Conservation Laws in Subatomic Physics
A conservation law is a fundamental principle of physics stating that certain key quantities - such as energy, momentum, electric charge, or baryon number - remain unchanged in every natural process, regardless of the transformations that take place within the system.
Put simply, these quantities may shift form or be redistributed among the particles involved, but the total value before and after any interaction is always the same. Every physical process is bound to respect these conservation principles.
Such laws are the cornerstone of particle physics: they define which reactions can occur, which decays actually happen, and which are ruled out entirely.
Example. In beta decay, a neutron transforms into a proton, an electron, and an electron antineutrino: $$ n \;\to\; p^+ + e^- + \bar{\nu}_e $$ The neutron carries zero electric charge. After the decay, the proton has +1, the electron - 1, and the neutrino 0. The total is $+1-1+0 = 0$, so the neutron’s initial charge is conserved. $$ n^{(0)} \;\to\; p^{+(+1)} + e^{(-1)} + \bar{\nu}_e^{(0)} $$
Some of these conservation laws are absolute, such as the conservation of electric charge, baryon number, and energy.
Others hold only under specific conditions, like flavor conservation or the OZI rule, which explain why certain decays are exceedingly rare - or practically forbidden.
Conservation Laws in the Fundamental Interactions
Here are the key conservation laws governing the behavior of elementary particles:
- Conservation of Electric Charge
The sum of the charges of the initial particles equals the sum of the charges of the final ones. This law holds universally across all fundamental interactions: strong, electromagnetic, and weak.Example: In a weak interaction vertex, $$ \nu_e \to e^- + W^+ $$ the initial charge is 0 (the neutrino), while the final charge is the electron ( - 1) plus the $W^+$ boson (+1), giving - 1 + +1 = 0. The balance works: charge is conserved.
- Conservation of Color (QCD)
In strong interactions, the color charge of quarks (red, green, blue) can change, but the gluon always carries away the difference. Since all observable particles are color-neutral (white), the rule is: zero in, zero out. No isolated particle can exist with an uncompensated color charge.Example. A proton consists of three quarks (red + green + blue): $$ u_r + u_g + d_b $$ If one quark changes color by emitting a gluon, the gluon carries the difference, ensuring the proton as a whole remains colorless.
- Conservation of Baryon Number
The total baryon number remains constant in every interaction. Each quark contributes +1/3, each antiquark - 1/3. Thus, baryons (three quarks) have baryon number +1, antibaryons (three antiquarks) - 1, and mesons (quark - antiquark pairs) 0. Baryons and antibaryons can never appear or vanish in isolation - they are always created or destroyed in pairs. This law is among the most robust, never observed to be violated in experiments, and it underpins the proton’s stability.Example. This reaction obeys baryon number conservation: $$ p + \bar{p} \;\to\; \pi^+ + \pi^- $$ The proton (p) has baryon number +1, the antiproton - 1, while pions carry 0. Both the initial and final totals are 0. $$ p^{(+1)} + \bar{p}^{(-1)} \;\to\; \pi^{+(0)} + \pi^{-(0)} $$ Baryon number is conserved.
- Conservation of Lepton Numbers
There are three independent lepton numbers: the electron number $L_e$, the muon number $L_\mu$, and the tau number $L_\tau$. Each is conserved separately in fundamental interactions - except in neutrino oscillations, where one type can morph into another. Only leptons carry lepton number; all other particles have zero. For example, $L_e$ is +1 for the electron and the electron neutrino, and - 1 for their antiparticles.
Quarks, by contrast, do not follow a strict generation-based conservation law, because weak interactions intrinsically mix quark flavors through the CKM matrix.Example. A classic case is the decay of the charged pion: $$ \pi^- \;\to\; \mu^- + \bar{\nu}_\mu $$ Assigning lepton numbers to each particle: $$ \pi^{- (0)} \;\to\; \mu^{- (L_\mu = +1)} + \bar{\nu}_\mu^{(L_\mu = -1)} $$ The initial sum is $0$, and the final is $+1 + (-1) = 0$. The muon lepton number $L$ is therefore conserved.
- Conservation of Flavor
Flavor conservation is not universal; it depends on the interaction:- In strong and electromagnetic interactions, quark flavors (up, down, strange, charm, bottom, top) are strictly conserved.
- In weak interactions, however, flavors can change: a quark may transform into another ($u \to d$, $s \to u$, etc.).
Example. In strong interactions, strange particles are always created in $s$ - $\bar{s}$ pairs, keeping total strangeness unchanged. In decays, though, a strange quark can change flavor through the weak interaction, which makes strange particle decays comparatively slow.
- OZI Rule (Okubo - Zweig - Iizuka)
Some decays that are kinematically allowed turn out to be extremely rare. This happens when the Feynman diagram of the process can be “cut” into two parts by slicing only gluon lines (without cutting any real particle lines). In such cases, the decay isn’t strictly forbidden but is heavily suppressed - the probability of it occurring is vanishingly small.
Alongside these, there are the more “obvious” kinematic conservation laws of physics:
- Conservation of Energy
The total energy of an isolated system can neither increase nor decrease; it can only change from one form into another. - Conservation of Momentum
In the absence of external forces, the total momentum of a system remains constant, even if the particles change direction or speed. - Conservation of Angular Momentum
If no external torques act on the system, the total angular momentum (both orbital and spin) remains unchanged in every interaction.
And the list goes on.
