Fractional Quantum Hall Effect: Emergent Particles with Fractional Charge

The Fractional Quantum Hall Effect (FQHE) is a quantum phenomenon observed in two-dimensional electron systems subjected to very strong magnetic

Quantum Hall Effect: Quantized Resistance in 2D Systems

The Quantum Hall Effect occurs in two-dimensional electron systems placed under strong magnetic fields at very low temperatures. In this

Topological Insulators: Edge States Protected by Topology

Topological insulators are a class of materials that act as insulators in their bulk but conduct electricity on their surfaces

Chiral Symmetry: The Physics of Handedness

Chiral symmetry is a type of symmetry that distinguishes between left-handed and right-handed versions of particles or fields, especially in

Spontaneous Symmetry Breaking: Hidden Order Behind Emergent Phenomena

Spontaneous symmetry breaking (SSB) occurs when the underlying laws (equations or Lagrangians) of a system are symmetric, but the state

Gauge Symmetry: The Foundation of Modern Field Theories

Gauge symmetry is a type of symmetry in which certain transformations can be performed on the fields of a physical

Noether’s Theorem: Symmetry Leads to Conservation

Noether’s Theorem is one of the most profound and unifying principles in theoretical physics. It states that every continuous symmetry

Symplectic Geometry: The Mathematical Backbone of Classical Mechanics

Symplectic geometry is a branch of mathematics that studies geometric structures fundamental to the formulation of classical mechanics, especially in

Action: The Quantity Nature Minimizes

In physics, action is a fundamental concept in the formulation of mechanics, especially in Lagrangian mechanics. It is defined as

Lagrangian Mechanics: Motion from Energy Differences

Lagrangian mechanics is a powerful reformulation of classical mechanics that uses energy principles—specifically, the difference between kinetic and potential energy—to