In statistical mechanics, a "'grand canonical ensemble "'is the statistical ensemble that is used to represent the possible states of a mechanical system of particles that is being maintained in thermodynamic equilibrium ( thermal and chemical ) with a reservoir.
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Note that the invariant mass of a system of particles may be more than the sum of the particles'rest masses, since kinetic energy in the system center-of-mass frame and potential energy from forces between the particles contribute to the invariant mass.
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The conservation of both relativistic and invariant mass applies even to systems of particles created by pair production, where energy for new particles may come from kinetic energy of other particles, or from one or more photons as part of a system that includes other particles besides a photon.
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"In " and " out " states are states in Heisenberg picture so they should not be thought to describe particles at a definite time, but rather to describe the system of particles in its entire evolution, so that the S-matrix element:
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A quantitative description of the nuclear force relies on partially empirical equations that model the internucleon potential energies, or potentials . ( Generally, forces within a system of particles can be more simply modeled by describing the system's potential energy; the negative gradient of a quantum mechanical properties of the nucleon system.
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In statistical mechanics, the "'radial distribution function "', ( or "'pair correlation function "') g ( r ) in a system of particles ( atoms, molecules, colloids, etc . ), describes how density varies as a function of distance from a reference particle.
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1899 : Hendrik Lorentz derived the correct ( up to a certain factor \ epsilon ) relations for accelerations, forces and masses between a resting electrostatic systems of particles S _ { 0 } ( in a stationary aether ), and a system S emerging from it by adding a translation, with k as the Lorentz factor:
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We have a pschological sense that particles like electrons are more vital because we tend to work with them more often, but the entire system of particles is not seperable; you must take them all, because the laws that created the top quark also created the electron; you could not create a universe with one and not the other.
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In classical mechanics, the movement of a particle ( or system of particles ) is completely determined by the Hamiltonian H ( q, p, t ), a function of the generalized coordinates " q ", generalized velocities \ dot { q } = \ mathrm { d } q / \ mathrm { d } t and its conjugate momenta:
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In Lagrangian mechanics, the trajectory of a system of particles is derived by solving the Lagrange equations in one of two forms, either the " Lagrange equations of the first kind ", which treat constraints explicitly as extra equations, often using Lagrange multipliers; or the " Lagrange equations of the second kind ", which incorporate the constraints directly by judicious choice of generalized coordinates.
