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A conserved quantity is a property or value that remains constant over time in a system even when changes occur in the system. In mathematics , a conserved quantity of a dynamical system is formally defined as a function of the dependent variables , the value of which remains constant along each trajectory of the system.
In quantum field theory, internal symmetries also result in conserved quantities. For example, the U(1) gauge transformation of QED implies the conservation of the electric charge. Likewise, if a theory possesses an internal chiral or axial symmetry, there will be a conserved quantity, which is called the axial charge.
With respect to classical physics, conservation laws include conservation of energy, mass (or matter), linear momentum, angular momentum, and electric charge. With respect to particle physics, particles cannot be created or destroyed except in pairs, where one is ordinary and the other is an antiparticle.
In physics a conserved current is a current, , that satisfies the continuity equation =.The continuity equation represents a conservation law, hence the name. Indeed, integrating the continuity equation over a volume , large enough to have no net currents through its surface, leads to the conservation law =, where = is the conserved quantity.
The final column lists some special properties that some of the quantities have, such as their scaling behavior (i.e. whether the quantity is intensive or extensive), their transformation properties (i.e. whether the quantity is a scalar, vector, matrix or tensor), and whether the quantity is conserved.
Meaning SI unit of measure alpha: alpha particle: angular acceleration: radian per second squared (rad/s 2) fine-structure constant: unitless beta: velocity in terms of the speed of light c: unitless beta particle: gamma: Lorentz factor: unitless photon: gamma ray: shear strain: radian
Also, conjugate variables are related by Noether's theorem, which states that if the laws of physics are invariant with respect to a change in one of the conjugate variables, then the other conjugate variable will not change with time (i.e. it will be conserved). Conjugate variables in thermodynamics are widely used.
In physics, particularly in quantum field theory, configurations of a physical system that satisfy classical equations of motion are called on the mass shell (on shell); while those that do not are called off the mass shell (off shell).