Waves
7.3.6. Commuting and Anticommuting
7.3.7. Quantification of Dirac Field
7.3.8. Fock Space
7.3.9. Dirac Propagator

7.4. Electromagnetic Field

7.4.1. Classical Field of Electromagnetic Theory
7.4.2. Quantization of the Electromagnetic Field and its Problems
7.4.3. Fock Space
7.4.4. Gupta-Bleuler Formalism
7.4.5. Photon Propagator

7.5. S-Matrix Formalism

7.5.1. Lagrangian and Hamitonian of Interaction
7.5.2. S Matrix: Definition and Properties
7.5.3. Dyson Expansion
7.5.4. Wick Theorem
7.5.5. Dirac Picture

7.6. Feinman Diagrams in the Position Space 

7.6.1. How to Draw Feynman Diagrams? Rules Utilities
7.6.2. First Order
7.6.3. Second Order
7.6.4. Dispersion Processes with Two Particles

7.7. Feynman Rules

7.7.1. Normalization of States in Fock Space
7.7.2. Feynman Amplitude
7.7.3. Feynman Rules for QED
7.7.4. Gauge Invariance in the Amplitudes
7.7.5. Examples:

7.8. Cross Section and Decay Rates

7.8.1. Definition of Cross Sections
7.8.2. Definition of Decay Rate
7.8.3. Example with Two Bodies in Final State
7.8.4. Unpolarized Cross Section
7.8.5. Summation on Fermion Polarization 
7.8.6. Summation on Photon Polarization
7.8.7. Examples:

7.9. Study of Muons and Other Charged Particles 

7.9.1. Muons
7.9.2. Charged Particles 
7.9.3. Scalar Charged Particles
7.9.4. Feynman Rules for Scalar Quantum Electrodynamics Theory

7.10. Symmetries

7.10.1. Parity
7.10.2. Load Conjugation
7.10.3. Time Reversal 
7.10.4. Violation of Some Symmetries
7.10.5. CPT Symmetry

Module 8. General Relativity and Cosmology

8.1. Special Relativity

8.1.1. Postulates
8.1.2. Lorentz Transformations in Standard Configuration
8.1.3. Impulses (Boosts)
8.1.4. Tensors
8.1.5. Relativistic Kinematics
8.1.6. Relativistic Linear Momentum and Energy
8.1.7. Lorentz Covariance
8.1.8. Energy-Momentum Tensor

8.2. Equivalence Principle

8.2.1. Weak Equivalence Principle
8.2.2. Experiments on the Weak Equivalence Principle
8.2.3. Locally Inertial Reference Systems
8.2.4. Principle of Equivalence
8.2.5. Consequences on the Equivalence Principle

8.3. Particle Motion in the Gravitational Field

8.3.1. Path of Particles under Gravity
8.3.2. Newtonian Limit
8.3.3. Gravitational Redshift and Tests
8.3.4. Temporary Dilatation
8.3.5. Geodesic Equation

8.4. Geometry: Necessary Concepts

8.4.1. Two-Dimensional Spaces
8.4.2. Scalar, Vector and Tensor Fields
8.4.3. Metric Tensor: Concept and Theory
8.4.4. Partial Derivative
8.4.5. Covariant Derivative
8.4.6. Christoffel Symbols
8.4.7. Covariant Derivatives of Tensors
8.4.8. Directional Covariant Derivatives
8.4.9. Divergence and Lapacian

8.5. Curved Space-Time

8.5.1. Covariant Derivative and Parallel Transport: Definition
8.5.2. Geodesics from Parallel Transport
8.5.3. Riemann Curvature Tensor
8.5.4. Riemann Tensor: Definition and Properties
8.5.5. Ricci Tensor: Definition and Properties

8.6. Einstein Equations: Derivation

8.6.1. Reformulation of the Equivalence Principle
8.6.2. Applications of the Equivalence Principle
8.6.3. Conservation and Symmetries
8.6.4. Derivation of Einstein's Equations from the Equivalence Principle

8.7. Schwarzschild Solution

8.7.1. Schwartzschild Metrics
8.7.2. Length and Time Elements
8.7.3. Conserved Quantities
8.7.4. Equation of Motion 
8.7.5. Light Deflection. Study of Schwartzschild Metrics
8.7.6. Schwartzschild Radius
8.7.7. Eddington-Finkelstein Coordinates
8.7.8. Black Holes

8.8. Linear Gravity Limits Consequences

8.8.1. Linear Gravity: Introduction
8.8.2. Coordinate Transformation
8.8.3. Linearized Einstein Equations
8.8.4. General Solution of Linearized Einstein Equations
8.8.5. Gravitational Waves
8.8.6. Effects of Gravitational Waves on Matter
8.8.7. Generation of Gravitational Waves

8.9. Cosmology: Introduction

8.9.1. Observation of the Universe: Introduction
8.9.2. Cosmological Principle
8.9.3. System of Coordinates
8.9.4. Cosmological Distances
8.9.5. The Hubble’s Law 
8.9.6. Inflation

8.10. Cosmology: Mathematical Study

8.10.1. Friedmann’s First Equation
8.10.2. Friedmann’s Second Equation
8.10.3. Densities and Scale Factor
8.10.4. Consequences of Friedmann Equations Curvature of the Universe
8.10.5. Primitive Universe Thermodynamics

Module 9. High-Energy Physics

9.1. Mathematical Methods: Groups and Representations

9.1.1. Theory of Groups
9.1.2. SO (3), SU(2) and  SU(3) and SU(N) Groups
9.1.3. Lie Algebra
9.1.4. Representations
9.1.5. Multiplication of Representations

