interchanged without affecting the physics. Any (complex) linear combination of these two particles give the same physics, as long as the combinations are orthogonal, or perpendicular, to each other. In other words, the theory possesses symmetry transformations such as , where and are the two fields (representing the various generations of leptons and quarks, see below), and is any unitary matrix with a unit determinant. Such matrices form a Lie group called SU(2) (see special unitary group). This is an example of flavour symmetry. In quantum chromodynamics, flavour is a conserved global symmetry. In the electroweak theory, on the other hand, this symmetry is broken, and flavour changing processes exist, such as quark decay or neutrino oscillations. Flavour quantum numbers Leptons All leptons carry a lepton number . In addition, leptons carry weak isospin, , which is − for the three charged leptons (i.e. electron, muon and tau) and + for the three associated neutrinos. Each doublet of a charged lepton and a neutrino consisting of opposite are said to constitute one generation of leptons. In addition, one defines a quantum number called weak hypercharge, , which is −1 for all left-handed leptons. Weak isospin and weak hypercharge are gauged in the Standard Model. Leptons may be assigned the six flavour quantum numbers: electron number, muon number, tau number, and corresponding numbers for the neutrinos. These are conserved in strong and electromagnetic interactions, but violated by weak interactions. Therefore, such flavour quantum numbers are not of great use. A separate quantum number for each generation is more useful: electronic lepton number (+1 for electrons and electron neutrinos), muonic lepton number (+1 for muons and muon neutrinos), and tauonic lepton number (+1 for tau leptons and tau neutrinos). However, even these numbers are not absolutely conserved, as neutrinos of different generations can mix; that is, a neutrino of one flavour can transform into another flavour. The strength of such mixings is specified by a matrix called the Pontecorvo–Maki–Nakagawa–Sakata matrix (PMNS matrix). Quarks All quarks carry a baryon number and all anti-quarks have They also all carry weak isospin, The positively charged quarks (up, charm, and top quarks) are called up-type quarks and have the negatively charged quarks (down, strange, and bottom quarks) are called down-type quarks and have Each doublet of up and down type quarks constitutes one generation of quarks. For all the quark flavour quantum numbers listed below, the