In our three-dimensional (plus time) reality, particles are generally considered to have three spatial dimensions, along with the dimension of time. However, it is possible to discuss the concept of particles that exist in fewer dimensions.
When we talk about a particle being "two-dimensional," we are referring to its spatial extent or its motion being confined to a two-dimensional plane. This concept is often used in simplified models or theoretical frameworks to study specific properties or phenomena. It's important to note that this is a mathematical abstraction and not a literal representation of particles in our physical world.
One example of a two-dimensional particle is the "point particle" often used in classical mechanics. A point particle is an idealized concept representing a particle with zero size and mass concentrated at a single point in space. It simplifies calculations and allows us to study the motion and interactions of particles without considering their internal structure or detailed properties.
In certain physical systems, especially at extremely small scales or in condensed matter physics, phenomena can emerge that effectively behave as if they exist in lower dimensions. For instance, in certain materials, electrons can be constrained to move along a surface, effectively behaving as if they are confined to two dimensions. These systems are referred to as two-dimensional electron gases (2DEGs).
While these simplified models and systems provide valuable insights and help us understand various physical phenomena, they are not representative of the entirety of reality. In our three-dimensional universe, particles have three spatial dimensions, and their behavior is influenced by interactions and dynamics in all of these dimensions.