9.2. Symmetries

9.2.1. Symmetries and Conservation Laws
9.2.2.  C, P, T Symmetries
9.2.3. CPT Symmetry Violation and Conservation
9.2.4. Angular Momentum
9.2.5. Addition of Angular Momentum

9.3. Feynman Calculus: Introduction

9.3.1. Average Lifetime
9.3.2. Cross Section
9.3.3. Fermi’s Golden Rule for Decay
9.3.4. Fermi’s Golden Rule for Dispersion
9.3.5. Dispersion of Two Bodies in the Center of Masses of Reference Systems

9.4. Application of Feynman Calculation: Toy Model 

9.4.1. Toy Model: Introduction
9.4.2. Feynman Rules 
9.4.3. Average Lifetime
9.4.4. Dispersion
9.4.5. Higher Order Diagrams

9.5. Quantum Electrodynamics

9.5.1. Dirac Equation
9.5.2. Solution for Dirac Equations
9.5.3. Bilinear Covariants
9.5.4. The Photon
9.5.5. Feynman Rules for Quantum Electrodynamics
9.5.6. Casimir’s Trick
9.5.7. Renormalization

9.6. Electrodynamics and Chromodynamics of Quarks

9.6.1. Feynman Rules
9.6.2. Production of Hadrons in Electron-Positron Collisions
9.6.3. Feynman Rules for Chromodynamics
9.6.4. Color Factors
9.6.5. Quark-Antiquark Interaction
9.6.6. Quark-Quark Interaction
9.6.7. Pair Annihilation in Quantum Chromodynamics

9.7. Weak Interaction

9.7.1. Weak Charged Interaction 
9.7.2. Feynman Rules
9.7.3. Muon Decay
9.7.4. Neutron Decay
9.7.5. Pion Decay
9.7.6. Weak Interaction between Quarks
9.7.7. Weak Neutral Interaction
9.7.8. Electroweak Unification

9.8. Gauge Theories

9.8.1. Local Gauge Invariance
9.8.2. Yang-Millis Theory
9.8.3. Quantum Chromodynamics
9.8.4. Feynman Rules
9.8.5. Mass Term
9.8.6. Spontaneous Symmetry Breaking
9.8.7. Higgs Mechanism

9.9. Neutrino Oscillation 

9.9.1. Solar Neutrino Problem
9.9.2. Neutrino Oscillation
9.9.3. Neutrino Masses
9.9.4. Mixing Matrix 

9.10. Advanced Topics Brief Introduction

9.10.1. Higgs Boson
9.10.2. Grand Oscillation
9.10.3. Matter-Antimatter Asymmetry
9.10.4. Supersymmetry, Strings and Extra Dimensions
9.10.5. Dark Matter and Energy

Module 10. Information and Quantum Computing

10.1. Introduction: Mathematics and Quantum

10.1.1. Complex Vector Spaces
10.1.2. Linear Operators
10.1.3. Scalar Products and Hilbert Spaces
10.1.4. Diagonalization
10.1.5. Tensor Product
10.1.6. The Role of Operators
10.1.7. Important Theorems on Operators
10.1.8. Checked Quantum Mechanics Postulates

10.2. Statistical States and Samples 

10.2.1. The Qubit
10.2.2. Density Matrix
10.2.3. Two-Part System
10.2.4. Schmidt Decomposition
10.2.5. Statistical Interpretation of the Mixing States

10.3. Measurements and Temporary Evolution

10.3.1. Von Neumann Measurements
10.3.2. Generalized Measurements
10.3.3. Neumark Theorem 
10.3.4. Quantum Channels

10.4. interwoven and its Applications

10.4.1. ERP States
10.4.2. Dense Coding
10.4.3. State Teleportation
10.4.4. Density Matrix and its Representations 

10.5. Classic and Quantum Information

10.5.1. Introduction to Probability
10.5.2. Information
10.5.3. Shannon Entropy and Mutual Information
10.5.4. Communication

10.5.4.1. The Bynary Symmettric Channel
10.5.4.2. Channel Capacity

10.5.5. Shannon Theorems
10.5.6. Difference between Classic and Quantum Information
10.5.7. Von Neumann Entropy
10.5.8. Schumacher Theorem
10.5.9. Holevo Information
10.5.10. Accessible Information and Holevo Limit

10.6. Quantum Computing

10.6.1. Turing Machines
10.6.2. Circuits and Classification of Complexity
10.6.3. Quantum Computer
10.6.4. Quantum Logic Gates
10.6.5. Deutsch-Josza and Simon´s Algorithm
10.6.6. Unstructured Search; Grover´s Algorithm
10.6.7. RSA Encryption Method
10.6.8. Factorization: Shor Algorithm

10.7. Quantum Theory of the Light-Matter Interaction

10.7.1. Two-Level Atom
10.7.2. AC-Stark Splitting
10.7.3. Rabi Oscillations
10.7.4. Light Dipole Force

10.8. Quantum Theory of the Light-Matter Interaction

10.8.1. Quantum States of the Electromagnetic Field
10.8.2. Jaynes-Cummings Model
10.8.3. The Problem of Decoherence
10.8.4. Treatment of Weisskopf-Wigner Model of Spontaneous Emission

10.9. Quantum Communication

10.9.1. Quantum Cryptography: BB84 and Ekert91 protocols
10.9.2. Bell Inequalities
10.9.3. Generation of Individual Photons
10.9.4. Propagation of Individual Photons
10.9.5. Detection of Individual Photons

10.10. Quantum Computing and Simulation

10.10.1. Neutral Atoms in Dipolar Traps
10.10.2. Cavity Quantum Electrodynamics
10.10.3. Ions in Paul Tramps
10.10.4. Superconducting Cubits

A 100% online program that will allow you to delve into astrophysics and cosmology through the most innovative multimedia content in academic education"