**Particles and the Standard Model:**

The Standard Model: The 17 most fundamental particles in nature (from which all matter is composed) and the 3 fundamental forces facilitating interactions between them.

Quantum Numbers: A set of numbers associated to each particle describing the way that particle interacts with the rest of the Standard Model. Includes charge, spin, color, flavor, and mass.

Spin: Quantum number governing the “statistics” of a fundamental particle. That is, how that particle can accumulate in the space of possible quantum states. Quantized in units of h-bar, Planck’s reduced constant.

Electric Charge: Quantum number governing the electromagnetic interactions of a fundamental particle. Quantized in units of e, the charge of the electron.

Color: Quantum number governing the strong interactions of a fundamental particle. Takes on the values of red, green and blue.

Flavor: Quantum number governing the weak interactions of a fundamental particle. There is a flavor charge associated to each quark and lepton.

Field: A mathematical object which assigns a number or set of numbers to every point in space and time.

Quantum Field: A field associated to a fundamental particle, roughly communicates the number of that particle at each location in space and time. Endowed with the ability to create and destroy its designated particle.

Fermions: Particles with spin which is a half integer multiple of h-bar. Obey the Pauli-Exclusion Principle, which means that no more than one fermion an occupy a given quantum state. The Pauli-Exclusion Principle gives rise to the elements of the periodic table, and, thus, fermions form the basis of all matter.

Bosons: Particles with spin which is an integer multiple of h-bar. Do not obey the Pauli-Exclusion Principle, any number of bosons can occupy a given quantum state. The fundamental interactions of the Standard Model are facilitated by field bosons.

Leptons: A kind of fermion that constitutes a fundamental particle on its own. Examples of fermions include the well-loved electron and its less familiar cousins the muon and the tauon.

Quarks: A kind of fermion that does not constitute a fundamental particle on its own. There are six quarks in the Standard Model: up, down, charm, strange, top, and bottom. Combinations of two or three quarks form composite particles known as hadrons.

Photon: Particle of light responsible for facilitating the electromagnetic interaction.

Gluon: Particle responsible for facilitating the strong interaction.

W and Z Bosons: Particles responsible for facilitating the weak interaction.

Electromagnetism: The fundamental interaction between charged particles and currents of flowing charges.

Strong Interaction: The fundamental interaction responsible for holding quarks together inside hadrons.

Weak Interaction: The fundamental interaction responsible for radioactive decay.

Gravitational Interaction: The fundamental interaction between massive objects responsible for free fall and planetary orbits. Gravity is notably absent from the Standard Model. Physicists theorize that Gravity should be facilitated by a messenger particle named the Graviton, but no Graviton has ever been observed.

**Action and the Lagrangian:**

The Principle of Least Action: Every system in nature will evolve in time so as to minimize the quantity known as the action.

The Lagrangian: A mathematical function containing all relevant information about the setting of a physical problem. Strictly speaking the Lagrangian of any system is the difference between its kinetic and potential energies.

Kinetic Energy: The energy of a system associated with the motion of all its composite particles. The kinetic energy of any single particle is proportionate to its mass multiplied by the square of its velocity.

Potential Energy: The energy of a system associated with the fundamental interactions of its particles with each other and the environment. For example, the potential energy of a particle in a gravitational field is proportionate to that particle’s mass multiplied by its height above the ground.

The Action: The sum of the Lagrangian at each instant over some fixed amount of time. Roughly speaking, the cost to go from one state of being to another.

**Quantum Mechanics:**

Quantum Mechanics: A branch of physics concerned with very small systems moving at speeds much less than the speed of light. It is on these length and energy scales that systems begin to exhibit Heisenberg’s Uncertainty Principle, forcing Physicists to take up a probabilistic approach to solving problems rather than a deterministic one.

Classical Mechanics: A branch of physics concerned with large systems moving at speeds much less than the speed of light. At this length and energy scale the dynamics of a system can be predicted with complete certainty using the Principle of Least Action. In truth, however, since every system is composed of the particles of the Standard Model every system must be described Quantum Mechanically.

Heisenberg’s Uncertainty Principle: One cannot know, with perfect accuracy, where a particle is and where it is going at the same time.

Quantum Superposition: Since a quantum system cannot be said to occupy any single state between measurements, we are forced to concede that it exists in a combination of varying degrees of every possible state it could occupy. The degree to which the system occupies a given state is related to the probability the system would be found to occupy that state upon measurement.

Probability Amplitude: The degree to which a quantum system is “in” a given state prior to measurement.

Phase: The phase of a wave is a description of where the wave is up, and where the wave is down. The phase of a probability wave associated with a quantum transition is proportionate to the action required to make such a transition.

Constructive Interference: When waves in phase are added together their total intensity is the sum of their individual intensities.

Destructive Interference: When waves out of phase are added together their total intensity is the difference of their individual intensities.

Path Integral: The sum over all probability waves associated with potential transitions of a quantum system.

The Feynman Diagram: A pictorial representation of a quantum state transition used to compute the probability amplitude for a given event.

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