This is far too general for us to be of much use without writing a textbook style introduction. You say you have read the Wiki page, exactly what about them did you run into problems with?bengeof said:What is grassman numbers? I didn't understand the wiki article on it. . and how is it used in the quantization of fermionic fields ?
Thanks
Grassman numbers are mathematical objects used in quantum field theory to represent fermionic fields. They are non-commuting numbers that satisfy the rules of anti-commutation, similar to how ordinary numbers satisfy the rules of multiplication and addition.
Grassman numbers are used to describe fermionic fields, which are fields that represent particles with half-integer spin. They are also used to construct the Lagrangian of a quantum field theory, which is a mathematical expression that describes the dynamics of a system.
Unlike ordinary numbers, Grassman numbers do not commute when multiplied together. This means that the order in which they are multiplied matters. They also have the property of anti-commutation, meaning that the product of two Grassman numbers is equal to the negative of the product in the opposite order.
Grassman numbers are important in quantum field theory because they allow us to describe fermionic fields, which are crucial in understanding the behavior of elementary particles. They also play a key role in constructing the Lagrangian, which is essential for making predictions about the behavior of quantum systems.
Yes, there are practical applications of Grassman numbers in fields such as physics, mathematics, and computer science. They are used in quantum field theory to study the behavior of particles, in mathematics to solve problems involving non-commutative algebra, and in computer science to develop efficient algorithms for certain types of calculations.