Symmetries and conservation Laws: Part 1

• Every conservation principle corresponds to symmetry in nature
• A symmetry of a particular kind exists when a certain operation leaves something unchanged.
• There is an intimate connection between symmetry and so called conserved quantities.
• Well known conserved quantity is energy and corresponding symmetry in this case is time translation.

Momentum Conservation

• Holds for all type of interactions
• Related to the invariance of physical laws under translation in space.
• Thus laws of interaction do not depend on the place of measurement so the space is homogeneous.
• This transnational uniformity of space leads to the conservation of linear momentum.
• Particle at rest have no momentum. If it  decays into two less massive particles , momentum conservation requires that the two particles travel away in exactly opposite directions.

Conservation of Energy

• Holds for all type of interactions.
• related to the invariance of physical laws under translations along the time axis i.e., homogeneity of time.
• laws of interaction do not depend on the time of measurement

Angular momentum conservation

• In addition to transnational symmetry , space also has a rotational symmetry.
• This symmetry of space gives rise to another conserved quantity , angular momentum.
• This law is also of general validity for all types of interactions.
• It is related to the invariance of the physical laws under rotation (isotropy of space).
• The orbital and spin angular momentum may be separately conserved.

Parity Conservation

• Holds for strong, nuclear and electromagnetic interactions but is violated in case of week interactions.
• related to the invariance of the physical laws under inversion of space co-ordinates. x,y,z are replaced by -x.-y,-z.
• is equivalent to combined reflection and rotation.
• physical laws do not depend on the right handedness of co-ordinate system.
• Parity operation symmetry represents discrete symmetry (reflection and rotation through 180 degree)
• Every particle with non zero mass has an intrinsic parity  π which can either be +1(even) or -1 (odd). Thus total parity of a system of n particles is the product of their intrinsic parities and the orbital parity (-1)^l.
Thus, π_tot=π₁π₂π₃.......π_n(-1)^l
• Intrinsic parity of pions is odd.

Conservation of charge

• Conservation of electric charge is related to gauge transformations which are shifts in the zeros of the scalar and vector electromagnetic potentials V and A
• Gauge transformations leave E and B unaffected since the latter are obtained by differentiating potentials , and this invariance leads to charge conservation.
• Charge and baryon number are conserved in all interactions.